PHYSICS LAB DUE 30TH

One-Dimensional Collisions - 7 Data and Work Sheets - Print or bring it on an electronic device One-Dimensional Collisions - Physics 1201A 2022-2023 Please circle the appropriate values Course 1101A 1201A 1401A 1501A Lab Section 002 003 004 005 006 007 008 009 010 013 014 Lab Subsection A B C D Name First: Last: Student # Lab Partner First: Last: Lab Station # Date Demonstrator Disclaimer: Please note that some but not all questions in this lab writeup will be graded. PART I: INVESTIGATIONS OF ELASTIC AND INELASTIC COLLISIONS EXPERIMENT 1: PRELIMINARY ADJUSTMENTS OF THE TRACK, CARTS AND THE MOTION SENSORS Figure 5: Linear track with collision carts. Linear Track The experiments in this lab utilize a smooth linear metal track.

One-Dimensional Collisions - 8 Levelling the Track Center a bubble level on the track at the 60 cm mark. Use the adjustable levelling feet on the linear track (see Figure 5) to center the air bubble in the bubble level. Turn the bubble level 90 degrees to level the track in the perpendicular direction to travel. When the track is level a cart centered at the 60 cm mark should remain stationary. Collision Carts This lab uses two carts with low-friction ball bearing wheels that allow the carts to roll down the track with minimal resistance caused by friction. One end of each cart is labeled ‘ elastic ’ and is used when performing elastic collision experiments. Magnets are mounted underneath the ‘ elastic ’ ends of the carts in order to facilitate elastic collisions. The other end of the cart is not labeled but can be identified from the mounted velcro tabs, which are used to facilitate inelastic collisions. Each cart is labeled either A or B. Cart B contains a spring-loaded plunger held in place by a ‘plunger lock’. The plunger is used to facilitate the ‘explosion’ in Experiment 4. Check that you have one of each type of cart as in Figure 5 . Figure 6: Connecting Motion Sensor A to port A on the PowerLink hub. Motion Sensors Each experiment requires a measurement of the velocity of the carts before and after a collision. For this pur- pose you will use motion sensors mounted to the ends of the linear track as in Figure 7. The motion sensors emit pulses of ultrasound that reflect off ends of the carts and return to the motion sensors where they are detected and used to measure the position of the carts as a function of time. The position vs time information is sent to the com- puter where it is recorded and converted to velocity vs time data. The motion sensors have a switch on top with ‘ person ’ or ‘ cart ’ selections. Each motion sensor will produce smoother data in either one or the other mode, you should adjust your own sensors for best results. The motion sensors are labeled A, B or C, as shown in Figure 6. The ports on the PowerLink hub are also la- beled A, B or C. Ensure that each motion sensor is connected to the correct port on the PowerLink hub. The collision carts should be placed in each experiment such that they are closest to their matching motion sensor at the beginning of the experiment. In each experiment the motion sensors will begin collecting data when the velocity of one of the carts goes above v = 0.200 m/s. This helps to ensure good quality data with less noise in each experiment. If you see a message indicating that the initial conditions was not reached, try taking data again.

One-Dimensional Collisions - 10 EXPERIMENT 1(b): HOW TO TAKE MEASUREMENTS Open ”1D Collisions.cap”. Different pages will be available in this file. You can toggle among the pages by clicking on the heading names. The first page by default shows the experiment’s outline. Click on the page video ”Instruction 1” to learn how to use the PASCO Capstone graph interface and how to take measurements from a graph. Click the on the video to have it started. You can re-click on the video to pause the video as well. During the course of this video, the initial and final velocities of Cart A, from the data on the graph will be measured. Record the values given in the video below in Table 1. Table 1: Velocities measured in the instructional video Data Run Results Run #1 Initial Velocity = Final Velocity = EXPERIMENT 1(c): ELASTIC COLLISIONS Figure 8: An elastic collision between two carts. Showing (a) before the collision: cart A has initial velocity v iA , and cart B is at rest, v iB = 0; (b) after the collision: cart A has final velocity v fA , and cart B has final velocity v fB . 0 297 M/s 0 077 m/s

One-Dimensional Collisions - 11 OBSERVATION: ELASTIC COLLISION BETWEEN CARTS WITH EQUAL MASS APPARATUS Linear track, two motion sensors, two collision carts, computer with PASCO Cap- stone software. METHOD (1) Watch the collision videos in the page heading ”Collisions Video” - A Simple Experiment. Click I to start a video. (2) Make a prediction as to which video best represents an elastic collision between two carts of equal mass where one cart is initially at rest. Circle your prediction below. Prediction: (A) (B) (C) Note: you will not lose marks if your prediction is wrong, but you will if you don’t make a predic- tion! (3) With the track satisfactorily levelled, place both collision carts on the track so that the sides of the carts labelled ‘ elastic ’ are facing each other. With one cart stationary, give the other cart a gentle push so that it rolls towards the other at constant velocity. Watch how the velocities of each cart change after they collide. Was your prediction correct? (Yes) (No) (4) Now, roll one cart slowly, and the other at least twice as fast, towards each other so that they collide. Observe again how the velocities of the carts change after they collide. Question: Carts of equal mass collide in an elastic collision, where cart A has an initial mo- mentum p A and cart B has an initial momentum p B . What would you expect the final momenta of cart A and cart B to be? Cart A will have a final momentum that is equal to the initial momentum of cart B because [Pf = EPi . This means that PfB = PiA -

One-Dimensional Collisions - 13 Table 2: Experiment 2: Elastic collision measurements for two carts with different masses Trial v iA (m/s) v iB (m/s) p i (kg m/s) K i (J) v fA (m/s) v fB (m/s) p f (kg m/s) K f (J) % Diff p i & p f % Diff K i & K f 1 2 3 Do not delete your last data run for this activity. You will need these graphs to answer a post-lab question at the end of this manual. The last two columns in Table 2 show the percentage difference between the initial and final values of momenta and kinetic energy. CALCULATIONS Sample Calculation: linear momentum before and after the elastic collision Select one of the trials from Table 2 and provide a sample calculation for the initial and final momenta values ( p iA , p fA and p fB ) of the collision carts. Record the trial number. Use SI units. Trial #: p iA p fA p fB Total initial momentum of the two carts p i Total final momentum of the two carts p f M = 0 9964 E = Emu MB = 0 4983 p : MVA + MVB 0 4656 0 0 0 4639 0 1080 0 2038 0 4780 0 4413 0 0776 5 0 % 32 7 % 0 3364 0 0 0 . 3352 0 0564 0 1239 0 3813 0 3135 0 0439 6 7 % 25 0 % 0 3262 0 0 0 3250 0 0530 0 2679 0 5691 0 5505 0 1164 51 5 % 74 9 % 2 = MAVix = (0 9965)(0 3364) = 0 3352226 kym/s = MAVfA 30 9965) (0 1239) = 0 12346635 kgm/ = MB VfB = 10 4983)(0 3813) = 0 28358253 kgm/s = MAViA + MBViB = (0 9965kq)(0 3364 m/s) = 0 3352726 kgm/s = MAUfA + MBVfB = 10 9965kg)(0 1239 m/s) + 10 4983ky)(0 3813 m/s) = 0 31346814 kym/

One-Dimensional Collisions - 14 For the trial you have selected, compare the initial and final total momentum of the carts using the percent difference test. % difference test = p f - p i ( p i + p f ) / 2 ⇥ 100 < 10% What is your conclusion about the total linear momentum of the two carts? Sample Calculation: kinetic energy before and after the elastic collision Provide a sample calculation for the initial kinetic energy K iA and the final kinetic energies K fA and K fB of the collision carts. Use the data from the same trial used in the previous sample calculation. K iA K fA K fB Total initial kinetic energy of the two carts K i Total final kinetic energy of the of the two carts, K f For the trial you have selected, compare the initial and final total kinetic energies of the carts. % difference between K i and K f = K f - K i ( K i + K f ) / 2 ⇥ 100 < 10% What can you conclude about the total kinetic energy of the two carts? 0 44/25372 0 46392384 x 100 0 46392384 + 0 44125372 = 5 0 % The total linear momentum of cart A and cart B should have been conserved because this collision was supposed to be elactic , but perfectly elastic collisions are nearly impossible doe to experimental and human errow this could be because of the energy turning into heat dre to friction . = t m + Vix = 510 9964)(0 3364)" = 0 0563787835 = jMAVfA = t(0 9964)(0 1239) 2 = 0 0076479725 = EMBV + B = +(0 4983)(0 3813) = 0 036223841 j = 0 056378783 J = KfA + KfB = 0 007647972 + 0 036223841 0 043871813 J 0 10800 147 0 077619246 % difference between Ki and Kf = 1 kf - Ki x100 = 10 043871814 0 05637876 X 100 = 24 95 % 10 043871814 + 0 056378783)/2 The percent difference of initial Kinetic energy and Final Kinetic energy was much above 10 % which could have been due to human error , instrument reading error , or experimental error . Since this collision was elastic , the Kinetic energy should have been conserved from initial to final

One-Dimensional Collisions - 16 PASCO Capstone will use the velocity data and the mass measurements entered as experimental constants to produce graphs of total momentum vs time and total kinetic energy vs time . From these plots displayed on the computer, measure the total momentum just before the collision p i and just after the collision p f , as well as the total kinetic energy just before the collision K i and just after the collision K f . Take three data runs, and record your results in Table 3. DATA Table 3: Inelastic collision measurements for two carts. Mass of cart A, m A , Mass of cart B, m B Trial v iA (m/s) v iB (m/s) p i (kg m/s) K i (J) v fAB (m/s) p f (kg m/s) K f (J) % Diff p i & p f % Diff K i & K f ( K i - K f )/ K i 1 2 3 CALCULATIONS Linear momentum before and after an inelastic collision: What can you conclude about the total linear momentum of the two carts? Kinetic energy before and after an inelastic collision: What can you conclude about the total kinetic energy of the two carts? 498 29 = 0 4982kg 0 4983 kg 0 5328 0 0 0 2654 0 1327 0 . 3328 0 3316 0 0 552 22 2 % 24 7 % 0 2195 0 4780 0 0 0 2381 0 0569 0 3020 0 3009 0 0454 23 3 % 22 5 % 0 2021 0 6697 0 0 0 . 3336 0 1117 0 3073 0 3062 0 047 8 57 % 8 1 4 % 0 5783 Linear momentum in trial 3 was best conserved out of all the trials We know this because the % difference of final momentum & initial momentum was close to 10 % In trial 3 the % difference of Kinetic energy is 81 4 % which is greater than 10 %. In this case the total Kinetic energy was not conserved

One-Dimensional Collisions - 17 Fractional kinetic energy lost ( K i - K f ) / K i The last column of Table 3 gives the fraction of kinetic energy lost compared to the initial kinetic energy. What happens to the lost energy in this situation? Table 3 shows three inelastic collisions with varying velocities and kinetic energies but for the same cars with constant mass. What can you say about the fraction ( K i - K f ) / K i for the three collisions? PART II: INVESTIGATIONS OF EXPLOSIONS AND IMPULSE IN ONE-DIMENSIONAL COLLISIONS In Experiment 4, you will study the conservation of momentum in an explosion when there are no external forces acting on the system. In Experiment 5, you will take data to verify that the impulse J or the change in momentum during a collision is given by J = p f - p i . EXPERIMENT 4: CONSERVATION OF LINEAR MOMENTUM IN ONE-DIMENSIONAL EXPLOSIONS Figure 10: One-Dimensional Explosion. (a) Before explosion, carts A and B are together at rest. (b) After explosion, carts A and B move in opposite directions. APPARATUS Linear track, two motion sensors, two collision carts, metal bar, computer running PASCO Capstone . The energy might have been lost through friction force (increased because of their combined masses turning into heat or the sound energy coming from the vibrations everytime the two carts brmp into each other According to the fraction (Ki-F) , Kinetic energy lost for the inelastic collision in this experiment t will be the same , although differing in Ke and Velocity .

One-Dimensional Collisions - 19 EXPERIMENT 5: CHANGE OF MOMENTUM AND IMPULSE IN ELASTIC COLLISIONS AND IMPULSE Figure 11: Setup for measuring the impulse and change of momentum in Experiment 5. APPARATUS Linear track, motion sensor, collision cart, force sensor with magnetic bumper, computer running PASCO Capstone , pan balance. Figure 12: Inserting the linear track onto the force sensor bracket. INTRODUCTION In Experiment 5 the change of momentum that an cart undergoes during an elastic collision is measured. The forces that occur during the collision are measured as a function of time and related to the change in momentum experi- enced by the collision cart. METHOD The video ”Instruction 2” explains how to mea- sure the area under the force vs time curve. Use cart A for this experiment. Remove motion sensor B from the linear track. Mount the linear track onto the bracket holding the force sen- sor and magnetic bumper on the right side of the table. The two pins on the bracket slide into slots on the end of the linear track to secure it in place as shown in Figure 12 (note: do not undo the clamp holding the force sensor and bracket to the table). If setup properly, the apparatus should look like that in Figure 11. Click on ”Change of Momentum and Impulse” Page. Important: Press the ‘zero’ button on the top of the force sensor before each data run. Important: PASCO Capstone will use the mass of cart A in it’s calculations. Ensure that you use collision cart A for this experiment. Position the collision cart so it is centered on the 20 cm mark on the track with the elastic end of the cart facing the force sensor. Click the PASCO Capstone record button, , to begin collecting data then push the cart so that it rolls towards the force sensor and magnetic bumper. Push the PASCO Capstone record button again to stop the recording, after the cart bounces back from the magnetic bumper.

One-Dimensional Collisions - 20 You should now have a smooth graph of velocity vs time , momentum vs time and force vs time . If the cart was pushed too hard, the graph of force vs time will have a sharp spike at the centre. In this case, erase the last data run and repeat. Determine the initial velocity v i and momentum p i and the final velocity v f and momentum p f from the PASCO Capstone graphs. Enter the results in Table 5. The area under the force vs time graph is equal to the total impulse J . PASCO Capstone measures the area under the entire force vs time curve and lists it in the graph legend. The default selection for the area under the curve will include the whole curve which includes ‘noise’ that the force sensor picks up when there is no force applied to the sensor. To get a more accurate value for the area under the force vs time curve, click and drag a square over the area that corresponds to the duration over which the collision occurs. Enter the results in Table 5. DATA AND CALCULATIONS Table 5: Velocities of the Collision Cart and Impulse. Mass of cart A, m A Trial Initial Velocity Final Velocity Initial Momentum Final Momentum Change in Momentum Impulse J (kg m/s) % Difference v i (m/s) v f (m/s) p i (kg m/s) p f (kg m/s) D p (kg m/s) (Area under F vs t graph) between | D p | and | J | 1 2 What conclusion can you draw from the results in the last column? 0 4982 0 6680 0 53380 3327976 0 4614 6 4 % 0 265939/6 0 59873676 0 4737 0 40580 23599734 0 . 4788 0 20216956 0 4381669 2 . 15 % % difference between Up and impolse is < 10 %. This proves that 80 = Impulse .

One-Dimensional Collisions - 22 CONCLUSIONS AND DISCUSSION (In this section, summarize the conclusions from Experiments 2 to 5. What physics concepts did you study? Did you get the expected results? If not, why? What are the sources of errors in this lab?) In experiment I we liked the law of conservation of mentru for an elastic collision . We did not get the expected results by ring the difference in % of It and i . We got a % higher than 10 % and un thank it is because of hum or experimental error . Expervant I was all about Kinetic energy and how in an inelastic collision , linear momentum is conserved while EK is not Not expected results but enemy could been lost through heat or sound exemp : Experiment 4 was about 8p = I . In they experiment our momentine was conserved become our % o difference value was less than 10 %. Concluding that Empolic = Pf-pi Experiment 5 was about change in momentum like expriment 4 but there was an elastic collision measured . Our % difference betwe J (impulse) and Op (momentum) was less than 10 %. meaning o Impulse The sources of error in the labres the change in energy whether that be from Kinde energy to heat , or fireho or vibrations through sound Some somes of possible errors could have been human or readmy erron , or just errors like the cart want mrkry .

One-Dimensional Collisions - 23 Final Mark