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Investigations in Physics 101 R J Reimann S H Schroeder T R Watkins Boise State University December 2013 Forward Welcome to PHYSlOl Introduction to Physics The following laboratory investigations are intended to provide hands on experiences that supplement the textbook and lectures They use a guided discovery approach that allows some exibility in how you accomplish the assigned tasks Consider your instructor as a facilitator to keep you on track rather than an authority with all of the right answers We are mostly concemed with leaming how physics works Usually you will work in groups of 3 to operate the apparatus facilitate discussions and keep everyone involved Groups of 2 or 4 are allowed only if necessary Consider your other group members as learning partners Can you understand the subtle concepts and explain them to each other Such confirmation is vital to the learning process Enjoy yourselves but please stay on task LAB REPORT FORMAT All lab reports must contain the following 1 data sheet when provided 3 computer printouts andor handdrawn graphs when requested and 4 support pages Many labs in this manual utilize data sheets for recording information If one is needed it will follow its corresponding lab Some labs do not include a data sheet The data for these labs can be written on the same pages as the required drawings written descriptions etc It is important that labeled measurements all calculations and the questions for these labs be included in an organized fashion Some labs may also require additional data such as hand drawn graphs diagrams or computer printouts Good organization and neatness are important Most labs will require one or more percentage errors A to be include in the data sheet The percentage error can be calculated by dividing the experimental value by the accepted value experimental value 1 x 100 accepted value Some labs may also require an imprecision percentage EE This can be calculated in three steps First determine the mean value of the measurement in question Then determine which of the measurements deviates most from the mean and calculate the difference the tolerance Lastly divide the tolerance by the mean and convert the resulting decimal to a percentage tolerance mean 11 cm 14 cm 16 cm and 12 cm the mean would be 13 cm The greatest deviation from the mean is 16 cm so the tolerance is 16 cm 13 cm 3 cm The imprecision percentage would then be 23 EE 133 c n x 100 23 and converting the resulting decimal into a percentage A X 100 For example if the length of a metal rod is measured to be 12 cm The support page should include all required calculations observations and answers to lab questions These questions are easy to spot as they are written in italicbold type The support page should also include a conclusion and an error analysis This page should be neat and orderly All labs require an error analysis and a conclusion The error analysis should be limited to proceduralrelated factors which may affect the results of the experiment The use of the phrase human error should be avoided Be specific as to the cause of error For example if a lab asks you to use a stopwatch to time a falling ball your reaction time would be a source of procedural error Describe at least two possible procedural errors and discuss how each might have affected the results of the lab Matl1 errors are not to be considered as procedural errors The conclusion consists of two to three short paragraphs explaining what the group leamed from the lab Use experimental evidence to support your conclusion A group discussion should determine what is included in the conclusion Labs are a group exercise All members should have a designated job to perform Divide up the tasks but respect everyone s input Work as a group and discuss everything If there is disagreement include that in the conclusion TABLE OF CONTENTS FORWARD LAB REPORT FORMAT LINEAR MOTION FORCE TABLE FREEFALL PROJECTILES IMPULSEMOMENTUM UNBALANCED FORCES THE PHYSICS OF TOYS DENSITY PRESSURE Takehome Lab HEATING AND COOLING WAVES TRAVELING amp STANDING SOUND RESONANCE ELECTROSTATICS ELECTRIC FIELDS BULBS MAGNETISM SIMPLE MOTOR MIRRORS LENSES MIRRORS amp LENSES SPECTRA RADIOACTIVITY iii 10 13 16 19 22 24 25 27 31 33 36 37 38 40 43 48 50 52 54 58 LINEAR MOTION OBJECTIVE To analyze the graphical relationships of position and velocity with respect to time THEORY When describing the motion of an object knowing where it is relative to a reference point and how fast and in what direction it is moving is essential In this laboratory exercise a motion sensor will be the reference point or point of origin The motion detector is a sonar ranging device that emits hundreds of ultrasonic pulses per second These pulses re ect from an object to determine its position Based on the information collected the position and velocity of an object as a function of time can be displayed on the computer screen This is similar to the process used by bats for navigation PROCEDURE APPARATUS Computerized motion detector cardboard re ector inclined plane cart wooden blocks IMPORTANT In the following procedures use the cardboard reflector to direct the echoes back to the motion detector Hold the reflector perpendicular to the floor and keep it steady for the entire plot Erratic plots are due to echoes returning to the detector from other objects Repeat each procedure until a smooth plot is obtained 1 Open the Vernier Logger Pro software The motion detector should be about waist high for best results If necessary use the support rod to clamp the detector at the correct height Have each member of your group move the cardboard re ector in front of the detector to see the relationship between the motion and the position graph generated The green E button must be clicked to begin collecting data 2 Have each member of the group generate a Vshaped position graph by walking in front of the detector Describe in detail ie walking motion required to produce ie Vshaped position graph Be sure to include such things as direction with respect to ie detector and any variation in speed Print out each member s graph and include hisher name on the back 3 Observe the graph below carefully and without discussing it with the other members of your group describe in detail how you would move in order to create an exact duplicate of this graph Open Graph A in Logger Pro It can be found in the PHYS101 folder on the desktop u lvr w vuIvvuiu1v39vrrv Position tn Time luconds 10 11 12 13 14 15 Share your description with the other members of your group Do all members agree If not discuss the different ideas expressed and develop a group consensus Describe the group s consensus as to how a person would have to move in order to create an exact duplicate of the graph Each group member should now attempt to make the motion described in the group consensus Repeat as many times as needed until a pretty good match of the graph is obtained The graph you are matching will not erase when you click the start button so make as many attempts as needed It is very important that E person a Get the times right b Get the distances right and c Make a labeled print out of hisher best match Did you have to depart from the group s consensus description in order to match me graph What details of the motion did you have to change in order to get a good match with the graph How did you move differently in producing ie two differently sloped potions of the graph Is it possible for a real object to move toward or away from the detector so that it produces a vertical line on a positiontime graph Explain Compare the shape of a positiontime graph when walking toward me motion detector to me shape when walking away from me detector How does ie shape of a positiontime graph change as the motion speeds up or slows down How would you define the word position based on the positiontime graphs produced in this lab Under the le menu select Quit Do not save any data Observe the graph below carefully and without discussing it with the other members of your group describe in detail how you would move in order to create an exact duplicate of this graph Open Graph B in Logger Pro It can be found in the PHYS101 folder on the desktop Velocity Iris tlule seconds Share your description with the other members of your group Do all members agree If not discuss the different ideas expressed and develop a group consensus Describe the group s consensus as to how a person would have to move in order to create an exact duplicate of the graph Each group member should now attempt to make the motion described in the group consensus Repeat as many times as needed until a pretty good match of the graph is obtained The graph you are matching will not erase when you click the start button so make as many attempts as needed It is very important that each person 2 16 17 18 19 20 21 22 23 24 25 26 27 a Get the times right b Get the velocities right and c Make a labeled print out of hisher best match Did you have to depart from the group s consensus description in order to match the graph What details of me motion did you have to change in order to get a good match with the graph What places on ie graph seemed to give the most problems What were you and your group members doing iat led you not to match initially Does it matter where you stand to start this velocitytime graph Explain Is it possible for a real object to move toward or away from the detector so that it produces a vertical line on a velocitytime graph Explain What was the difference in the way you had to move to produce the two different parts of me graph involving movement Compare the shape of a velocitytime graph when walking toward me motion detector to the shape when walking away from me detector How would you de ne the word velocity based on me velocitytime graphs produced in this lab Under the le menu select Quit Do not save any data Elevate one end of the track so that it is about 10 cm above the surface of the lab table Roll a cart up the incline so it just reaches the top and then rolls back down As a group discuss how the position time and velocitytime graph of this motion should look Make a fullpage labeled sketch of E graph Be sure to label what me cart is doing at each point on ie graphs Position the motion detector at the top of the ramp Set Logger Pro to produce a position time graph Click the button and gently push the cart up the ramp Take care not to touch the detector at the top Collect data until the cart has returned to its starting position A few trials may be needed to get a smooth graph Print out the best resulting graph How does me resulting graph compare with the positiontime graph you predicted in procedure 25 Describe any major differences Have Logger Pro now show the velocitytime graph which corresponds to the position time graph produced by the cart Print out the best resulting graph How does me resulting graph compare with the velocitytime graph you predicted in procedure 25 Describe any major differences Be sure to include an error analysis and a conclusion FORCE TABLE OBJECTIVE To explore vector combinations THEORY For the sake of convenience in this exercise only you may use g 10 ms2 instead of 98 ms2 Consequently a mass of 100 g has a convenient downwards weight mg of 10 N Measurements of quantities such as mass distance time speed volume temperature and energy are completely described by a single number and are called scalars However another type of quantity also requires specifying the direction in which it points along with its value magnitude These include displacement velocity acceleration momentum and force which are called vectors Displacements are easily drawn and serve as the prototype of all other vectors Two dimensional vectors can be analyzed as two mutually perpendicular components The magnitude of the vector is related to the components by the Pythagorean Theorem The net force acting on a body is equal to the total vector sum of all of the forces acting on the body For example if a 5 N force pushes an object to the right and a 3N force pushes the same object to the left the net force acting on the body would be 2 N to the right If the net force on a body is zero it will not accelerate If the body is also at rest it is said to be in static equilibrium If an unbalanced force acts on the body it will be accelerated However if an additional force equal to the vector sum resultant of the individual forces in magnitude but opposite in direction is applied to the particle equilibrium will again be achieved Such a force is called the equilibrant The net force resultant can be found graphically using either the parallelogram method or the head to tail method The parallelogram method illustrated at the left is used when combining two force vectors First two vectors are drawn to scale from the same point a Two lines are then constructed each one parallel to one of the force vectors and of the same length b The resultant is found by drawing a straight line from the tails of the two vectors to the opposite comer c The length of this diagonal line is measured according to the scale and its direction is measured with a compass 5 55 The head to tail polygon method illustrated at the right is used when combining more than two force vectors One of the vectors is first drawn to scale Each successive vector is then drawn to scale with its tail starting from the head of the previous vector in its proper direction Once all of the vectors have been added the resultant is drawn from the tail of the first vector to the head of the last vector The length of the resultant is measured according to the scale and its direction is measured with a compass PROCEDURE APPARATUS Force table 4 weight hangers weight sets ruler protractor graph paper and shared long tape measure 1 As a preliminary class exercise choose a reference point in the front of the room and mark a distance 3 m away across the room From there go 4 m allg the room so you have created a large 90 triangle Use the long tape measure to determine the direct distance from the starting place origin to the nal position What would happen to ie distance measured by the tape measure if ie original distances were doubled At the end of the lab each group will turn in 4 labeled plots on 4 pages of graph paper For each plot choose an origin on one of the lines near the center of the page and use a ruler to carefully draw both vertical and horizontal axes Give labeled values and answer the related questions on the page with the respective plot Each plot should ziso include 1l 1beled resultant and a labeled eguilibrant On the first plot label the vertical axis North at the top of the page and South at the bottom Similarly label the horizontal axis East on the right side and West on the left Now imagine a scale where 10 cm represents a real distance of 10 km and draw out the following treasure map A pirate starts at the origin and walks 80 km due SW He then tums and hikes 12 km due North followed by 90 km due East where he nds a nice spot and buries his treasure What is ie distance from the origin directly to the treasure the resultant What is ie direction gle with respect to North for ie direct path to the treasure What is ie total distance that the pirate hiked How far North or South net NorthSouth distance did ie pirate hike from the origin to the treasure How far East or West net EastWest distance did the pirate hike from the origin to ie treasure How do ie answers in questions D and E relate to the answer to question A How far and in what direction would ie pirate have to travel to retum to the origin the eguilibrant Label all distances and directions on ie plot FPFFPDF On the second plot let 80 cm represent a force of 10 N Label the horizontal axis X and the vertical axis Y Draw an 80 cm long arrow to the right from the origin to represent a force of 10 N in the x direction Draw another 80 cm long upwards from the origin to represent a force of 10 N in the y direction A Use ie parallelogram method to determine ie magnitude of the resultant force based on these 2 vector components B What is ie direction of ie resultant force measured in degrees away from ie xaxis C Draw ie equilibrant based on ie above answers D Label ie value and angle of all forces on ie plot A force table consists of weight hangers attached to strings which pass over pulleys and are connected to a common ring in its center A nail keeps the ring in place Note if a nail is not present have one member of the group hold the ring in place until all weights are in place The pulleys may be moved around the table to the desired angles Various masses may be added to the hangers to achieve the desired forces Use the force table with 10 N weights 010 kg including hangers hanging at 0 and 90 Set a third weight hanger with the appropriate weight and angle to represent the equilibrant determined in procedure 4 Verify that your prediction for procedure 4 does indeed provide the proper balance by lifting the nail inside the ring Discuss the results and any discrepancies that may have occurred You are comparing your theoretical value from step 4 to ie experimental value of step 5 Determine the percentage error using the calculated value as the accepted value Note The formula for calculating this is found in the Lab Report Format section of this lab manual See page ii Replace the nail Double the weight hanging at 90 to 20 N and determine the required equilibrant by trialand error not calculation When the nail is removed the ring should not move Draw a plot this is your third drawing of ie resulting forces when equilibrium is achieved Include the force values and angles of all forces including the resultant and the equilibrant 10 11 Use the parallelogram method to plot and calculate the values of the resultant and equilibrant of the two forces in procedure 6 Include the force values and angles of all forces including the resultant and ie equilibrant Determine the percentage error using the calculated value as the accepted value You are comparing your experimental value from step 6 to the theoretical value of step 7 Replace the nail Place a 10 N force at 0 another 10 N force at 90 and a 2 N force at 120 Determine the required equilibrant again by trialanderror not calculation When the nail is removed the ring should not move Draw a plot iis is your fourth drawing of ie resulting forces when equilibrium is achieved Include the force values and angles of all forces including ie resultant and the equilibrant Use the headtotail method to plot and calculate the values of the resultant and equilibrant of the three forces in procedure 8 Include ie force values and angles of all forces including the resultant and ie equilibrant Determine the percentage error using the calculated value as the accepted value You are again comparing what you experimentally found on the force table to what your drawing predicts Put the names of your group members at the top of your rst plot along with the date Arrange the labeled plots in order and staple them together Be sure to include an error analysis and a conclusion FREEFALL OBJECTIVE To measure the acceleration due to gravity g for freely falling objects THEORY A freely falling object gains speed at a constant rate that is referred to as the gravitational acceleration g Near the surface of the earth g 98 InS2 32 ftS2 22 mphSNote that the object s speed does not remain constant but steadily increases until air resistance becomes signi cant While air resistance is negligible the vertical speed V of an object at time t that was released from rest at time zero is given by V g t The corresponding 1 2 distance y that the object travels is given by y E g t2 This relationship gives g Conversely the time t required for an object to fall freely from rest through a particular distance is given by t 12 y g The acceleration of a freely falling object can also be determined by looking at a velocity versus time graph V Acceleration is a description of how the velocity is changing with time a It is the slope of the velocity versus time graph PROCEDURE APPARATUS stopwatch 100m measuring tape ruler tennis or hand ball computerized sonic ranger and mini basketball As the lab progresses enter all data on the one data sheet which follows the lab Be sure to include any calculations that the lab requires you to make 1 Check your reaction time as follows Group members take tums resting a st on a table with the thumb and forefinger extended and separated about a centimeter Another group member suspends a ruler with its zero marking between the poised pinch Without warning the ruler is dropped by the holder and caught as quickly as possible by the pincher Note the distance marking on the ruler where it is caught and record it on the back of the data sheet Repeat at least 10 times for each member of the group Enter each member s average in the data sheet Calculate the reaction time using the final equation in the Theory section Take turns to determine your quickest group member How does your average group reaction time compare with that of other groups 2 Take the stopwatch and the shared 100 m measuring tape along with either a tennis ball or hand ball outdoors to the top of the parking garage Choose a release point for the ball and determine its height Drop the ball from this point at least 5 times and have the group determine the fall time t Return to the lab Calculate g from the height of the release point y and the drop time t Determine the percentage error A How does your group s value of g compare with the ndings of the other groups 3 Determine g by dropping the mini basketball below the Sonic Ranger Be sure the basketball starts at least 50 cm from the sonic ranger to prevent software errors Highlight a linear portion of the velocity versus time graph and use a linear fit to determine the acceleration from the slope Do this 5 times to get an average slope Determine the percentage error A for the average slope of the graph in procedure 3 Note The formula for calculating this is found in the Lab Report Format section of this lab manual See pageiL Describe the position versus time graph How is the distance traveled each second changing If the mass of the cart is increased how would ie results of this lab be affected Be speci c Be sure to include an error analysis and a conclusion PHYS 101 FREEFALL LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt Group Average 1 Reaction distance m Reaction time s 2 Object release height m Measured fall time s Calculated g mss A acceleration mS2 Trial 1 T m2 T m3 T m4 T m5 7 Average Slope ms2 8 A Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis a conclusion and printouts for procedures 6 and 7 PROJECTILES OBJECTIVE To predict the landing point of a projectile THEORY The total mechanical energy in a system is a constant if there are no outside forces acting such as friction As an example suppose a box is resting at the top of a hill The box would have gravitational potential energy due to its height but no kinetic energy since it is at rest The total energy of the system would be all potential energy Emmi P E g mg II If the box slipped and fell down the hill its total energy would remain constant At any point between the top and the bottom of the hill Emmi PE K E At the bottom of the hill the total energy 1 would be all kinetic Emmi K E E mvz Since the total energy is the same at the top of the hill as it is at the 1 bottom of the hill the equation for potential energy must equal the equation for kinetic energy mgh E mvz By rearranging this relationship the velocity of the box at the bottom of the hill can be found to be 17 2 h A projectile which is launched horizontally has both a horizontal and a vertical motion which are completely independent of each other Gravity never acts horizontally If friction is ignored the horizontal velocity will remain constant while the vertical velocity will be affected by the acceleration of gravity Horizontal velocity can be found by 17 E where x is the horizontal distance traveled and t is the total time in the air Assuming the initial 2 downward vertical velocity of a projectile is zero the total time that it is in the air can be determined by t y g 98 ms2 PROCEDURE APPARATUS Ring stand with clamp and horizontal support rod large diameter straw small diameter straw 15 cm long wood block rubber band string masking tape clay dry black powdered paint ramp to fit steel balls meter stick 2 large washers large steel ball small steel ball and carbon paper 1 A hunter spies a mischievous monkey sitting in a banana tree The hunter climbs a nearby tree and aims the barrel of his sightless tranquilizing gun horizontally at the monkey But just as he res the monkey drops from the tree Does the monkey escape the tranquilizing dart or does he get hit Upon what facts does your prediction depend Discuss this as a group and record your prediction 2 Tape the large diameter straw securely to the top of the wood block For optimum results make sure the back of the straw is securely attached to the block Next heavily tape one end of the rubber band to the top center of the straw This will be the tranquilizer gun See the sketch 3 The dart is made by rolling some clay in the powdered black paint and sticking it in one end of the smaller diameter straw Make sure some of the clay is sticking out of the end of the straw 4 Draw a target on a sheet of paper and tape a washer to each of the two bottom comers Tape two long lengths of string 34 m to the top comers of the target paper pass them over the horizontal support and extend them to the dart gun wood block Make sure both strings are equal in length 5 CAUTION Mzge sure that no other lgb groups are in line with vour target Insert the dart into the larger straw of the dart gun and move it a few meters from the target To re the dart both strings from the target and the rubber band from the dart gun are stretched together over the back end of the dart pulled back and released Aim the dart horizontally at the target and re It might take more than one try to get the timing down Take turns until each person in the group has fired the dart Does the monkey get hit Was your prediction from step lcorrect 10 10 11 12 13 14 15 16 17 18 19 20 21 22 Reset the dart gun and target Aim from an angle below the target and take turns firing the dart Does the monkey get hit this time Reset the dart gun and target Aim from an angle above the target Does ie monkey get hit this time What generalizations can be made conceming the dart and the monkey What would happen if ie monkey did not fall when the dart was fired Try it What happened Return the monkey gun supplies to their proper places Pick a side of the table that will not interfere with another lab group Cut a string which is slightly longer than the height of the table Construct a plumb line by tying a large washer to one end of the string Attach the other end of the string to the edge of the table near the top Make sure the washer just touches the oor Place the lower end of the wood ramp directly above the string at the edge of the table The purpose of the plumb line is to locate the spot on the oor directly below the end point of the ramp Measure the height of the table to the nearest 01 cm Calculate how long a steel ball would be in the air if it fell this distance Hold the large steel ball LSB next to the top edge of the ramp Measure to the nearest 01 cm the vertical distance from the bottom of the ball to the table top Use this distance to determine the horizontal velocity with which the LSB should leave the table Calculate the horizontal distance at which the LSB should hit the oor Construct a target paper by placing a sheet of carbon paper face up under a sheet of paper Draw a straight line completely across the long center of the paper Position the target paper on the oor so the distance between the drawn line and the plumb line equals the distance calculated in step 12 The target line needs to be parallel with the edge of the table Place the LSB next to the top edge of the ramp Allow it to roll off the table and onto the target paper Be careful not to give the ball a push or a pull when releasing it Be prepared to catch the ball after it bounces on the target paper Extra marks will make the analysis more difficult Repeat until the ball has hit the target paper at least seven times Label this target paper L Repeat steps 11 14 with the small steel ball SSB Label this target paper S Measure the perpendicular distance from each landing point to the line drawn on target paper L and record the values on the paper Do the same for each landing point on target paper S These distances represent the difference between the predicted values and the experimental values for each ball Do not be concerned if the landing points are spread across the paper Determine the average value for each ball Calculate the percentage error A and imprecision percentage EE for each ball Note Formulas for calculating each of these is found in the Lab Report Format section of this lab manual See page ii What might account for any difference between the predicted value for each ball and ie experimental value Was there a signi cant difference between ie average value for ie LSB and the average value for the SSB If so what might account for ie difference If a ping pong ball having ie same size as the SSB was used would the results be similar Why or why not Be sure to include an error analysis and a conclusion 11 PHYS 101 PROJECTILE LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt 9 Height of lab table cm Calculated time in air for steel ball s 10Ramp height for LSB cm Calculated horizontal velocity of LSB cms Ramp height for SSB s Calculated horizontal velocity of SSB cms 11 Calculated horizontal distance LSB should travel cm Calculated horizontal distance SSB should travel cm 16 Average distance from target line L cms Average distance from target line S cms 17 A for L EE for L A for S EE for S Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis and a conclusion Include target papers L and S each signed by all members of the group 12 IMPULSE MOMENTUM OBJECTIVE To verify the impulse momentum theorem THEORY Impulse J is defined as the product of the average force Fave acting on an object multiplied by the time At during which that force is applied J F AVEAt Momentum p represents the inertia of a body in motion and is equal to the mass of the body times its velocity p Inv Both impulse and momentum are vector quantities Av l Rearranging this equation shows that the In impulse delivered to an object equals the change in momentum of that object This is known as the impulsechange in momentum equation FaVeAt mAv We will attempt to verify this relationship by jumping and landing on a force plate The launching impulse will be compared with the landing impulse and the change in momentum The launching and landing impulses will be found by determining the area under their corresponding force time curves plotted on the computer screen The change in According to Newton s second law of motion a 1 momentum can be found using the following equation mAv E mgT where T is the timeof ight for the jump APPARATUS Computer with Vernier LoggerPro and force plate WARNING The force plate is more fragile than it looks A leap consists of two forces your weight plus the force needed to launch you off the platform If the 800 pound range is exceeded the force plate can be permanently damaged Please resist making large leaps 1 Open the Vernier LoggerPro software and verify that the clock is set for 5 seconds at 1000 sampless and the force plate Range slide switch is set on 8003500 N Zero the force plate and check it by pressing the virtual Collect key and waiting for the computer to capture and display the data The response time is a bit slow due to the collection of so much data 2 Determine the weight mg of a group member standing stationary on the force plate Enter the result on your group data sheet 3 Have that person stand on the force plate and crouch down Start data accumulation and then have the crouched person leap vertically upwards and land on the force plate in a crouched position without exceeding the 3500 N limit If necessary repeat until a set of usable data is obtained Move the cursor along the F versus t curve and the time and force for any point will be visible in the lower left corner of the screen From the F versus t curve determine the peak launch force and the peak landing force and record each in the data sheet Make a hardcopy of your group s best F versus t curve 4 Determine the time interval At associated with the leap ie the time from when the leap first began until the force fell to zero There will be preliminary rise followed by a drop in the force before the actual leap This is due to the crouching force just before the leap Arrow A on the sample graph below is a representation of the leap time interval Determine the time interval associated with the landing Arrow B is a representation of this time What do you suppose is ie cause of the secondary rise of force after ie landing A 3 P I K I E I I I Lkji i Cl fluke 3 13 IquotalC c 10 The impulse associated with the leap is equal to the area under the F versus t curve corresponding to the leap time It can be found by highlighting the area and selecting Integral from the Statistics menu at the top of the screen This would be area A in the sample graph The integral function calculates the area under the selected segment of the graph The selected area is filled with a solid color and its Value is displayed on the plot Subtract the product of the person s weight as measured in procedure 2 times the time of the leap At as measured in procedure 4 to obtain the net impulse associated with the launch In a similar fashion obtain the net impulse associated with the landing Determine the time of ight T while the force plate reads zero See arrow C in the sample graph Compute the change in momentum according to the nal equation in the Theory section Repeat 2 6 for each group member who is physically able Calculate the imprecision percentage EE for the launch impulse the landing impulse and the change in momentum How does ie launching impulse compare to the landing impulse How does the change in momentum relate to the launching and landing impulses Be sure to include an error analysis and a conclusion 14 PHYS 101 IMPULSEMOMENTUM LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt 2 Weight N 3 Peak launch force N Peak landing force N 4 Time Interval of launch At s Time Interval of landing At s 5 Area under launch force curve N Weight At correction Net launch impulse Ns Area under landing force curve N Weight At correction Net landing impulse Ns 6 Time of ight T s Change in momentum kgms 8 EE Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis a conclusion and the labeled printout for procedure 3 15 UNBALANCED FORCES OBJECTIVE To study the effect of unbalanced forces on objects THEORY A simple Atwood39s machine consists of two masses ml and ml connected by an ideal cord hung over an ideal pulley If m2 gt ml then m2 will accelerate downward while ml accelerates upward at the same rate The application of Newton s second law to each mass leads to a m theoretical acceleration given by a 2 1 g While mass may be transferred from l A m1 m2 V ml to quot12 or from mg to ml it is important that the total mass ml m2 be held constant I T throughout the experiment Since the masses are attached to each other both will 7 undergo the same acceleration in opposite directions This acceleration can be quot l m determined experimentally from a L for an object released from rest where h is the if L 2 t p height dropped and t is the corresponding time measured with a stopwatch PROCEDURE APPARATUS Stopwatch tall ring stand or table clamp with long rod short rod clamp Atwood pulley string 2 mas S containers and pennies 1 Attach the Atwood pulley to the top of a long vertical rod at least a meter above the oor Connect one end of the string to a mass container drape the string over the elevated pulley and attach the other end of the string to another mass container as illustrated above Adjust the length of the string so that ml does not reach the pulley when ml is on the oor Start with mlequal to the mass of the container plus 5 pennies and m2 equal to the mass of the container plus 6 pennies The pennies represent the small masses that can be shifted to unbalance the system Elevate m2 and check the system by initiating motion in one direction and then the other to see if it undergoes a constant acceleration If it does not shift one penny from ml to m2 so that m2 accelerates smoothly downward when released from rest Begin with ml resting on the oor Release m2 and determine the time it takes to reach the oor Record the time t and the distance between the two masses h Repeat 5 times and record the average time of fall Using the lit equation in the Theory section calculate the acceleration of the system Shift another penny from ml to m2 and determine the new acceleration of the system Continue this process one penny at a time until all of the pennies from ml have been shifted to m2 Calculate the theoretical accelerations for the various combinations of ml and m2 using the it equation in the Theory section Compare the theoretical accelerations with those experimentally determined for the various combinations of ml and m2 Calculate the percentage error A in each case Do you notice any trends Use Excel or Graphical Analysis to plot the mass differences m2ml along the xaxis and the corresponding accelerations a along the yaxis Add an appropriate title and descriptive axis labels to the plot Have the program draw a best fit linear line and determine the slope and intercept for the plot Make a printout of the labeled plot with the slope and intercept fully visible 16 6 Calculate the value of g m1 m2 Calculate the percentage error A between this theoretical value and the experimental slope of the graph 7 What does the value of the intercept represent 8 Draw separate labeled force diagrams for ml and m2 which show how the greater weight dominates the system 9 How does the tension in the string holding ml compare to me tension in me string holding m2 Upon what physics law or principle is you answer based 10 Be sure to include an error analysis and a conclusion 17 PHYS 101 UNBALANCED FORCES LAB Today s date Table Names of group members gt Member 1 Member 2 Member 2 Drop Drop 2ht2 Theory A M1 kg M2 kg h m t s a ms2 a ms2 34 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 5 Slope Intercept 6 gH11 H12 A Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis a conclusion and the printout for procedures 5 18 THE PHYSICS OF TOYS OBJECTIVE To review force and motion relationships work and energy relationships and circular motion using various everyday toys THEORY Who would guess that toys are just applied physics All toys must obey the conservation of energy principle Since the total energy in a system must remain constant the kinetic energy needed to lift a toy from the ground must equal the gravitational potential energy the toy gains at its highest point if friction is ignored The equations for kinetic 1 energy and gravitational potential energy are K E E mvz and P E g mg h respectively A person can nd the launch velocity needed to obtain a given height by combining the two equations The result is 17 2 gh The workenergy theorem states that the net work required to move a toy is equal to its change in energy whether kinetic or potential W AK E AP E The force required to move a toy can be found from the basic work equation W F Ax where X is the distance the force acts The force could also be found from the impulse change in momentum relationship F At mm which is an application of Newton s second law F ma Be careful with this one when dealing with vertical motion The upward force is only acting for the time up and the downward force is only acting for the time down The power required to move a toy can be found from P AK Again At must be time up or time down for vertical motion Ax The average speed of a toy can be found using the basic motion equation vave A t where At is the time required to travel the total distance AX The final speed of a toy can be calculated using another motion equation 17 17 vave T0 if the toy is undergoing constant acceleration The centripetal force acting on a toy moving in circular mvz motion can be found using F T where m is the mass V is the average velocity and r is the radius of the circular path As you can see a toy can involve a lot of physics Owning a toy is like owning a physics laboratory PROCEDURE APPARATUS Metric ruler meter stick stop watch platform balance string jumping toys such as dogs or dropper poppers ying toys such as airplanes or pigs bouncing toys balls and slide toys such as penguins or monsters J UMPING TOYS 1 Select a toy from this group and find its mass As accurately as possible measure how high the toy jumps into the air and the total time the toy is in the air Use the center of gravity of the toy as the base line for its jump height Each member of the group is to collect data for two jumps Determine the average jump height and time in the air for your toy based on the group trials 2 Calculate the following for the jumping toy a its potential energy at the top of its jump b its initial velocity as it leaves the ground c the power utilized in lifting the toy from the ground 3 Draw a labeledforce diagram for ie toy when it is at its highest point of the jump 19 FLYING TOYS 4 Select a toy from this group and find its mass Start its circular motion and wait until it reaches a constant speed in a horizontal circle Each person in the group is to time the period of rotation for the toy Discuss as a group the best way to make this measurement Determine the average period of rotation based on the group trials Determine the average diameter of the circular path traced by the toy 5 Calculate the following for the ying toy a the circumference of its path b its average velocity c the force holding it in the circular path and d the centripetal acceleration acting on the toy 6 Draw a labeledforce diagram for me toy at any point in its pa m BOUNCING TOYS 7 Select a toy from this group and find its mass Drop it from a pre measured height and have each person in the group determine its first two bounce heights Find the average bounce heights based on the group trials 8 Calculate the following for the bouncing toy the energy lost after the first bounce the energy lost after the second bounce the average amount of energy lost between the two bounces how high would you expect it to bounce on the third rebound Why QOO 33 PENGUIN OR MONSTER SLIDE if available 9 10 11 12 13 14 Select a slide toy and make the following measurements a mass of sliding object penguin or monster b height of moving stairs from bottom stair to top c length of slide from top of stairs to bottom of stairs Determine the average time it takes the object to climb the stairs and the average time required to travel down the slide based on two trials by each group member Calculate the following regarding the object while it is on the slide a its initial speed at the top of the slide b its average speed while on the slide c its nal speed at the bottom of the slide using energy conservation theoretical speed d its final speed at the bottom of the slide using you timing data actual speed e the theoretical kinetic energy f the actual kinetic energy g the percent of energy lost h the power required to lift the object Draw a labeledforce diagram for me object as it moves down the slide If energy is conserved where did it go Be sure to include an error analysis and a conclusion for the lab as a whole 20 PHYS 101 THE PHYSICS OF TOYS LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt J UMPING TOY 1 Mass kg Height of jump m trial 1 Group Ave trial 2 Total time in air s trial 1 Group Ave trial 2 2a Potential energy J b Initial velocity ms c Power W FLYING TOY 4 Mass kg Group Ave Period of rotation s Average diameter m 5a Circumference m b Average velocity ms c Force N d Acceleration ms BOUNCING TOY 7 Mass kg Release height m Group Ave 1 bounce height m 2 bounce height m 8a Energy lost 1 bounce J b Energy lost 2 bounce J c Average energy lost J d expected height of 3rd rebound m PENGUINMONSTER SLIDE 10 Mass kg Height of stairs m Length of slide m Group Ave 11 Stair time s Slide time s 12a Initial speed ms b Average speed ms c Final speed ms theory d Final speed ms actual e Kinetic Energy J theory f Kinetic Energy J actual g Percent Energy Lost h Power required to lift object W Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis and a conclusion 21 DENSITY OBJECTIVE To identify materials from their calculated densities THEORY The average density D of a body is de ned as its mass M divided by its volume V or D E If the object s V composition is uniform the density is an intrinsic property of the material and any size of sample will yield the same result This fact enables us to identify the material composition of such objects If the body has a regular shape V can be calculated from simple geometrical considerations For a rectangular solid of length 1 width w and height h V 1 W h For a cylinder of radius r and height h V 7L 1 2h For a sphere of radius r V E 7 I3 The volume may also be determined by immersing the object in water and measuring how 3 much uid is displaced This technique also applies to irregularly shaped objects However beware of materials like wood that might absorb some of the water PROCEDURE APPARATUS Double beam balance ruler graduated cylinder and 6 unknown objects 1 Start with the silver colored rectangular block Measure the mass with the balance and the dimensions with a ruler Calculate the volume and resulting density Enter all values in the data sheet Determine the density of 3 of the remaining regularly shaped objects by measuring their mass with the balance and their dimensions with a ruler At least one object must be a cylinder Enter all values in the data sheet Be sure to write a description of each object in the data sheet Determine the density of the silver colored rectangular block by using immersion in water to nd the volume V0 is the initial volume of water in the graduated cylinder V1 is the combined volume of water with the object totally immersed The volume of the object is the difference V1V0 Repeat for the E 3 objects used in procedure 2 and for 3 irregularlyshaped objects Using the various density determinations decide as a group which objects are made of similar materials Use the Density Table provided to decide as a group what material compositions are most likely for each object and record the answers in the data sheet Determine the percentage error A for calculated density of each object and the given density obtained from the Density Table Compare your results with other groups Be sure to include an error analysis and a conclusion 22 PHYS 101 DENSITY LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt Mass Length Width Height Volume Density Possible A g cm cm cm cm3 gcm3 Material 1 Silvercolored block 2 Regularlyshaped Mass Length Width Height Volume Density Possible A Objects g cm cm cm cm3 gcm3 Material a b c 3 Regularlyshaped Mass gt V0 ml V1 ml Volume Density Possible A Objects g cm3 gcm3 Material Silvercolored block a b c d e f Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis and a conclusion DENSITY TABLE SUBSTANCE DENSITY kgm3 Aluminum 2700 Brass 8400 Copper 8920 Gold 19300 Iron 7870 Lead 1 1340 Nickel 8700 Silver 10490 Steel 7800 Tin 73 10 Zinc 7100 23 PRESSURE Take Home Lab OBJECTIVE To measure the normal force of a car THEORY Pressure is defined as the force F divided by the unit area A over which the force is applied or P E The amount of pressure depends on how a force is distributed over a given area While the metric units for pressure are Nm2 it is more common to see it measured as pounds per square inch psi in nonscienti c applications PROCEDURE APPARATUS shoe car with owner s manual bathroom scale tire pressure gauge and graph paper NOTE 9 You may use the regular team approach for this exercise if you can gather for it Otherwise each individual is responsible for a complete report You are required to make your own spreadsheet data table for this lab Neatly show all calculations performed with units and answer questions from the lab on a separate sheet of paper Do not forget to include an error analysis and a conclusion Draw a line along the perimeter of your shoe on a sheet of graph paper Determine the area of this perimeter Label this graph paper and include it with your writeup What average pressure do you exert on the ground when standing on one foot in psi What average pressure would you exert if you stood equally balanced on both feet in psi How should you stand with bo m feet to approximate atmospheric pressure 147 psi How are me soles of a iletic shoes different man the soles of dress shoes Why is there a difference Position a car on a clean at surface Place a sheet of graph paper in front of each tire Roll the car onto the graph papers so each tire is centered on the paper This may take a couple of trials to achieve Draw an outline of each tire where it makes contact with the graph paper Use the tire gauge to measure the pressure in each tire in psi and record these values on the corresponding graph papers Convert each of these pressures to metric units Back the car off the graph papers Observe the tread patterns inside the outline of each tire Which part of this pattem actually makes contact with the road Determine the area of contact between each tire and the road in m2 Label each graph paper and include it with your writeup Calculate the force each tire exerts against the road in N What is the normal force of the car Draw a labeled force diagram for the car The actual weight of the car can usually be found on the driver s side door or in the owner s manual Use this value as the standard and determine the A A tire gauge measures relative pressure the difference between atmospheric pressure outside the tire and the pressure in the tire What is the absolute pressure inside each tire Why is the absolute pressure of each tire not used when the weight of the car is calculated 10 Would the calculated weight of ie car he changed if one of the tires was at Why or why not 11 Why is it important in terms of pressure to have good tread on your tires particularly in rainy weather 12 Be sure to include an error analysis and a conclusion 24 HEATING AND COOLING OBJECTIVE To measure the heating rate of ice water until it boils and then the cooling rate of the thermometer THEORY As ice water is heated it involves three distinct stages First all remaining ice must melt Second the cold water temperature rises Finally the water boils away Each of these processes has its own characteristic behavior The rate AT At at which the water temperature rises depends on the power P delivered by the heater the mass m of the water and its speci c heat c 4190 Jkg K The relationship is given by A L At Inc As something cools it should follow Newton s law of cooling which predicts that the temperature gradually approaches that of the surroundings room temperature PROCEDURE APPARATUS Balance computerized temperature probe 200 or 300watt electrical immersion heater with half power adapters 3 large Styrofoam cups cold tap water and ice 1 Measure and record on the bottom of the plot in step 8 the temperature of the room Your instructor will demonstrate the use of the computerized thermometer which should sample temperature once each second for up to 20 n1inutes 2 Add about 50 cc 50 grams of cold tap water to a double Styrofoam cup thermal chamber 3 Obtain about 200 cc of crushed ice 4 Submerge the unplugged electrical heater in the cold water in the thermal chamber and mix in the ice Insert the temperature probe and use both it and the heater to stir the system until the temperature falls close to 0 C 5 Simultaneously plug in the electrical heater and restart the computerized data acquisition Keep stirring while the data accumulate but avoid direct contact between the heater and the probe Continue gathering data until the water is boiling vigorously This should take about 10 n1inutes depending on the power of your heater Halt data acquisition at this stage and note the temperature of the boiling water 6 Unplug the heater and set the hot water system safely aside for further use Determine the mass of the water by weighing the system and then subtracting off the weight of the container 7 Fit a best t linear line to the central region of your data Use the plotting program to determine the slope of the line What is me signi cance of this line Double click on the plot and add an appropriate title Estimate the power rating P delivered by the heater from the relationship given in Theory 8 Find and record the actual power rating printed on the heater Determine the percentage error between the calculated power and the actual power A 9 If possible printout the computerized plot of your data Otherwise carefully sketch it and have your instructor observe the results Record the names of your group members on the back of the plotsketch 10 Discuss the results with other members of your group and then share with the rest of the class 11 Retrieve your hot water system and power the heater to bring the water back to a boil while monitoring the temperature with the probe 25 12 13 14 Unplug the heater and set the hot water system safely aside Quickly remove the probe wipe it off and place it in an empty Styrofoam cup at room temperature to shield it from drafts Quickly start the computerized data acquisition in order to monitor the probe until it cools below 25 C or for 15 minutes If possible printout the computerized plot of your cooling data Otherwise sketch it and have your instructor observe the results Record ie names of your group members on the back of the plotsketch Be sure to include an error analysis and a conclusion 26 WAVES TRAVELING AND STANDING Apparatus Springs slinkies stopwatch meter stick long tape measurer Note The written work you tum in must include concise responses to all the questions asked or hinted at in the following procedural directions but cannot consist solely of answers to these questions Not only must it include a description of what you actually did and the resulting data it must stand alone without a need for reference to these sheets Where appropriate use sketches or diagrams for clarity Try to explain any apparent inconsistencies When appropriate comment on the experimental errors or experimental limits etc Investigating Traveling Wave Characteristics For these beginning activities dealing with traveling waves we will use single pulses rather than trying for a continuous wave The fundamental aspects of the pulses and the continuous wave are identical but it is much easier to monitor the behavior of the individual pulses Investigate a pulse made by compressing and releasing one end of a slinky 1 While your partner holds one end of a slinky a long soft coil spring on a smooth oor pull on the other end until the slinky is stretched about six meters Do not let go while the slinky is stretched or the coils may become inextricably intertwined 2 While maintaining your firm grip on the end with one hand with your other hand grab the slinky about a meter from the end and pull to compress this meter length of slinky at the end Then release the compressed section of slinky and watch 3 Observe the pulse that travels along the slinky What type of pulse Wave is it How is this type of pulse characterized Investigate a pulse made by moving one end of the slinky to one side and back 4 While your partner maintains a firm grip at the far end move your hand sideways to one side and immediately back to the original position to produce another type of pulse 5 Practice until you make pulses that travel down only one side of the slinky What type of pulse wave is it How is this type of pulse characterized 27 6 Look at the pulse as it moves along the slinky i Does the shape change If so in what way ii Does the size change If so in what way iii Does the speed change If so in what way 7 Make Observations i Make quantitative observations ie make measurements of the parameters you need to know in order to support your answers to the previous questions If you are looking for changes you may need to determine the speed in different regions of the slinky e g separate halves You need to remember the definition of speed to do this ii What happens at the far end of the slinky iii Is the pulse that returns to you on the same side as the original pulse or on the opposite side 8 Make pulses of different sizes and shapes Does the speed depend on the size or shape of the pulse 9 Change the tension in the slinky Does the change in tension affect the speed of the pulse Should two springs stretched to different leng is be considered to be the same or different media Investigate what happens when pulses are in the same place at the same time 10 What do you think will happen when pulses are in the same part of the slinky at the same time Will they bounce off each other Will they travel on through without any change Will they travel on through with a change in size or shape 11 Try it You and your partner can both send pulses at the same time What happens when the pulses are in the same region of the slinky at the same time 12 Use pulses of different sizes and shapes traveling along the same side and along the opposite sides of the slinky to verify what you thought Why do you want to use different size and shape pulses 28 13 Consider the size shape speed and direction of the pulses when observing and recording the results 14 When the pulses are in the same place at the same time how does the maximum displacement of the slinky compare to the maximum displacement of each pulse alone You can produce measured displacements by controlling your hand motions You can measure displacements by having someone mark on the oor with chalk 15 What can you conclude about the effect caused by the simultaneous occurrence of two pulses waves at the same point in space Investigating Standing Wave Characteristics These activities deal with vibrating systems that are called standing waves and require us to use continuous waves in our springs This is best done as a class exercise Choose two volunteers to be the oscillators two people to be in charge of measuring the wavelength and everyone else to take time measurements This may require you to use your mobile device if enough stop watches are not present Determine the relationships between the physical constraints of the system and the patterns you can produce the placement of nodes and antinodes Make sure you keep the tension of the spring roughly constant throughout this portion of the experiment 1 How can we use the spring to demonstrate and investigate what occurs in a resonating string system when bOth ends are fixed How would the system behave if bo i ends were free Draw a diagram of the resulting standing waves for bo i boundary conditions Would there be any similarities 29 2 How can we use the spring to demonstrate what occurs when one end is xed and the other end is free It may require adding something to the spring There are strings and shiny metal rods available This is best done as a thought exercise than in practice Draw a diagram of the resulting standing Wave with these boundary conditions 3 Repeatedly shaking one end of the spring while the other end is rigidly held enables us to demonstrate What occurs when both termini ends of a resonating system are fixed Try it Carefully observe the relationships between the nodes or zeroes and antinodes or loops in terms of the lengths involved Make appropriate measurements to determine b0th the positions of the nodes and antinodes and the frequencies of shaking which produce each arrangement Make scaled diagrams of the standing waves that show the locations of the ends of the spring the nodes and the antinodes for each situation Shake the end of the spring in different appropriate ways ie rates of shaking so that you produce three different patterns wi i different numbers of nodes and antinodes along the leng i of your spring 4 Determine the speeds of the waves 5 Can you direc y measure the wave speed when you shake repeatedly 6 Can you use the values of the frequencies and corresponding wavelengths to determine the wave speed If so explain how and do so 7 In this case does the speed of the wave depend on the frequency How can you tell 8 Be sure to include and error analysis and conclusion 30 SOUND OBJECTIVE To measure the speed of sound THEORY The speed of sound can be determined by measuring the time required for sound to travel through a measured distance and using rate distancetime The speed of sound V depends slightly on temperature and is given by V 3314 060T where T is in degrees Celsius and V is in ms PROCEDURE APPARATUS Stopwatches 100 m measuring tape large wooden blocks seamstress tape computer with Vernier Logger Pro interface temperature probe and 2 microphones 1 Take stopwatches and a shared 100m measuring tape outdoors along with a pair of large wooden blocks to smack together Locate an unobstructed view at least 200 m away from the person holding the blocks The greater the distance the better the results will be Pick a relatively quiet location such as the Green Belt Smack the wooden blocks together to generate a very loud abrupt sound and then listen for the sound to arrive at the distant location Lab members are to time the interval from when the sound is created until it is heard Each lab member should record at least 5 timings Record the times and enter the average time and the actual distance on the data sheet and calculate the speed of sound Determine the imprecision percentage EE for all of your lab group s times Move back into the lab and use the web to determine the current temperature outside Try wVvwktVbcom gt Weather or some other website Compare results with other groups Calculate the speed of sound expected outdoors based on the temperature Determine the percentage error A between the experimental speed of sound found using the blocks and the theoretical speed of sound calculated using the outside temperature Use the Vernier temperature probe to measure the temperature in the lab Calculate the expected speed of sound in the room based on the temperature measurement Remove the temperature probe from the interface and connect 2 microphones Place the microphones at least one meter apart and facing the same direction Restart Logger Pro and choose Data Collection from the Experiment menu Set the accumulation time to 003 s and the sample rate to 5000 sampless Click the Triggering tab and check the triggering box Start data accumulation quickly followed by a sharp snap of the fingers in front of the microphone plugged into Channel 1 on the Vemier interface One microphone will produce a red wave and the other will produce a blue wave These two waves will be superimposed over each other on the computer screen Select the rst portion of this waveform enlarge it The time between the first distinct red peak and the first distinct blue peak represents the time difference between the signals received by the microphones Repeat this procedure at least 5 times and determine the average time difference and the imprecision percentage EE of the times Calculate the speed of sound based on the exact distance between the two microphones Print a hardcopy of the computer screen showing the enlarged data capture area Label the blue and red waves Determine the percentage error A between the experimental speed of sound found using the microphones and the theoretical speed of sound calculated using the temperature probe Be sure to include an error analysis and a conclusion 31 PHYS 101 SOUND LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt 2 Distance m Group Average Trial 1 time s Trial 2 time s Trial 3 time s Trial 4 time s Trial 5 time s EE for times Average time for sound to arrive s Average speed of sound ms 3 Outdoor temperature C 4 Expected speed of sound ms A 5 Room temperature C Expected speed of sound ms 7 Trial 1 Travel time for snap s Trial 2 Travel time for snap s Trial 3 Travel time for snap s Trial 4 Travel time for snap s Trial 5 Travel time for snap s EE for times Average time for snap s 8 Microphone separation m Average speed of sound ms 9 A Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis a conclusion and the labeled printout for procedure 8 32 RESONANCE OBJECTIVE To observe resonance of sound in pipes and determine the speed of sound THEORY Sound waves inside organ pipes echo off of both closed and open ends If the wavelength 1 lambda of the sound matches the length L of the pipe in particular ways as shown below the re ections can interfere constructively and build up longitudinal standing wave resonances of extraordinary amplitude If the frequency f of the sound and consequently the wavelength are fixed the length of the pipe may be adjusted like a trombone to achieve resonance conditions and enhance the proper note Sound waves are longitudinal waves having regions of compressed and expanded air which travel outward from the source As a sound wave travels through a pipe the compressed air and expanded air oscillate parallel to the pipe If the pipe is closed at one end the air at the closed end is restricted and cannot oscillate This lack of vibration produces a node a point on a standing wave having zero amplitude When a sound wave reaches an open end some of the wave energy escapes the pipe while some of it is re ected back into the pipe These re ections produce standing waves in a pipe that is open at one or both ends The boundary condition discontinuity is different at the open end than it is at the closed end Since the open end allows maximum vibration an antinode is formed a point of maximum amplitude on a standing wave For convenience nodes and antinodes are shown below schematically as transverse waveforms Remember sound is not a transverse wave In the figures the vertical axis represents the pressure of the wave The physical distance between two adjacent nodes or between two adjacent antinodes is half of the wavelength Wavelength Z and frequency f are related to the speed of the wave V by 7 f v The expected speed of sound depends slightly on temperature T according to V 3314 06 T ms where T is in degrees Celsius A LA74 B LB3 l4 ltquotquot lt2quotquotquot 2Z Node N AntinodeA N A N A C LC3912 D LB1 quot gtltZ 2 quot39quotquot 2 quot A N A A N A N A PROCEDURE APPARATUS Plastic ruler meter stick transparent container of water more than 4 cm in diameter and 20cm tall thermometer rubber tuning fork striker 512 Hz and 480 Hz tuning forks plus 2 plastic resonance pipes that fit over a 3rd pipe and slide like a trombone 1 Fill the container with water nearly to the top Take the apparatus to a quiet location remote from other groups perhaps in opposite corners of the lab or the hallway or even outdoors Hit a tuning fork on the rubber striker and listen for the lowest tone Notice how the fork must be oriented with respect to your ear in order to produce the loudest sound Use this same orientation to produce echoes in the pipes Ignore any higher frequency ringing 33 10 11 Submerge the bottom edge of one of the plastic pipes in the water to produce a closed end at an adjustable position Strike the 512 Hz tuning fork and hold it in the optimal orientation near the top of the pipe Adjust the effective length of the pipe by carefully lowering or raising it in the water until the loudest resonance is heard Measure the distance from the water level to the top of the pipe and enter the value on the data sheet as L A It should be between 15 and 20 cm Repeat for each group member in order to obtain an average length Use that f 4L Repeat with the 480 Hz tuning fork Aave average to calculate the speed of sound V Now submerge the bottom edge of the plastic pipe in the water and slide a smaller pipe inside to effectively increase the total length of the pipe Strike the 512 Hz tuning fork near the top of the smaller pipe Find the length required to produce the resonance corresponding to resonance diagram B It should be about 45 to 60 cm Use your average length to calculate the speed of sound V f 4LBaVe 3 Repeat with the 480 Hz tuning fork Remove the pipe from the water dry it and place it on a horizontal surface Insert the smaller pipe to produce an adjustable length with both ends open Strike the 512 Hz tuning fork and hold it in an optimal position near one end and adjust the combined pipe length to obtain the resonance corresponding to diagram C It should be between 30 and 40 cm Use your average length to calculate the speed of sound V f 2LCave Repeat with the 480 Hz tuning fork Insert the third pipe and strike the 512 Hz tuning fork to obtain the resonance corresponding to diagram D It should be 60 to 80 cm Use your average length to calculate the speed of sound V f Repeat with the 480 Hz tuning fork ave Measure the temperature and calculate the theoretical speed of sound You may use the web if you conduct this experiment outdoors and need to find the temperature Antinodes are usually not exactly at the ends of open pipes We will correct for this by taking the difference in lengths LB LA and LD LC and using these as the correct halfwavelengths Complete the data sheet to get these corrected values for the speed of sound Determine the percentage error A between the theoretical speed of sound and the experimental values What would happen to the resonant frequencies if me room temperature was lowered If me experiment was repeated in an atmosphere of pure carbon dioxide gas would me results be the same Why or why not Be sure to include an error analysis and a conclusion 34 PHYS 101 RESONANCE LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt Group Average 2 512 Hz Length A m Speed of sound ms 480 Hz Length A m Speed of sound ms 3 512 Hz Length B m Speed of sound ms 480 Hz Length B m Speed of sound ms 4 512 Hz Length C m Speed of sound ms 480 Hz Length C m Speed of sound ms 5 512 Hz Length D m Speed of sound ms 480 Hz Length D m Speed of sound ms 6Celsius temperature Theoretical speed of sound ms 7 HZ LBLA LnLc Average A2 m Speed of sound ms A h HZ LBLA LnLc Average A2 m Speed of sound ms A Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis and a conclusion 35 ELECTROSTATICS Objective To study electrostatic interactions between charged bodies Apparatus Rubber balloons a variety of materials including glass polyester eece silk or polyester cloth plastic sheets aluminum foil sewing thread and a computer with intemet access Procedure 1 Stroke an in ated rubber balloon against a piece of wool until crackling is heard and then use the balloon as a standard called S The balloon should have a piece of thread tied onto it hold it by the thread when observing the interactions listed below 2 Ob h l h b 11 fr 1 39 Interactmg Ohlect Interactmn serve ow strong yt e a oon om interacts with various objects in close proximity Use the following Wall designations W d SA if strong attraction In OW MA if medium attraction Sheet of Paper WA if weak attraction Plastic sheet ERifFtr IC111 eP 1Si in 1 me 1um repu s1on Metal Water plpe WR if weak repulsion Stream of water NOT if no signi cant interaction 2nd Charged balloon Note the interactions in the provided table of the balloon StI390k d W001 with i the wall ii a window iii a sheet of paper iv a Charged glass plastic sheet v a metal water pipe and vi a nearby stream of steadily dripping water Stroked silkpolyester Neutral aluminum foil 3 Repeat step 1 and then use the descriptions of step 2 for interactions of the balloon with i a second balloon prepared in the same manner as the rst ii the wool that was stroked iii a glass object rubbed with silk or polyester iv the silk or polyester that was rubbed and v a piece of neutral aluminum foil 4 Is there a common type of observed interaction Can you explain why 5 Go to httpphetcoloradoeduensimulationballoons Play with this simulation and answer the following questions Explain why your interactions tumed out the way iey did What would happen to your interactions if the balloon started with the opposite charge 6 Connect to wwwphetcoloradoeduensimulationelectric hockey Launch the Electric Field Hockey software and read the instructions 7 Play the Electric Field Hockey game and complete the rst two levels Make a printout of your team s highest successful level 8 Be sure to include an error analysis and a conclusion 36 ELECTRIC FIELDS OBJECTIVE To explore electric fields THEORY Fields are simply regions of space with values defined at every point For example a topographical map shows the elevation of the terrain Vector fields also associate directions with the values An electric field represents the electric force per unit charge exerted on a small positive test charge Various arrangements of other electric charges provide the source of such fields Computer software allows the easy drawing of electric eld maps based on the user s selection of source charges Realistic computer games can help us understand how charges behave in electric elds PROCEDURE APPARATUS Computers with web access 1 Connect to wwwphvsicswebereduSchroedersoftwareEField Use Print Screen to make a copy of the each of the field maps produced in this simulation If this option does not work sketch each map Read the directions for the simulation Select only the lines option Click and drag one red positive charge onto the palate Click a second time to release it at the desired location Select the arrow which represents a eld vector Click the mouse at various distances and directions around the source charge to map out the vector eld Try some that are quite close to the charge A minimum of at least 12 points should provide a good picture of the electric eld Move the charge strength indicator to see how the field vectors change Clear the arrows and charge and repeat for a a single blue negative charge b a Dipole selected from the Patterns button c three point charges of your choice How would you expect the map to look if bo i charges of ie dipole were ie same Clear the arrows and charges Click on the Patterns button and select Line of Click on the Patterns button a second time and select Line of Place a few field vectors at various locations above the line of positive charges and below the line of negative charges Also place at least 10 eld vectors at various locations between the two lines What does this distribution of positive and negative charges represent Why is it useful Clear the arrows and charges Click on the Patterns button and select Large Circle of Place a minimum of 15 eld vectors at various locations on the outside and inside of the circle Do not allow any of the eld vectors inside the circle to touch any of the actual charges What does this map tell you about the electric field inside conductors Clear the arrows and charges Click on the Patterns button and select Large circle of Click on the Patterns button a second time and select Small circle of Place a minimum of 15 field vectors at various locations on the outside of the positive circle between the two circles and inside of the smaller negative circle Do not allow any of the eld vectors inside either circle to touch any of the actual charges How is iis patter similar to and how is it different from ie pattem in 7 What does this tell you about electric fields Connect to wwwphetcoloradoeduensimulationelectric hockev Launch the Electric Field Hockey software and read the instructions Play the Electric Field Hockey game and complete the rst two levels Make a printout of your team s highest successful level Discuss your findings with the rest of the class and then tum in your eight print outs Remember to write your names on each sheet 10 Be sure to include an error analysis and a conclusion 37 BULBS OBJECTIVE To examine the resistance of light bulbs singly and in various combinations THEORY Resistance is a measure of the opposition to the ow of charge Think of it as electrical friction It is dependent upon the conducting material as well as the length and cross sectional area of the conductor Any device in an electric circuit will contribute some degree of resistance The total resistance equivalent resistance in a circuit depends upon how the components of the circuit are connected In a series circuit the equivalent resistance can be calculated from Req R1 R2 Rn As more components are added the equivalent resistance increases In a parallel circuit the equivalent resistance is calculated 1 from Req R R K Ri Unlike a series circuit as more components are added to a parallel circuit the 1 2 N equivalent resistance decreases In a complex circuit components connected in series must follow series rules and components connected in parallel must follow parallel rules PROCEDURE APPARATUS Digital power supply digital multimeter DMM 3 socket connectors with bulbs labeled A B amp C 4 short electrical leads with banana connectors 2 long leads 1 battery and 1 extra bulb 1 Devise a way to light the separate bulb using only one lead the battery and the bulb Demonstrate the successful method to your instructor Make a detailed sketch of the arrangement 2 Without connecting ie power supply use the DMM as an ohmmeter to measure the equivalent resistances in each of the circuits listed below Record the values in the data sheet and draw a labeled circuit diagram not a sketch for Q circuit a Bulb A only b Bulb B only c Bulb C only d Bulbs A and B in series e Bulbs A and B in parallel f Bulbs A B and C in series g Bulbs A B and C in parallel h Bulb A connected in series with a parallel combination of B and C i Bulb A connected in parallel with a series combination of B and C 3 Calculate the equivalent resistance and corresponding percentage error A for each of the con gurations a through i Use the calculated value as the theoretical value 4 Set the power supply to its maximum voltage output z18 V Connect it to each of the configurations a through i and record the relative brightness Qff Qim Medium or Bright of each bulb on the corresponding circuit diagrams 5 Connect the power supply across a single bulb and then vary the output voltage to determine I as a function of V over the domain of 0 to18 V For each trial ip the switch on the power supply between voltage and current to obtain the needed values A good set of voltage data points would be 0 2 4 8 12 16 and 18 V Use Excel or Graphical Analysis to create a labeled plot of these data points with V on the x axis and I on the yaxis Clearly mark each data point and then connect them with a smooth line Is the line straight What might be some possible reasons for its shape 6 Be sure to include an error analysis and a conclusion 38 PHYS 101 BULBS LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt 23 Req with DMM Calculated Req A a Bulb A b Bulb B c Bulb C d Bulbs A amp B in series e Bulbs A amp B in parallel f Bulbs A B amp C in series g Bulbs A B amp C in parallel h Bulb A in series with B amp C in parallel i Bulb A in parallel with B amp C in series 5 Values for IV plot Voltage Current Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis a conclusion and a labeledprintout for procedure 5 39 Magnetism Lab OBJECTIVE To explore magnetic elds THEORY Magnetic fields are caused by moving charges sometimes by charges moving on the atomic level electrons moving around atomic nuclei for example and sometimes moving on a macroscopic scale such as through the wires in an ordinary circuit Similar to how electric fields are both produced by and act on charged particles magnetic fields are both produced by and act on moving charges The unit of measurement of magnetic field is the Tesla the earth s magnetic field is about 000005 Tesla and a refrigerator magnet creates a field of about 001 Tesla In this lab you will be using bar magnets as the source of the magnetic field All magnets as far as we know each have two poles North and South IMPORTANT The convention for magnetic field lines is that they point away from a magnetic North pole and towards a magnetic South pole analogous to how electric field lines point away from positive charges and towards negative charges As mentioned above magnetic fields are also produced by moving current The direction of the magnetic field around a current carrying wire can be determined by the righthand rule Namely if you point your thumb in the direction of the current your fingers will curl in the direction of the magnetic field lines which surround the currentcarrying wire APPARATUS Two bar magnets compass magnaprobe transparent plastic sheeting or tracing paper iron filings power supply wires solenoid PROCEDURE 1 Place one of your bar magnets on a piece of paper B Place the plastic over the magnet and sprinkle the iron filings from a height of about 10 cm C Continue sprinkling until a distinct pattern emerges The iron filings fall on the plastic and align themselves with the magnetic field Describe the field What is the most unique characteristic of the field 2 Draw a simplified version of the field pattern that emerged when the iron filings were placed on the bar magnet Be sure to show the shape of the field and include at least 10 lines 40 7 Use the north pole of your compass to determine the direction of the magnetic eld lines Add arrows to your picture showing the direction of the magnetic field lines as determined by your compass Note Only show the field lines as they appear between the bar magnets 8 Now take your power supply with the current and Voltage knobs turned all the way down and connect enough wires to have about 2 m of wire coming from the positive terminal to the negative terminal Turn the current knob IA of a turn clockwise and turn up your Voltage until you have between 5 and 10 Volts Use your compass or Magnaprobe to determine what the magnetic field looks like around the wire Draw a picture of your setup below Be sure to include the direction of the current and magnetic field in your drawing How does the field change With distance How can you tell How does increasing the current affect the magnetic field streng i 9 Now make a loop with your wiring and use your compass or Magnaprobe to determine what the field looks like inside and outside of the loop Draw a picture of your setup below Be sure to include the direction of the current and magnetic field lines in your drawing 9 Finally explore the field in a solenoid A solenoid is basically many loops of wire Draw a picture of your setup below Be sure to include the direction of the current and magnetic field in your drawing How is a solenoid s eld different than just one loop 42 SIMPLE DC MOTOR Adapted from httpwebmiteducmseeducationalmotor 11 kristVpdf Objective To understand how a simple DC motor Works and to build your own Working model Apparatus Base Wood block or plastic cup rectangular magnet 15 meters of Wire 9Volt battery battery snap large paper clips tacks razor blade or utility knife Theory Motors convert electrical energy from a battery or Voltage source into mechanical energy used to cause rotation When a wire that carries current is placed in a region of space that has a magnetic field the Wire experiences a force The size of the force which determines how fast the motor spins depends on 0 the amount of current in the Wire 0 the length of the Wire 0 the strength of the magnetic field Force Current Wire Length Magnetic Field Strength The direction of the force which determines which direction the motor spins depends on 0 the direction of the current in the Wire 0 the direction of the magnetic field The Right Hand Rule is used to determine the direction of the force when the direction of the current and the direction of the magnetic field are known Thumb direction of current Finger direction of magnetic eld Palm direction of force 39n2 xrgr1 win ll Tcfquot 1 5225 Physiology of a Motor The ceramic bar magnet provides the magnetic eld in this simple DC motor With the magnet in position the magnetic field is directed Vertically out of or into the magnet depending on which side of the magnet is exposed When the rotor sits in the paperclip supports so that the plane of the loop is oriented Vertically the top and bottom sections of the loop act as current carrying wires in the region of a magnetic field 43 Q Why only the top and bottom sections Doesn t the rest of the loop matter A Only the sections of wire oriented perpendicularly to the magnetic field experience forces Since the magnetic field is oriented Vertically here only the sections of wire where the current runs horizontally matter experience forces The current only runs horizontally in the top and bottom sections of the loop One loop of wire carrying current in the region of a magnetic field would experience a force Two loops of wire carrying a similar current would experience twice the force If the rotor contains 12 15 loops of wire it experiences 1215 times the force of one loop Q What about the direction of the force A As mentioned above the direction of the force on a current carrying wire in a magnetic field and thus the direction that the motor turns can be determined by the Right Hand Rule Let s apply the Right Hand Rule to the simple DC motor Consider the case where the bar magnet is oriented so that the magnetic field is pointing away from the magnet and the current runs clockwise in the rotor Tuqp of Loop 6 T1u111lb Eli1 Ei2i 1i3Ifi2l1ITE 1 right Fillg f i dir of111aetin ald up P llillli li1 en quotim1 of force H1rf ufplane fpaperquot E llml of Loop G l T1u111lb urliretim1of current left A Fillgers dir uf111aetic eld up Em Magma P lliltli ili1quotEETfiH11 of force info piunfe fpurpear Since the top of each loop experiences a force directed out of the plane of the paper and the bottom of each loop experiences a force directed into the plane of the paper the rotor experiences a torque or tendency to rotate The greater the number of loops the greater the experienced torque Thus the rotor begins to turn But consider the rotor after the loop has completed a half of a turn What was the bottom section carrying leftward current quickly becomes the top section what was the top section carrying rightward current is now on the bottom The current that used to be directed clockwise is all of a sudden directed counterclockwise it A simple application of the Right Hand Rule would indicate correctly that while a clockwise current caused the motor to turn one way a counterclockwise current causes it to turn the other way More specifically the top of the rotor used to experience a force directed out of the plane of the paper Now since the current has changed direction the top of the rotor experiences a force directed into the plane of the paper Here is the problem I 44 Ear Mangllet If left to its own accord the rotor would never make a single complete rotation The rotor Would oscillate back and forth first turning 180 degrees one Way then 180 degrees the other Way and so on never completing more than a half of a turn This would not make a very effective motor A simple technique that momentarily turns off the ow of current is used to eliminate this problem and thus allow for a rotor that turns continuously Recall that on one of the straight sections of the rotor only the top section is stripped This is a key point since the circuit is only complete and thus current only ows when the paperclip supports are in contact with the stripped section 0 The rotor is given a nudge so that the stripped section comes into contact with the paperclip support 0 The circuit is complete current ows and the rotor experiences a torque in the direction determined by the Right Hand Rule 0 The rotor completes one half of a tum and the circuit is broken as the paperclip support comes into contact with a nonstripped section of Wire 0 No current ows thus no opposing forces are experienced and the rotor does not get pushed into a cycle of altemating half turns 0 Instead the inertia from the initial half turn carries the rotor the rest of the Way around until it has completed a single tum 0 At this point the stripped section of the rotor again comes into contact with the paperclip support completing the circuit and beginning the cycle again 0 The rotor spins continuously providing a Working motor The direction that the motor spins can be controlled by varying the direction that the current runs through the rotor by switching the battery leads and varying the direction of the magnetic field by ipping the magnet from one side to the other The speed at which the motor spins depends on the size of the force experienced by the Wires that make up the rotor Recall that the force experienced by each individual loop is determined by the amount of current in the wire the length of the wire and the size of the magnetic field Thus it is possible to increase the size of the force and thus the speed at which the motor turns by 0 Increasing the number of current carrying wires number of loops in the rotor 0 Increasing the current in the rotor by using a bigger battery 0 Increasing the current in the rotor by using Wire with less resistance 0 Increasing the size of the magnetic field by using additional andor stronger ceramic magnets The Blueprint How to Build a Simple DC Motor 1 Wind the Wire around a small cylindrical object ie film canister Dcell battery making 1215 loops This pack of coils is called the rotor Leave about 2 inches of straight wire on each side of the rotor 2 Hold the loop vertically by placing your thumb through the center of the rotor Place one of the straight sections of Wire on a at surface Using a razor blade strip ONLY the TOP surface of the Wire Be sure not to strip the sides or the bottom just the top Strip the Wire from the coil all the Way to the end of the straight section 45 3 Strip the other straight section of Wire completely top bottom and sides 4 Prepare to assemble the motor Place the ceramic magnet in the middle of the base 5 Bend two large paperclips as shown below Using thumbtacks secure the paperclips to the base Secure one paperclip at each end of the magnet 6 Place the rotor in the paperclip supports When the loop of Wire is oriented vertically the plane of the loop should be directly over the magnet Adjust the magnet andor supports accordingly Attach the battery snap to the battery If desired secure battery to base using tape 7 Connect the black lead from the battery snap to the thumbtack that is securing one of the paperclips To complete the circuit connect the red lead from the battery snap to the thumbtack securing the other paperclip 8 Give the rotor a little nudge a If the rotor spins Ta dah A working motor b If the rotor does not spin try giving the rotor a nudge in the other direction c If the rotor still does not spin refer to the Troubleshooting Tips page 9 Be sure to disconnect either or both leads to turn off the motor Troubleshooting 0 Has the rotor been stripped correc y Hold the plane of the loop sothat it is oriented vertically One of the straight sections of the rotor should be stripped completely from rotor to end the other straight section should be stripped on the top only 0 Is the circuit complete Check each connection red lead to thumbtack thumbtack to paperclip paperclip to stripped section of rotor other stripped section of rotor to other paperclip paperclip to thumbtack thumbtack to black lead Any break in the circuit will prevent current from owing and thereby prevent motor from Working 0 Is the rotor level and direc y above the magnet Adjust the rotor paperclip supports and magnet until both straight sections of the rotor are perfectly horizontal both paperclip supports are at the same height and the magnet is directly undemeath the rotor when the rotor is oriented so that the plane of the loop is vertical 0 Is the rotor close to the magnet The magnetic field is strongest nearest to the magnet When the plane of the rotor is oriented vertically the bottom of the rotor should be as close to the magnet without touching as possible 0 Is the battery providing power Use a voltmeter or multimeter to check the voltage of the battery or simply replace with a fresh 9 volt battery 46 What Do I know about Motors 1 Motors are devices that convert energy into energy 2 The basic principle behind the simple DC motor is that wires that carry experience when placed in regions of space that have 3 Only sections of wire that carry current in a direction to a magnetic field experience forces 4 The speed at which the rotor of a motor spins depends on three important factors and 5 The direction that the rotor of a motor spins depends on the rule 6 Which of the following changes to a motor might decrease the speed at which it spins a Using two magnets instead of one b Using two batteries instead of one c Using a rotor with only six loops instead of twelve 7 When using your hand to determine the direction that the motor spins your thumb always points in the direction of a The current b The magnetic field c The force experienced by the wire 8 Consider the motor shown The magnetic field is oriented vertically so that it is directed into the magnet The current runs through the loop in a clockwise manner What will the direction of the force on the bottom section of the rotor be a Into the plane of the paper b Out of the plane of the paper A 0m c No force will be experienced by the bottom section quot l M quotEl ma TL 139 ni rn I 9 Consider the motor in the previous question What will happen to the direction that the motor spins if the bar magnet is flipped so that the direction of the magnetic field is reversed AND the battery leads are switched so that the direction of the current is reversed a The motor will continue to spin in its initial direction b The motor will reverse the direction that it spins 10 Two students build a DC motor during class one day When stripping the rotor the students don t follow the directions exactly instead they strip both straight sections completely top bottom and sides What will happen when they try to run their motor a The rotor will spin but more slowly than it would have if they had stripped correctly b The rotor will remain stationary not moving at all c The rotor will oscillate back and forth but never make a complete turn 47 MIRRORS OBJECTIVE To study the images formed by mirrors THEORY Rays are used to describe the direction that light waves travel Rays that come straight in along the perpendicular normal to a mirror surface are re ected straight back Rays incident at some angle 0 theta from the normal will be re ected out at the same angle as illustrated in the above sketch 0 01 This behavior is common both to at and curved mirrors For a spherical concave mirror rays entering parallel and near the symmetry axis are re ected through the focal point which is half of the radius of curvature away from the mirror Straight fences can be constructed by setting the end posts first Someone then stands behind one end post sights the other post and signals another person where to move in order to maintain a straight light with the intermediate posts This is also an effective way to de ne a ray of light for our experiment Straight pins play the role of fence posts In this lab the straight sighting pins will be lined up with the image of an object pin in a plane mirror as illustrated below P 13 j Image of pin Mirror C Ruler Once the pins are removed a ruler can be used to draw a line through the pin holes to the line representing the re ective surface of the mirror A line can be drawn back to the object pin from this point as shown in the sketch for pin line A The law of re ection can then be checked by drawing a normal and measuring the angles The image of the object pin can be located by extending all of the lines behind the mirror until they meet PROCEDURE Note Record all measurements calculations and answers on the appropriate drawings APPARATUS Cork board plain paper ruler protractor straight pins at mirror support block transparent grid real or arti cial candle small and large concave mirrors 1 Place a sheet of plain paper on the cork board and stick a pin upright at both the top and bottom of the page several centimeters in from the edges Have each group member sight with one eye along the pins and insert 5 other pins between them at various intermediate positions as if they were additional fence posts When looking at the pins from tablelevel all of the pins should appear to be directly behind the first pin Remove the pins and use the ruler to draw the best straight line through the 7 holes Sign your line 2 Place a fresh piece of plain paper on the cork board lengthwise and draw a horizontal line across the middle of the page with a ruler Use the wood block to hold the at mirror vertically and place the back surface of the mirror along the line near the center of the page Place a mark along each side of the wood block to insure its location should it get moved Stick an object pin upright about a 4 cm in front of the center of the mirror and label it P 48 10 11 12 Place a second pin about 2 cm to the left of the object pin and 10 cm in front of the mirror Align the pin with the image of the object pin When the alignment is set plant the pin Plant a third and fourth pin between the second pin and the mirror along the same line Refer to the sketch in the Theory section When all lab members have checked the alignment of the pins from tablelevel remove them and label the new holes with the letter A Now move the second pin 2 cm more to the left and repeat the process Label these pin holes B Move the second pin 2 cm more to the left and label the new pin holes C Remove all pins and use the straight edge to connect pinholes having the same letter Extend each line to the horizontal line representing the surface of the mirror Finally use dotted lines to extend the three lines behind the mirror s position until they intersect What is the signi cance of this intersection point Measure the distance from the object to the horizontal line Measure the distance from the point where the three dotted lines intersect to the horizontal line How do these measurements compare Calculate a percentage error A assuming the object distance e is the accepted value Draw a line from where A intersects the horizontal line to P Construct a normal as shown in the sketch in the Theory section Use a protractor to determine the incident and re ected angles Repeat for B and C Record the angles in tabular form Calculate a percentage difference for each set of angles Percentage Difference x 100 E139E2 Place the smaller concave mirror on the cork board facing upright like a bowl Describe the re ection of your eye as you get closer and closer to the mirror Repeat for the larger concave mirror Place the transparent grid with the word up on top of the concave mirror Illustrate the appearance of the re ection along with the original grid and the word upquot together on the same sketch Pay particular attention to the relative appearance of the word up and its re ection How does the re ected grid behave near ie edge of ie mirror What might be ie cause of this Repeat for the larger concave mirror Slowly lift the transparent grid away from the surface of the concave mirror Describe in detail how the relative appearance of the re ection with the original grid and word up changes as ie distance increases up to 20 cm At what distance between the bottom of ie mirror and the transparency does ie re ection change dramatically Repeat for the larger concave mirror Measure the particular distance between the bottom of the mirror and the transparency where the size of the re ection is the same as that of the original grid This distance equals the radius of curvature of the mirror What is the mirror s radius of curvature and focal point Repeat for the larger concave mirror Activate the candle or the light emitting diode candle simulation Turn the smaller concave mirror sideways facing the light source and separate them by the radius of curvature of the mirror Describe the image formed by the mirror Move the light source and mirror closer together in order to project an image on a wall or screen at least a meter away Adjust for optimum focus Describe the image that is formed Repeat with the larger concave mirror Compare ie relative brightness from the two differently sized concave mirrors What might account for any observed difference Be sure to include an error analysis and a conclusion 49 LENSES OBJECTIVE To study lenses and their applications THEORY A light ray entering optically dense materials such as water or glass at an angle to the surface is bent towards the normal inside the material This phenomenon is called refraction As rays exit the material they bend away from the normal Measurements of such ray bending at water surfaces were made by Ptolemy in 140 AD and properly modeled by Snell in 1621 A key parameter is the index of refraction n of the material which is defined as the ratio of the speed of light in a vacuum divided by its speed in the material For water n 13 For most glasses n is between 14 and 16 For a rectangular glass plate with polished edges light rays that enter at some angle from the normal will bend towards the normal in the material and then exit parallel to the incoming ray but displaced sideways We will determine n from the amount of sideways displacement For converging lenses with an outwards convex spherical surface rays parallel and near to the symmetry axis are bent slightly towards the normal while those further away from the symmetry axis are bent progressively more The consequence is that these rays converge at some focal point located at the focal distance from the lens on the opposite side as a distant object Doubleconvex surfaces enhance the effect Diverging lenses have an inwards concave spherical surface and show similar behavior except that exiting rays appear to spread out from some focal point on the same side of the lens as the distant object PROCEDURE APPARATUS Cork board glass plate straight pins 4 lenses focal length 5 5 10 and 20 cm meterstick optical bench lens holders protractor ruler paper and shared 150 W distant light source Handle lenses only by their edges to avoid smudging the optical faces Similarly avoid touching the polished edges of the glass plate A B 30 30 11gt Width w x V lt gt 1 Draw a horizontal line across the middle of a blank sheet of paper Use a protractor to draw a perpendicular bisector to the line which will serve as a normal Draw a line that makes an angle of 30 to the normal as shown in illustration A Next put the paper on the cork board and place the glass plate as shown in illustration B Carefully draw a line around all four sides of the glass plate Place 2 upright pins along the incoming ray and view them from table level through the polished edges of the plate so they form a single ray Place a 3rd pin against the bottom edge where the original 2 pins appear in alignment when viewed from table level Finally place a 4th pin in common alignment further out to define the exit ray Remove the pins and glass plate and then connect the holes to form the incoming and outgoing rays that are shown in B Repeat for an angle of 45 on a separate sheet of paper 50 The width w of the glass plate and the sideways displacement X of the exit ray from the normal can be measured directly The index of refraction is given by n 11 w x2 sine where sin 30 050 Determine n from your measurements Repeat for the 45 angle sin 45 0707 Are me nal exit rays parallel to me corresponding original rays Explain why this should or should not be true All group members should sign the completed ray diagram Determine the imprecision percentage EE for the n values determined with the 30 and 45 angles Record this value on the 45 angle sketch Discuss your values of the index of refraction as a group and then share results with the class Include these values calculations and answers to questions in your group report Obtain three converging lenses and one diverging lens Label the large focal length converging lens A the middle focal length converging lens B the short focal length converging lens C and the diverging lens D Measure the focal length of each of 3 converging lenses directly by focusing a distinct image of a distant object such as a bright light bulb or the sun onto a sheet of paper and measuring the distance from the lens to the paper Position the diverging lens D above a sheet of lined or graph paper so that parallel lines appear half as far apart through the lens as beside it At this position the distance from the paper to D will equal the magnitude of its focal length Include a table of all these values in your group report and discuss them as a group Finally share results with the class Use each lens as a hand lens Observe a few close objects and then some more distant objects Describe the images as upright or inverted and their sizes as enlarged reduced or unchanged compared to the original size of the objects Include a table of these observations in your group report Discuss the results as a group and then share them with the class Construct a simple telescope using A for the objective lens and C for the eyepiece mounted on the meter stick optical bench Hold the eyepiece close to one eye Observe a distant object with one eye unaided and the other looking through bo m lenses of the telescope Estimate how much me nal image appears to be magni ed by comparing me aided and unaided views Compare your answer with me ratio of the focal length of me objective lens divided by me focal leng m of me eyepiece Is me nal image upright or inverted Repeat using lens D for the eyepiece How does eyepiece D compare to eyepiece C Finally discuss your telescope results as a group and then as a class Be sure to include an error analysis and a conclusion 51 MIRRORS and LENSES OBJECTIVE To study the images formed by mirrors and to study lenses and their applications THEORY Rays are used to describe the direction that light waves travel Rays that come straight in along the perpendicular normal to a mirror surface are re ected straight back Rays incident at some angle 0 theta from the normal will be re ected out at the same angle as illustrated in the above sketch 0 01 This behavior is common both to at and curved mirrors Straight fences can be constructed by setting the end posts first Someone then stands behind one end post sights the other post and signals another person where to move in order to maintain a straight light with the intermediate posts This is also an effective way to de ne a ray of light for our experiment Straight pins play the role of fence posts In this lab the straight sighting pins will be lined up with the image of an object pin in a plane mirror as illustrated below P 039 f 39 0 Image 0 pin Once the pins are removed a ruler can be used to draw a line through the pin holes to the line representing the re ective surface of the mirror A line can be drawn Mirror C back to the object pin from this point as shown in the sketch for pin line A The law of re ection can then be checked by drawing a normal and measuring the angles The image of the object pin can be located by extending all of the lines behind the mirror until they meet Ruler 311 EV 39 A light ray entering optically dense materials such as water or glass at an angle to the p surface is bent towards the normal inside the material This phenomenon is H an called refraction As rays exit the material they bend away from the normal Measurements of such ray bending at water surfaces were made Wjg thl by Ptolemy in 140 AD and properly modeled by Snell in 1621 A key W parameter is the index of refraction n of the material which is defined as W the ratio of the speed of light in a vacuum divided by its speed in the material For water n 13 For most glasses n is between 14 and 16 For a rectangular glass plate with polished edges light rays that enter at some angle from the normal will bend towards the normal in the material and then exit parallel to the incoming ray but displaced sideways We will determine n from the amount of sideways displacement PROCEDURE Note Record all measurements calculations and answers on the appropriate drawings APPARATUS Cork board graph paper ruler protractor straight pins laser at mirror support block and at pr1sm 1 Place a sheet of plain paper on the cork board and stick a pin upright at both the top and bottom of the page several centimeters in from the edges Have each group member sight with one eye along the pins and insert 5 other pins between them at various intermediate positions as if they were additional fence posts When looking at the pins from tablelevel all of the pins should appear to be directly behind the first pin Remove the pins and use the ruler to draw the best straight line through the 7 holes Sign your line 52 2 Place a fresh piece of plain paper on the cork board lengthwise and draw a horizontal line across the middle of the page with a ruler Use the wood block to hold the at mirror vertically and place the back surface of the n1irror along the line near the center of the page Place a mark along each side of the wood block to insure its location should it get moved Stick an object pin upright about a 4 cm in front of the center of the n1irror and label it P 3 Place a second pin about 2 cm to the left of the object pin and 10 cm in front of the mirror Align the pin with the image of the object pin When the alignment is set plant the pin Plant a third and fourth pin between the second pin and the mirror along the same line Refer to the sketch in the Theory section When all lab members have checked the alignment of the pins from tablelevel remove them and label the new holes with the letter A Now move the second pin 2 cm more to the left and repeat the process Label these pin holes B Move the second pin 2 cm more to the left and label the new pin holes C 4 Remove all pins and use the straight edge to connect pinholes having the same letter Extend each line to the horizontal line representing the surface of the mirror Finally use dotted lines to extend the three lines behind the mirror s position until they intersect What is the signi cance of this intersection point 5 Measure the distance from the object to the horizontal line Measure the distance from the point where the three dotted lines intersect to the horizontal line How do these measurements compare Calculate a percentage error A assuming the object distance e is the accepted value 6 Draw a line from where A intersects the horizontal line to P Construct a normal as shown in the sketch in the Theory section Use a protractor to determine the incident and re ected angles Repeat for B and C Record the angles in tabular form Calculate a percentage difference for each set of angles E239E139 x1oo Percentage Difference rglgzl 7 Draw a horizontal line across the middle of a blank sheet of paper Use a protractor to draw a perpendicular bisector to the line which will serve as a normal Draw a line that makes an angle of 30 to the normal Next put the paper on the cork board and place the glass plate as shown in illustration B Carefully draw a line around all four sides of the glass plate Place 2 upright pins along the incoming ray and view them from table level through the polished edges of the plate so they form a single ray Place a 3rd pin against the bottom edge where the original 2 pins appear in alignment when viewed from tablelevel Finally place a 4th pin in common alignment further out to de ne the exit ray Remove the pins and glass plate and then connect the holes to form the incoming and outgoing rays that are shown in B Repeat for an angle of 45 on a separate sheet of paper 8 The width w of the glass plate and the sideways displacement x of the exit ray from the normal can be measured directly The index of refraction is given by n 1 w x2 sine where sin 30 050 Determine n from your measurements Repeat for the 45 angle sin 45 0707 You should have four n values 2 from each drawing Are ie nal exit rays parallel to ie corresponding original rays Explain why iis should or should not be true All group members should sign the completed ray diagram 9 Determine the imprecision percentage EE for the n values determined with the 30 and 45 angles Record this value on the 45 angle sketch 10 Be sure to include an error analysis and a conclusion 53 SPECTRA OBJECTIVE To identify elements from their atomic spectra THEORY Thomas Young demonstrated in 1801 that light passing through adjacent slits will interfere like waves The effect is greatly enhanced if many closely spaced slits are used in the form of a diffraction grating This device will break white light into a rainbow of colors or separate the combined output from a gaseous discharge lamp into its component colors The resulting pattern of colors can be used to identify the light source Suppose a diffraction grating is attached like a monocle to the end of a meter stick with a vertical discharge lamp at the other end A straight View of the source through the grating gives an ordinary View of the combined output but a glance off to the side reveals the component colors Their sideways positions can be measured with a second meter stick at right angles to the first as illustrated below The wavelength lambda 2 of the light can be found with the following equation where d is the Very small spacing between adjacent slits in the diffraction grating x yin meters quotT Varies with T the color x 39 Iv lt gtLamp Grating X 10 m PROCEDURE APPARATUS Discharge lamp with hydrogen mercury and 2 unlabeled tubes 2 ring stands 2 meter sticks diffraction grating masking tape WARNING Beware of high voltage and hot tubes Turn off the power and allow the tubes to cool before removing them from the lamp Only handle the glass ends of the tubes never the thin centers 1 Set up the apparatus as shown above with the mercury tube in the lamp Balance and tape the meter sticks to ring stands with a 90 angle between them This can be set for a 345 triangle with a 3rd meter stick Place the diffraction grating at the end of one meter stick opposite the lamp Look through the grating as you would through an eyepiece and sight along it so that the zero order maximum coincides with the lamp itself The first order constructive interference pattern of the green line of mercury should appear somewhere near the middle of the other meter stick 54 Determine the slit spacing d for your diffraction grating by using the green line of mercury as a standard with a known wavelength 2 546 nm Rearranging the equation given in Theory gives 2 2 ds46jVX quotLy Y l ll39l l Tum off the lamp and let the tube 11 enough to handle by the glass ends Carefully replace the mercury with the hydrogen discharge tube without disturbing the geometry Locate the positions of the characteristic red blue green and violet lines produced by atomic hydrogen Use the value of d calculated above to determine the respective wavelength for each of these lines How do ie calculated wavelengths compare with the accepted values in the spectral lines table Determine the percentage error A for each line Note The broad orange and yellow bands are due to molecular hydrogen and will be ignored in this experiment Tum off the lamp and let the tube Q enough to handle by the glass ends Carefully replace it with one of the unlabeled tubes tum the lamp on and view the spectrum Compare the general pattern of colored lines with your team members Include a sketch of ie spectrum with the major colors labeled your report Calculate the wavelengths of at least 4 spectral lines from different areas of the spectrum Fill in the blanks space in the data sheet with the color of the line Compare the values to those in the spectral lines table and try to identify ie element in ie lamp Determine the percentage error A for each line Repeat for a second unlabeled tube Use the diffraction grating to observe the overhead uorescent lights in the lab Describe your observations and include a labeled sketch What lines would you expect to find in a spectrum of water vapor Describe your reasoning Discuss the cosmological implications of redshifts in spectra and include a summary in ie group report Be sure to include an error analysis and a conclusion 55 PHYS 101 SPECTRA LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt Group Average 2 Spacing of d nm 3 Calculated A of red nm A Calculated A of bluegreen nm A Calculated A of violet nm A 4 Unlabeled tube 1 Calculated K of line nm A Calculated K of line nm A Calculated K of line nm A Calculated K of line nm A 4 Unlabeled tube 2 Calculated K of line nm A Calculated K of line nm A Calculated K of line nm A Calculated K of line nm A Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis and a conclusion 56 SPECTRAL LINES OF ELEMENTS nm MERCURY KRYPTON OXYGEN BlueViolet 436 Violet 455 Violet 440 Green 546 Blue 490 Blue 490 Yellow 577 Green 560 Green 520 579 570 540 Red 623 Yellow 590 550 Red 610 570 630 Red 620 HYDROGEN 650 660 Violet 410 665 665 BlueViolet 434 Green 486 Red 656 NEON XENON Green 540 Blue 470 Yellow 585 Green 485 BROMINE 600 500 Violet 420 Orange 640 Red 625 450 Red 670 640 Blue 480 685 700 715 ARGON CHLORINE Violet 460 Violet 450 Green 500 Blue 485 NITROGEN 530 Green 510 Violet 400 550 520 410 560 540 420 570 570 Blue 500 Yellow 595 Yellow 590 520 Red 610 Red 600 Green 530 630 625 540 640 635 550 650 655 560 660 665 Yellow 580 670 590 680 Red 600 710 HELIUM 620 720 Violet 389 630 Blue 471 640 Green 501 650 Orange 588 660 Red 668 670 706 680 57 RADIOACTIVITY OBJECTIVE To simulate a chain reaction half life and to observe radioactivity THEORY Radioactivity refers to the spontaneous disintegration of atomic nuclei This is regarded as a completely random process usually accompanied by the emission of high energy alpha 1 particles which are stable helium nuclei beta particles which are electrons or gamma O rays which are very high frequency photons PROCEDURE APPARATUS Stopwatch 100 dominoes shoe box with lid 200 pennies a single cloud chamber for demonstration of ionizing radiation and computers with web access 1 Place 200 pennies in a shoe box and place the lid on it Shake the box for several seconds remove the lid and then place the box sideways on the lab table Carefully tip the box until all of the pennies are on the table Remove and count all of the pennies which a head side up Record this number on the data sheet along with the number of pennies remaining in the box Do not place any of the hez sup pennies bag in the box Replace the lid on the shoe box and repeat this process until all none of the pennies are left in the box Use Excel or Graphical Analysis to plot the number of pennies remaining along the yaxis and the number of shakes along the x axis Describe ie shape of the plot Approximately what percent of the pennies remain after shake Based on your answer how many of ie original 200 pennies should remain after 7 shakes Compare this number to the actual number that remained after 7 shakes and determine the percentage error A What does each shake represent in terms of radioactive decay Use the plot to determine how many pennies should have remained after 45 shakes Carefully construct a straight line of dominoes as long as your lab table permits The spacing between dominoes should be about the length of half a domino This distance should be as consistent as possible Push the first domino and have each group member determine the time it takes for the entire line to fall over Determine the average group time Does ie rate at which the dominoes fall increase decrease or remain ie same as the dominoes fall This time set up the dominoes similar to the arrangement shown in the sketch As before the spacing should be about the length of half a domino Push the first domino and have each group member determine the time it takes for all or most of the dominoes to fall over Determine the average group time How does this average time compare with iat of the r dominoes set up in a straight line Does the rate at which the dominoes fall increase decrease or remain ie same as ie dominoes fall Connect to wwwcoloradoeduphvsicsphet and click on Simulations Select Quantum Physics and then scroll toward the bottom of the simulations Choose Nuclear Fission and play each of the tabs One Nucleus Chain Reaction and Nuclear Reactor Be sure to try all options available under each tab Also play the Alpha Decay and Beta Decay simulations again selecting each tab and trying all options available for each one Discuss your group findings Write a short summary of what your group leamed from Q simulation How are the falling dominoes in procedure 6 similar to ie chain reaction which occurs during atomic fission How are they different 58 9 Observe an operating cloud chamber and the different ionizing behavior of alpha and beta particles You can see roughly what to expect at wwwphvsicsenterprisesandrewsedu by selecting PRODUCTS and then choosing the Diffusing cloud chamber Click Watch Product Video and carefully observe the close up paths of the particles near the end of the video Disregard what the narrator says as both alpha and beta rticles are being observed How can you tell which cloud trails are due to alpha particles and which are due to beta particles Discuss this as a group 10 Be sure to include an error analysis and a conclusion 59 PHYS 101 RADIOACTIVITY LAB Today s date Table Member 1 Member 2 Member 3 Names of group members gt Group Average 1 Pennies in the Shoe Box Number of Heads Number Remaining Start 0 200 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8 Trial 9 Trial 10 Trial 11 Trial 12 Trial 13 Trial 14 Trial 15 3 remaining after each shake Remaining pennies predicted after 7 shakes Actual remaining pennies after 7 shakes A 4 Remaining pennies after 45 shakes 5 Dominoes time of fall s 6 Dominoes time of fall s Neatly show all calculations performed and answer questions from the lab on a separate sheet of paper Don t forget to include an error analysis a conclusion and the plot for procedure 2 60
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