College Physics I Lab
College Physics I Lab PHYS 244
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This 15 page Class Notes was uploaded by Sonny Breitenberg on Monday September 28, 2015. The Class Notes belongs to PHYS 244 at George Mason University taught by Staff in Fall. Since its upload, it has received 66 views. For similar materials see /class/215195/phys-244-george-mason-university in Physics 2 at George Mason University.
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Date Created: 09/28/15
Physics 244 Projectile Motion Introduction Previously you studied motion in onedimension by analyzing the vertical motion of a bouncing ball Now you will examine both vertical and horizontal components of motion For Part I of the experiment you will use the World In Motion software to examine twodimensional projectile motion of an object thrown in the air You will investigate the relationship between acceleration velocity and position of the horizontal and vertical components For Part II you will track the motion of a parachute falling and observe the effect of air resistance and its relationship to the terminal velocity of the parachute Materials World In Motion software Excel Reference Giancoli Physics 6th Edition Chapter 3 sections 5 6 7 Theory Part I Theoretically it is known that the motion in various directions is separable ie one can analyze the vertical component separately from the horizontal component of the motion If we throw an object on the surface of the Earth then the downward acceleration should equal acceleration of gravity since it is in free fall We should have no acceleration in the horizontal since gravity acts in the downward direction and thus 2 2 ay g 98ms and ax0ms 1 Since acceleration is the slope of the velocity vs time graph the velocity versus time of the vertical and horizontal motions have different slopes For horizontal velocity the slope of the velocity vs time graph should be 0 ms so we expect a horizontal line For the vertical velocity the graph is a line with a slope of 7 98 ms Now we can write equations for the two different components of projectile motion We know that the vertical velocity equation must have the slope of ay g therefore vy vyo gt 2 Since the horizontal acceleration is zero vx VXO constant 3 For the position vs time graph of vertical motion we get the familiar equation 1 2 y y0vy0t Egt 4 Since the horizontal velocity is constant the equation for the position vs time must be linear since acceleration is zero and thus the squared term drops out The slope of this graph is the horizontal velocity We can then write the equation as x x0 vxot 5 You will use these equations to analyze the video of a projectile in Part I Part II An object with a large surface area and low density behaves differently than objects in free fall because it is subject air resistance For a falling object like a parachute air resistance acts counter to the acceleration of gravity A velocity vs time graph will show increasing velocity over time until the point at which the velocity becomes constant because the downward force of gravity is balanced by the upward air resistance This velocity is referred to the terminal velocity The force of air resistance is proportional to the square of the velocity of the parachute F a v2 6 mr Initially the air resistance is small but as velocity increases it will increase to a point where it equals the acceleration due to gravity At that point the net force on the object is zero and velocity is constant This constant maximum velocity is known as the terminal velocity and is related to the force of air resistance by a constant K that depends on the shape of the object K me mg 7 Procedure Part I Twodimensional motion of a projectile 1 Click on the World in Motion icon on your screen you may need to go to the Start bar and select ProgramsgtW0rld in Motion 2 Once you have opened World in Motion select Video Analysis to open the video file Your instructor will tell you where it is located and which file to select 3 Now step through your video by hitting Step Determine the best starting point at which to begin taking data For example if the object is launched from someone39s hand make sure you don t take data until after it has left the hand Note the frame number and select Min Frame enter the frame number for the starting point Step through the video until you reach an appropriate stopping point note the frame and select Max Frame to mark the end point Depending on the file you are using you may need to establish a scale between physical distance and pixels in the video To do this select Vide0gtNew Scale and follow the instructions given The points you mark should be the ends of a meter stick in your video and the scale is then set to 10 meter After you have completed this check the accuracy of your scale by reading the coordinates of the two ends of the meter stick to be sure that the difference in distance is 10 meter Hit Play to return to the beginning of the motion Place your cursor over the center of mass of the projectile in each frame Mark the center of mass in each frame by clicking the mouse then hit Step to proceed to the next frame Advance the video in this fashion stepping and clicking for a data point until the end of the motion Once you have marked all of the data points click on Save and choose Copy Data to Clipboard Before you leave the World in Motion program estimate the uncertainty in the x and y components of the position of the projectile that you have recorded This estimate should be based on your ability to accurately mark the center of the projectile Assume that the uncertainties in the x and y components are equal Open Excel and Paste the data into the spreadsheet Your spreadsheet should have separate columns for t x1 and y1 You may also have x and y in two additional columns The time in seconds is in the first column then the position data for the projectile are given in x1 y1 and finally the second data set x2 yz The second data set should be deleted In Excel calculate the x and y components of the velocity and acceleration just as you did in the in the Free Fall lab Perform an uncertainty propagation to calculate the uncertainty in the ycomponent of velocity and acceleration using the estimate of the uncertainty in y that you made in step 5 and assuming that there is no uncertainty in the time Perform this calculation for the first value of vy and ay and assume that all values have the same absolute uncertainty This is true because of the assumption that there is no uncertainty in time Include the calculation in your sample calculation Assume that the uncertainty in v and ax has the same absolute value Produce graphs of position vs time velocity vs time and acceleration vs time for both the x and y coordinates horizontal and vertical motion Plot error bars for all position velocity and acceleration points Physics 244 Conservation of Energy Introduction In this lab there are two parts both of which will measure how energy is conserved in a system In Part I you will measure the potential and kinetic energies of a roller coaster rolling down a track using those values to nd the total energy of the roller coaster over time You will use the World In Motion software for your data Part II will involve measuring the velocity and position of a cart on an inclined track in its path up and back down a dynamics track These measurements are taken so that potential and kinetic energies and therefore total energy may be calculated Materials Part I World In Motion software Excel Part II Data Studio Excel dynamics track cart motion sensor see Figure 1 Reference Giancoli Physics 6th Edition Chapter 6 Sections 3 4 6 and 7 Theory Conservation principles play a very important role in physics If the value of a physical quantity is conserved then the value of that quantity stays constant The total energy of a system is the sum of its kinetic energy and potential energy In today39s lab the potential energy is gravitational potential energy given by PE mgy Thus Total Energy Kinetic Energy Gravitational Potential Energy 1 E KE PE constant 2 1 2 E Emv mgy 3 If the total energy is conserved a graph of E vs time should be a horizontal line Gravity is a conservative force so if it is the only force involved we expect the total energy to be conserved For this lab we will assume that the force of friction is negligible Ideally the motion would be measured at the center of mass For Part I this will be possible but for Part II the measurement taken by the motion sensor will be from the front of the cart This is not a problem because the track is straight Theory for Part 11 You will use a coiledspring launcher to launch a dynamics cart at the bottom of an inclined track and the cart will go up the track reverse its motion and come back down If the friction is essentially zero then energy should be conserved and you can analyze the data from the standpoint of energy conservation Figure 1 Experimental Setup showing launcher The motion sensor is mounted on the track so the position it records is the distance from the top of the track The position data are therefore taken along the track which makes the calculation of the velocity of the cart straightforward However it complicates the calculation of the vertical displacement h which is necessary to calculate the potential energy Figure 2 In Figure 2 P is the distance to the cart as measured by the position sensor and Z is the distance the front of the cart has moved up the track You can calculate Z by the equation ZPPo Po P 4 The vertical height of the cart h above the level of P0 is given by h Z sin 9 5 Where 9 is the angle of the tracks incline The reference point P0 is the point where the cart leaves the launcher This will correspond to your reference height ho In the procedural section you will receive more detailed instructions on how to determine values of h from your data The graph of position vs time that you plot will be parabolic The minimum value of the curve corresponds to the maximum height of the cart where potential energy is at a maximum and P P0 is the point of maximum kinetic energy Procedure Part 1 Roller Coaster This measurement will be made from the analysis of a video file of Valleyfair Amusement Parks quotWild Thingquot which used to be one of the five tallest roller coasters in the world Open the World in Motion software and follow your instructor s directions to open file quot10aviquot The program will also load a data file with calibration data so that your measurements will be in meters and the software will know the mass of the coaster and the number of frames per second In order to test conservation of energy you should mark the midpoint of the coaster If you examine the video you will see that the coaster is segmented into six cars and the midpoint is between two segments Mark the midpoint of the coaster on each frame as you did in the projectile motion lab and then save your data with a unique file name When you have marked all the points press the Graphs button on the lower right comer of the screen Answer the questions and request graphs of energy versus time and acceleration versus time Discuss the energy versus time graph Is energy conserved Discuss the acceleration versus time graph Does the acceleration of the coaster approach free fall N E 9399 Part 11 Conservation of Energy in the Laboratory 1 To take data using the setup shown in Figure 1 set up the DataStudio interface with a motion sensor set to take data at 40 Hz and the switch at the top of the motion sensor set to record motion at short distances Hold the track firmly so it will not recoil when the cart is launched 2 Press the Start button and launch the dynamics cart up the track so that it will reverse its direction ofmotion before getting too close to the motion sensor You may need to do this a couple of times for practice If it goes too high the data will not be parabolic and it is necessary to adjust the angle or the compression of the spring in the launcher 3 Press the Stop button a er the cart has bounced off the launcher 4 Make graphs in Data Studio of the velocity and position vs time and inspect the data You want to have a position graph that looks somewhat like Figure 3 which shows the cart bouncing off of the launcher The horizontal line shows the position of the cart when it is sitting on the launcher after it has been sprung Figure 3 On the far le part of the graph the data traces a horizontal line because the cart is at rest on the coiled spring launcher When the cart is launched it moves toward the motion sensor it then reverses its course land moves away from the sensor Remember the motion sensor records itself as position zero so when you move toward it you get closer to zero and as you move away you get larger numbers The minimum value of the curve corresponds to the maximum height of the cart where potential energy is at a maximum and PD is your maximum for kinetic energy The points reached a minimum as indicated by the arrow in Figure 3 At this minimum the vertical height of the cart was at a maximum and it began to reverse its direction back down the ramp Physics 244 Ideal Gas Law and Heat Engine Introduction In this lab you will explore the Ideal Gas Laws In Part I you will observe the proportional relationship between temperature and pressure create a graph from data points and use it to infer the proportionality constant You will also determine a the temperature for absolute zero In Part II you will use a heat engine apparatus to explore the relationship between temperature pressure and volume You will observe the conversion of heat into work and mechanical energy Materials Part I Data Studio temperature sensor pressure sensor gas chamber coffee pot cold waterice paint stirrer Part 11 Data Studio rotary motion sensor pressure sensor heat engine cold waterice bath hot water bath Reference Giancoli Physics 6th Edition Chapter 13 sections l2467910 Chapter 15 sections 125 Theory Part I The ideal gas law relates the pressure P volume V and absolute temperature T in Kelvin of an ideal gas PVnRT 1 where n is the number of moles of gas in the volume and R is the Ideal Gas Constant equal to 831 JmolK We can rewrite Equation 1 as E P TCT 2 V where C nRVis a constant in the case where volume is xed In summary with xed volume we expect P C T 3 We thus expect a linear graph that passes through the origin if the temperature units are Kelvin or absolute temperature That is when the pressure is zero the absolute temperature will be zero The constant C can be determined since we know that that there will be 224 liters of V volume per mole of gas at STP ie n 224 mole Assuming our volume is lled with gas at approximately STP we get C nR V R R 8314Pam3moleK V 224 224 mole 00224m3mole 371PaK 4 In the lab you will use a xed volume of gas vary its temperature and record the pressure You will then plot P versus T where T is in Celsius units and extrapolate the straight line t to nd where it intersects the xaxis ie where the pressure is zero to determine the point at which the absolute temperature should be zero This point in Celsius should equal absolute zero Absolute zero is the temperature at which the pressure of the gas extrapolates to zero meaning that the molecules have the lowest kinetic energy possible Part II The heat engine cycle is a repeatable closed thermodynamic cycle that is often represented by a pressurevolume diagram shown in Figure 1 below V Figure 1 Heat Engine Cycle The cycle has four transitions In the horizontal segments 61 a andb c the volume changes due to changes in temperature while pressure remains constant During the other two steps a b and c d the volume changes due to changes in the external pressure on the piston while the temperature is essentially constant The heat engine used in this experiment uses a gas con ned to a cylinder with a moveable piston plus a xed chamber connected to the cylinder by exible tubing When the heat engine undergoes a transition at a constant pressure P and the volume changes by the amount AV as in the horizontal segments above the work done by the engine is W P AV That is work is done when the volume changes If the volume increases the work done by the gas in the heat engine is positive and when the volume decreases the work done by the engine is negative To see how the engine will work review the picture above and the equipment at your table shown in Figure 2 below You will start by placing the chamber connected to the cylinder into a cold water bath This will lower the temperature of the gas while the pressure will remain constant because the piston will adjust and allow the volume to contract decrease The system will then be at Point a in Figure 1 Next you will place a mass on the piston pushing the piston down causing the volume to decrease and the pressure to increase This will bring the system to Point b With the mass still on the cylinder you will place the chamber in a hot water bath causing the volume of gas to expand raising the piston This will cause the temperature to increased while the pressure will be constant This brings you to Point c Finally you will remove the mass from the piston This will decrease the pressure and allow the volume to expand putting the system at Point d To return the system to the beginning of the cycle you will return the chamber to the cold water bath The temperature and volume will both decrease returning us to Point 4 gt7 a We will next examine the work done by the system The change in volume is directly proportional to the change in position Ax as measured by the motion sensor We can measure the net work done over the cycle by measuring the area of the enclosed parallelogram To nd this area we must nd the area under each of the horizontal segments and subtract the area under the lower segment from the area under the upper In essence we add the negative work done when the volume decreases from d gt a transfer from hot to cold bath to the positive work done when volume increases from b gt 0 transfer from cold to hot bath For each transition PAV W and therefore W PIAV1 PZAV2 Because the quantity AV2 in this case is negative we find the net difference between the two work values The work done by raising the mass is also equal to the change in potential energy mgAh where Ah is the distance the piston has moved Figure 2 Procedure Part I Temperature and Pressure 1 Connect the pressure sensor to the chamber The pistonandcylinder unit is not used in this part and should not be connected to the chamber 2 Set up the pressure absolute pressure andtemperature sensors in Data Studio Set the data acquisition frequency tol Hz for both sensors 3 Fill the coffee pot with very cold water and some ice Make sure to leave enough room for the chamber and the temperature sensor 4 Put a paint stirrer in the coffee pot 5 Set up the graph to record changes intemperature and pressure inthe chamber Graph the data With the pressure on the vertical axis andtemperature on the horizontal axis To do this open the Graph Display from the list of quotDisplaysquot Now drag the Temperature Sensor from the quotDataquot list to the xaxis of the graph Do the same thing for the Pressure Sensor and drag it to the yaxis Click on start to start the data collection 6 Turn on the coffee pot You should be continuously collecting data While the water is heating and stirring the water at the same time When 60 C is reached click on stop to stop the data collection and turn off the coffee pot 7 Using the linear fit highlight the best data for fitting Using the equation provided determine the x intercept and estimate its uncertainty The xintercept is absolute zero in degrees Celsius while the slope should equal to g in indicated by Equation 3 8 Compare your experimentally determined x intercept with the accepted value of absolute zero 273 C i the experimental uncertainty Also compare the slope with Equation 4 above Part 11 Heat Engine 1 Set up the heat engine apparatus as shown in Figure 2 Connect the chamber to the pistonandcylinder unit with tubing The pressure sensor should also be connected to these As shown in the gure the pistonandcylinder should be attached to a stand with the rotary motion sensor above it There is a tray attached to the piston A string should be attached to this tray and looped over the large pulley of the rotary motion sensor and then to a hanging 20 g mass This string will cause motion of the piston to rotate the rotary motion sensor while the 20 g mass keeps the string taut Since the 20 g mass is kept in place throughout the cycle as is the mass of the piston itself the energy required to raise and lower it will be positive during part of the cycle and negative during the another part and will thus result in zero net work We need not concern ourselves with the work required to raise the 20 g mass 2 Connect the wires to the Pressure Sensor and the Rotary Motion Sensor to the Interface Doubleclick the Rotary Motion Sensor icon and under measurements select Position m This is the only data needed from this sensor 3 Set up graph of Pressure vs Position Open the Graph Display from the list of Displays Drag the Angular Position sensor from the data list to the xaxis of the graph Do the same thing for the Pressure Sensor and drag it to the yaxis 4 Do the following steps to collect data for this experiment A First put the chamber into the cold bath wait for the piston to sink This moves the system to Point a in Figure 1 Press the Start button in Data Studio to begin taking data B Place an additional 200g mass on top of the piston tray to increase the pressure This moves you to Point b C Leaving the 200 g mass in place move the chamber to the hot bath This moves you to Point c D Remove the 200 g mass to move to Point d E Complete the cycle by returning the chamber to the cold bath to get to Point a Physics 244 Torque Introduction In this lab you will study static equilibrium for a meter stick suspended horizontally Materials meter stick apparatus string force sensors Data Studio masses Reference Giancoli Physics 6th edition Chapter 8 sections 456 Chapter 9 sections 12 Theory When forces act on an extended body torques or rotations about axes on the body can result as well as translational motion from unbalanced forces Static equilibrium occurs when the net force and the net torque are both equal to zero We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components F n22 F1F2F30 1 Torques may be calculated about the axis of your choosing and because a meter stick is our body the length of the lever arm can be conveniently determined without resolving components rnztrlrz130 2 Each torque is specified by the equation 139 F d 3 Normally up is quotquot and down is s quotquot and counterclockwise as quotquot for forces For torques the convention is to de ne clockwise Procedure Static Equilibrium Force Sensors Figure 1 Diagram of Torque Experiment Setup 1 Weigh the meter stick you use Record the mass and estimate the uncertainty 2 Set up the meter stick and force sensors as shown in Figure l The meter stick will be suspended from a beam via the two force sensors These will also be used to determine the upward vertical forces at these positions The force sensors must be attached vertically anywhere that yields equilibrium by string tied tightly around the meter stick 3 Attach three masses to the meter stick using string Neglect the masses of the support strings 4 Attach the force sensor cords to the Interface box as you have done in previous labs 5 For today s lab you do NOT need to graph the force sensors over time instead drag the force icons to the Digits icon in the quotDisplaysquot menu This will give you a digital readout ofthe force sensor data at the given time Create two Digit displays one for each force sensor on the meter stick 6 Next tare each force sensor without weight to establish zero Then hang a known weight on each force sensor to verify that it is reading correctly Ifyou need to increase the precision of the display select the downwardfacing arrow on the icon that says quot314quot and select Increase Precision This will increase the number of signi cant gures 7 Hang the masses on the three remaining strings and balance your system by moving the three weights and watching the Digits displays All forces must be vertical to avoid difficulties so make sure the meterstick is level and be sure the force sensors are pulling straight upward 8 Record the position and mass on the meterstick for each mass 9 Using the following data sheet to record the results calculate the sum of the masses responsible for the positive forces and the sum of those responsible for the negative forces Forces 5 and 6 are the force meters Check to see if the sums are equal within calculated uncertainties Massg Force Force N m Fl X 2 F2 gtlt F3 m3 X g F4 m4mztzrstxck X g 10 Using the zero position x 0 m of the meter stick as the aXis of rotation and counterclockwise torques as positive determine the sum of the torques acting in both directions and record them on the data sheet Check for equality between positive and negative sums within the calculated uncertainties Repeat the calculation with the lever arm located at the aXis point in the middle of the meter stick x 050 m and recalculate torques Check for equality between positive and negative results within calculated uncertainties
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