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# PHYS 101

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Investigations in Physics 101 R J Reimann S H Schroeder TR Watkins F I E 0 TAT E P I E S I I March 2013 Forward Welcome to PH YS1 01 Introduction to Physics The following laboratory investigations are intended to provide handson 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 leaming partners Can you understand the subtle concepts and explain them to each other Such confirmation is vital to the leaming 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 and or 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 0 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 speci c 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 Math 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 HEATING AND COOLING WAVES TRAVELING amp STANDING SOUND RESONANCE ELECTRIC FIELDS BULBS MAGNETISM MIRRORS LENSES MIRRORS amp LENSES SPECTRA RADIOACTIVITY iii 10 13 16 19 22 24 25 27 31 33 36 37 39 42 44 46 48 52 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 re ector 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 Vemier 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 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 the walking motion required to produce the Vshaped position graph Be sure to include such things as direction with respect to the 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 1 l I 1 1l 1 Position Ijrn iili739IihI1lllJiIllIIIjiliiiulllllllllI1iE1iin1 I 39 lime userands my 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 Q person a Get the times right b Get the distances right and c Make a labeled printout of hisher best match Did you have to depart from the group s consensus description in order to match the 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 the 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 the motion detector to the shape when walking away from the detector How does the 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 file 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 1run IlVl UllVIlIl IIuIluanlnquullmuqu vmpcrw grids llilllllllllllIIII4IIlIIIJIIIIIILlIIgtI39iIIlII1ll E1 39l IIme saciiwn41s U 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 printout of hisher best match Did you have to depart from the group s consensus description in order to match the graph What details of the motion did you have to change in order to get a good match with the graph What places on the graph seemed to give the most problems What were you and your group members doing that 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 the graph involving movement Compare the shape of a velocitytime graph when walking toward the motion detector to the shape when walking away from the detector How would you define the word velocity based on the 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 positiontime and Velocitytime graph of this motion should look Make a fullpage labeled sketch of Q graph Be sure to label what the cart is doing at each point on the graphs Position the motion detector at the top of the ramp Set Logger Pro to produce a positiontime graph Click the 3 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 retumed to its starting position A few trials may be needed to get a smooth graph Print out the best resulting graph How does the 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 positiontime graph produced by the cart Print out the best resulting graph How does the 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 Twodimensional 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 5N 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 Ff 0 The headtotail 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 along 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 final position What would happen to the distance measured by the tape measure if the original distances were doubled 2 At the end of the lab each group will tum 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 also include a labeled resultant and a labeled equilibrant 3 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 finds a nice spot and buries his treasure What is the distance from the origin directly to the treasure the resultant What is the direction angle with respect to North for the direct path to the treasure What is the total distance that the pirate hiked How far North or South net NorthSouth distance did the pirate hike from the origin to the treasure How far East or West net East West distance did the pirate hike from the origin to the treasure How do the answers in questions D and E relate to the answer to question A How far and in what direction would the pirate have to travel to return to the origin the e uilibrant Label all distances and directions on the plot NQF1P1U 35Wgt 4 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 xdirection Draw another 80 cm long upwards from the origin to represent a force of 10 N in the ydirection A Use the parallelogram method to determine the magnitude of the resultant force based on these 2 vector components What is the direction of the resultant force measured in degrees away from the xaxis Draw the equilibrant based on the above answers Label the value and angle of all forces on the plot 595 5 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 the 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 6 Replace the nail Double the weight hanging at 90 to 20 N and determine the required equilibrant by trialand error E calculation When the nail is removed the ring should not move Draw a plot this is your third drawing of the resulting forces when equilibrium is achieved Include the force values and angles of all forces including the resultant and the equilibrant 10 ll 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 the 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 E calculation When the nail is removed the ring should not move Draw a plot this is your fourth drawing of the resulting forces when equilibrium is achieved Include the force values and angles of all forces including the 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 the force values and angles of all forces including the resultant and the 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 first 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 mS2 32 ftS2 22 mphSNote that the object s speed does not remain constant but steadily increases until air resistance becomes significant 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 t 2 This relationship gives g 392y Conversely the time t required for an object to fall freely from rest through a particular distance is given by t 12 y g When an object is allowed to slide down a frictionless incline the acceleration of the object is no longer g but can be found using the equation a g sin0 A car with wheels is more complicated than a sliding object because the rotation of the wheels contributes to the total kinetic energy but if the wheels are very light compared to the mass of the car then we can neglect them and model the car as a sliding block PROCEDURE APPARATUS stopwatch 100m measuring tape ruler tennis or hand ball dynamics track and cart rod with horizontal support meter stick masking tape 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 fist 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 tums 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 100m 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 Retum 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 P 9 Place the dynamics track on the horizontal support so the bottom of the track is about 010 m above the table top Measure the angle of the track This should be done very carefully See below diagram for one method Place a dynamics cart at the very top of the track and use masking tape to mark the position on the track exactly 1 m from the front of the cart P Q Di 7 g quotl 391H39il1l Wavf 1 M Release the cart and record the time it takes the front of the cart to reach the masking tape Repeat at least three times to get an average time for this angle Be sure to start the cart at the same position each time and avoid pushing or pulling it during the release You will be calculating the acceleration of the cart the same way you did in the balldrop portion of the lab by timing the time it takes to go a known distance Change the height of the track and again record the time it takes to reach the masking tape and the angle of the incline Repeat this process until you have ve average times at five different angles making sure the angle does not get too large Use Excel to plot the acceleration as a function of sintheta Label each axis and give the plot a meaningful title Include a copy of the plot with your report What is the meaning of the graph Choose a bestfit line for the plot and determine its slope This can be done by clicking and dragging across the straightest portion of the plot The resulting shaded area contains the selected data upon which a linear fit will be calculated Select Linear Fit from the Analyze menu at the top of the screen A box showing the slope yintercept and correlation coefficient of the regression line will be added to the plot Include a copy of the plot with your report What does the slope represent Determine the percentage error A for the slope of the graph in procedure 7 Note The formula for calculating this is found in the Lab Report Format section of this lab manual See page ii If the mass of the cart is increased how would the results of this lab be affected Be specific 10 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 45 Sin 0 Aoverage distance m acceleration Time s ms 7 Slope 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 PROJEC TILES 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 PE 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 would be all kinetic Emmi K E mv2 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 mg h 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 g where x is the horizontal distance traveled and t is the total time in the air Assuming the initial downward vertical velocity of a projectile is zero the total time that it is in the air can be determined by t 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 fires 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 M21ke sure that no other l21b groups are in line with your target Insert the dart into the larger straw of the dart gun and move it a few meters from the target To fire 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 fire It might take more than one try to get the timing down Take tums until each person in the group has fired the dart Does the monkey get hit Was your prediction from step 1 correct 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 ring the dart Does the monkey get hit this time Reset the dart gun and target Aim from an angle above the target Does the monkey get hit this time What generalizations can be made concerning the dart and the monkey What would happen if the monkey did not fall when the dart was red 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 concemed 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 the experimental value Was there a significant difference between the average value for the LSB and the average value for the SSB If so what might account for the difference If a ping pong ball having the 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 impulsemomentum theorem THEORY Impulse J is de ned as the product of the average force Fm acting on an object multiplied by the time At during which that force is applied J F AVE At Momentum p represents the inertia of a body in motion and is equal to the mass of the body times its velocity p mv Both impulse and momentum are vector quantities 3V6 4 m A t impulse delivered to an object equals the change in momentum of that object This is known as the impulsechange in momentum equation F We At m Av According to Newton s second law of motion a Rearranging this equation shows that the 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 forcetime curves plotted on the computer screen The change in 1 momentum can be found using the following equation mAv EmgT where T is the timeof ight for the jump APPARATUS Computer with Vemier 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 Vemier 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 80035 00 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 comer 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 the cause of the secondary rise of force after the landing Fem M 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 timeof ight T while the force plate reads zero See arrow C in the sample graph Compute the change in momentum according to the final equation in the Theory section Repeat 26 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 the launching impulse compare to the landing impulse How does the change in momentum relate to the launching and landing impulses 10 Be sure to include an error analysis and a conclusion l4 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 ml gt ml then ml will accelerate downward while ml accelerates upward at the same rate The application of Newton s second law to each mass leads to a theoretical acceleration given by a ml to ml or from ml to ml it is important that the total mass ml ml be held constant throughout the experiment Since the masses are attached to each other both will undergo the same acceleration in opposite directions This acceleration can be determined experimentally from a g for an object released from rest where h is the l t height dropped and t is the corresponding time measured with a stopwatch i m 2 1 g While mass may be transferred from ml m2 PROCEDURE APPARATUS Stopwatch tall ring stand or table clamp with long rod short rod clamp Atwood pulley string 2 mass 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 ml 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 ml 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 ml so that ml accelerates smoothly downward when released from rest Begin with ml resting on the oor Release ml 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 last equation in the Theory section calculate the acceleration of the system Shift another penny from ml to ml and determine the new acceleration of the system Continue this process one penny atatime until all of the pennies from ml have been shifted to ml Calculate the theoretical accelerations for the various combinations of ml and ml using the Q equation in the Theory section Compare the theoretical accelerations with those experimentally determined for the various combinations of ml and ml Calculate the percentage error A in each case Do you notice any trends Use Excel or Graphical Analysis to plot the mass differences mlml along the x axis and the corresponding accelerations a along the y axis 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 l6 6 Calculate the value of g m1 H12 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 m1 compare to the tension in the string holding mg Upon what physics law or principle is you answer based 10 Be sure to include an error analysis and a conclusion l7 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 gml m2 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 PE g mg h respectively A person can find the launch velocity needed to obtain a given height by combining the two equations The result is 17 2 g h 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 APE 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 impulsechange 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 Alt Again At must be time up or time down for vertical motion A The average speed of a toy can be found using the basic motion equation vave g 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 vave 17 if the toy is undergoing constant acceleration The centripetal force acting on a toy moving in circular 2 motion can be found using F 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 JUMPING TOYS 1 Select a toy from this group and fmd 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 the toy when it is at its highest point of the jump 19 FLYING TOYS 4 Select a toy from this group and nd 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 the toy at any point in its path BOUNCING TOYS 7 Select a toy from this group and find its mass Drop it from a premeasured 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 a the energy lost after the first bounce b the energy lost after the second bounce c the average amount of energy lost between the two bounces d how high would you expect it to bounce on the third rebound Why PENGUIN OR MONSTER SLIDE if available 9 10 ll l2 l3 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 its initial speed at the top of the slide its average speed while on the slide its final speed at the bottom of the slide using energy conservation theoretical speed its final speed at the bottom of the slide using you timing data actual speed the theoretical kinetic energy the actual kinetic energy the percent of energy lost the power required to lift the object croo gt076090 U93 Draw a labeledforce diagram for the 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 JUMPING 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 VV 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 2quot bounce height m 8a Energy lost 1 bounce J b Energy lost 2quot bounce J c Average energy lost J d expected height of 3quot 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 VV 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 defined as its mass M divided by its volume V or D K 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 l width w and height h V l w h For a cylinder of radius r and height h V 7139 rzh For a sphere of radius r V 1 3 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 Doublebeam balance ruler graduated cylinder and 6 unknown objects 1 Start with the silvercolored 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 regularlyshaped 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 silvercolored rectangular block by using immersion in water to find 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 1 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 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 11340 Nickel 8700 Silver 10490 Steel 7800 Tin 7310 Zinc 7100 23 PRESSURE OBJECTIVE To measure the normal force of a car THEORY Pressure is de ned as the force F divided by the unit area A over which the force is applied or P F 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 nonscientific applications PROCEDURE APPARATUS shoe car with owner s manual bathroom scale tire pressure gauge and graph paper NOTE 10 ll 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 both feet to approximate atmospheric pressure 147 psi How are the soles of athletic shoes different than 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 pattems inside the outline of each tire Which part of this pattern 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 Would the calculated weight of the car be changed if one of the tires was flat Why or why not 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 A T At at which the water temperature rises depends on the power P delivered by the heater the mass m of the water and its specific heat c 4190 Jkg K The relationship is given by L At me 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 minutes 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 minutes 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 bestfit linear line to the central region of your data Use the plotting program to determine the slope of the line What is the significance of this line Doubleclick 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 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 13 If possible printout the computerized plot of your cooling data Otherwise sketch it and have your instructor observe the results Record the names of your group members on the back of the plotsketch 14 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 de nition 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 lengths 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 y enough stop watches are not present Determine the relationships between the physical constraints of the system and the pattems 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 both ends were free Draw a diagram of the resulting standing waves for both boundary conditions Would there be any similarities 29 2 How can we use the spring to demonstrate what occurs when one end is fixed 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 xed 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 both 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 i e rates of shaking so that you produce three different patterns with different numbers of nodes and antinodes along the length of your spring 4 Determine the speeds of the waves 5 Can you directly 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 and intensity as distance changes 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 n1s PROCEDURE APPARATUS Stopwatches 100m measuring tape large wooden blocks seamstress tape computer with Vemier 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 aH of your lab group s times Move back into the lab and use the web to determine the current temperature outside Try wwwktvbcom 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 sarnpless 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 Charmel l 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 first 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 standingwave resonances of extraordinary amplitude If the frequency f of the sound and consequently the wavelength are xed 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 carmot 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 1 and frequency f are related to the speed of the wave v by 9 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 LB374 lt quot llt 39 quot x Node N Antinode A N A N A C Lc3912 D LD1 quot gtltZZ quot ZZ quotm gtltZ quot A N A A N A N A PROCEDURE APPARATUS Plastic ruler meter stick transparent container of water more than 4cm 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 comers 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 8 9 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 LA It should be between 15 and 20 cm Repeat for each group member in order to obtain an average length Use that average to calculate the speed of sound v f 4LAave Repeat with the 480 Hz tuning fork 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 soundv f 4LB 3 Repeat with the 480 Hz tuning fork ave 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 ZL Repeat with the 480 Hz tuning fork Cave 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 L p Repeat with the 480 Hz tuning fork Dave 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 the room temperature was lowered 10 If the experiment was repeated in an atmosphere of pure carbon dioxide gas would the results be the same Why or why not 11 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 7 512 Hz LBLA L1LC Average 22 m Speed of sound ms A 480 Hz LBLA LD39LC Average 22 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 ELECTRIC FIELDS OBJECTIVE To explore electric elds THEORY Fields are simply regions of space with values de ned 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 field maps based on the user s selection of source charges Realistic computer games can help us understand how charges behave in electric fields PROCEDURE APPARATUS Computers with web access 1 Connect to wwwphvsicswebereduSchroedersoftwareEField Use Print Screen to make a copy of the each of the eld 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 field vector Click the mouse at various distances and directions around the source charge to map out the vector field Try some that are quite close to the charge A minimum of at least 12 points should provide a good picture of the electric field 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 both charges of the dipole were the 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 field 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 field vectors at various locations on the outside and inside of the circle Do E allow any of the field 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 field vectors inside either circle to touch any of the actual charges How is this patter similar to and how is it different from the pattern in 7 What does this tell you about electric elds Connect to wwwphetcoloradoeduensimulationelectrichockey Launch the Electric Field Hockey software and read the instructions Play the Electric Field Hockey game and complete the first 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 printouts Remember to write your names on each sheet 10 Be sure to include an error analysis and a conclusion 36 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 38 Magnetism Lab OBJECTIVE To explore magnetic elds THEORY Magnetic elds 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 elds are both produced by and act on charged particles magnetic elds are both produced by and act on moving charges The unit of measurement of magnetic eld is the Tesla the earth s magnetic eld is about 000005 Tesla and a refrigerator magnet creates a eld of about 001 Tesla In this lab you will be using bar magnets as the source of the magnetic eld All magnets as far as we know each have two poles North and South IMPORTANT The convention for magnetic eld lines is that they point away from a magnetic North pole and towards a magnetic South pole analogous to how electric eld lines point away from positive charges and towards negative charges As mentioned above magnetic elds are also produced by moving current The direction of the magnetic eld around a currentcarrying wire can be determined by the righthand rule Namely if you point your thumb in the direction of the current your ngers will curl in the direction of the magnetic eld 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 lings from a height of about 10 cm C Continue sprinkling until a distinct pattern emerges The iron lings fall on the plastic and align themselves with the magnetic eld Describe the field What is the most unique characteristic of the field 2 Draw a simpli ed version of the eld pattern that emerged when the iron lings were placed on the bar magnet Be sure to show the shape of the eld and include at least 10 lines 39 Place your compass or Magnaprobe in your magnetic eld in the locations illustrated below Does your compass needle line up with the field lines Draw an arrow into each circle below to show the direction of the north pole of your compass in the eld If 139 0 9 ff EPW H i er i Q U A llraquot39quotquot39quotl 3 rt 39 39 r quot i Pis M N ijr fquoti rquot H J H fr quotH r quotH 0 R 3 R 3 quotaw 3 Look closely at the lings Where around the bar magnet is the magnetic field strength strongest How can you tell the field is the strongest there 4 The north pole of your compass will point towards the foothills What color is the north pole of your compass How would a physicist explain why the north pole of your compass points in this direction 5 Does the magnetic field of a bar magnet look similar to anything you saw in a previous lab What 6 Place the north end of a bar magnet about 4 cm from the south end of another bar magnet as shown below Place a piece of plastic over the two magnets and sprinkle iron filings in the region between the magnets Draw a simplified Version of the field pattem that emerged when the iron lings were placed on the bar magnets in these configurations 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 field lines Add arrows to your picture showing the direction of the magnetic eld lines as determined by your compass Note Only show the eld 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 A 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 eld 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 strength 9 Now make a loop with your wiring and use your compass or Magnaprobe to determine what the eld 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 eld 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 field different than just one loop 41 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 6 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 define 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 F ffr nmage of pin quot39 I F 39LElilI39 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 artificial 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 42 10 ll 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 significance 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 EE 392 139 x1oo Percentage Difference Place the smaller concave mirror on the cork board facing upright like a bowl Describe the reflection 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 up 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 the edge of the mirror What might be the 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 the distance increases up to 20 cm At what distance between the bottom of the mirror and the transparency does the 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 lightemitting 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 the relative brightness from the two differently sized concave mirrors What might account for any observed difference 12 Be sure to include an error analysis and a conclusion 43 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 150W 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 3 30 30 Igt Width w V ltxgt39 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 tablelevel 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 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 44 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 x 2 sin 9 where sin 30 050 Determine n from your measurements Repeat for the 45 angle sin 45 0707 Are the final exit rays parallel to the 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 meterstick optical bench Hold the eyepiece close to one eye Observe a distant object with one eye unaided and the other looking through both lenses of the telescope Estimate how much the final image appears to be magnified by comparing the aided and unaided views Compare your answer with the ratio of the focal length of the objective lens divided by the focal length of the eyepiece Is the final 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 45 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 6 This behavior is common both to at and curved mirrors Straight fences can be constructed by setting the end posts rst 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 define 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 Fquot i image of Din quot39 I t 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 P 30 E13 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 H i called refraction As rays exit the material they bend away from the 1 normal Measurements of such ray bending at water surfaces were made Wjl 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 2 is between 14 and 16 11 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 prism 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 46 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 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 significance 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 Percentage Difference Z x 100 E1 E2 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 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 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 x 2 sin 0 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 the final exit rays parallel to the corresponding original rays Explain why this 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 47 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 closelyspaced 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 pattem 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 1 of the light can be found with the following equation Ad 1x y where d is the very small spacing between adjacent slits in the diffraction grating 39 C y in meters quotC varies with C the color quot v 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 zeroorder maximum coincides with the lamp itself The firstorder constructive interference pattem of the green line of mercury should appear somewhere near the middle of the other meter stick 48 Determine the slit spacing d for your diffraction grating by using the green line of mercury as a standard with a known wavelength A 546 nm Rearranging the equation given in Theory gives 2 2 d546eVx y 3 nm Turn 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 bluegreen 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 the 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 Turn 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 the 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 the element in the 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 the group report Be sure to include an error analysis and a conclusion 49 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 of red nm A Calculated of bluegreen nm A Calculated of violet nm A 4 Unlabeled tube 1 Calculated 2 of line nm A Calculated 2 of line nm A Calculated 2 of line nm A Calculated 2 of line nm A 4 Unlabeled tube 2 Calculated 2 of line nm A Calculated 2 of line nm A Calculated 2 of line nm A Calculated 2 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 50 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 51 RADIOACTIVITY OBJECTIVE To simulate a chain reaction halflife 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 a particles which are stable helium nuclei beta 6 particles which are electrons or gamma 9 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 headside 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 xaxis Describe the shape of the plot Approximately what percent of the pennies remain after Q shake Based on your answer how many of the 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 the rate at which the dominoes fall increase decrease or remain the 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 that of the dominoes set up in a straight line Does the rate at which the dominoes fall increase decrease or remain the same as the dominoes fall Connect to wvvwcoloradoeduphvsicsphet and click on Simulations p pT 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 learned from Q simulation How are the falling dominoes in procedure 6 similar to the chain reaction which occurs during atomic ssion How are they different 52 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 closeup paths of the particles near the end of the video Disregard what the narrator says as both alpha and beta mrticles 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 53 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 54

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