Ekins P7A Lab 4

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Physics 7A Collisions lab, v. 5.0 p-1of8 LAB 4: COLLISIONS Lab Introduction This lab investigates collisions, both elastic and inelastic. By understanding these different kinds of collisions, you can develop better intuitions, which enables you to solve hard problems and to avoid making some common mistakes involving energy and /or momentum conservation. Equipment Your GSI will show how to use the photogate timers, and the plunger on the launch cart. Experimental Procedure Measuring velocity In the following experiments, we want to know the velocities of the carts both before and after the collisions. We will be using photogates, and a data acquisition program to measure times and calculate speeds. The metal tab on the cart will pass through a single photogate interrupting the light

Physics 7A Collisions lab, v. 5.0 p-20f8 beam. The computer will record the time the beam was interrupted and use that together with the known width of the tab (4 cm) to calculate the average speed of the cart. Note: the photogate doesn't care which way the cart passes through, so we are only finding magnitudes not directions. Also keep in mind this is an approximation (Ax/At) to the instantaneous velocity (dx/dt). NOTE : If you haven't already done so, turn on the computer now. The program you will be using can be started by double clicking on the 7A_Collisions.mbl icon. It is set up to record two times and compute two speeds, one for each photogate. When you click on the START button (or simply hit RETURN) the computer will be ready to collect data (though it only collects it when something passes through the photogates.) You should position the photogates to measure the speeds you are looking for. For example, the figure shown would measure the initial speed of the launch cart and the post collision speed of the second cart. Make sure you pay attention to which cart is passing through which photogate, if you don't it is easy to get mixed up as to which time and speed is which. For example, in the first experiment you will do, the carts will stick together after the collision, that means the tab from cart #2 will pass through photogate #2 followed by the tab from cart #1, i.e. you will have triggered photogate #2 TWICE. A Couple of Suggestions ¢ Make sure the two photogates are set up appropriately to measure the speeds you are looking for and allow enough space for the carts to reach "constant" speeds. E.g. for launch velocity make sure the photogate is not in the region where the cart is accelerating. For the post collision speed, make sure the photogates are after the collision is complete. 4 To launch the cart, set the plunger to its middle (medium) notch. Make sure the compressed plunger is touching the wall. Using a metal bar, hit the plunger release button with a quick, firm vertical stroke. Practice this a few times. With two photogates, you will always be able to compare before and after values for a single collision, but if you want to compare one collision to another, it is useful to try and be consistent in your launching style. 4 Place the carts in the positions you want by picking them up and moving them, if you just slide the carts back along the track, you will trigger the photogates again and get more data that may tend to confuse things. The computer program records data in pairs (time for photogate #1 and time for photogate #2), if you do accidentally trigger one of the photogates, you may have to trigger the other by hand to ready the computer before your next run. Or you can also STOP the data collection and START it again. 1. Without the second cart on the track, launch the first cart several times, letting it pass through BOTH photogates. Record the speeds in your notebook. Are you able to launch the carts reasonably consistently? Is the use of average speed a reasonable approximation in this case? Trial 1: v1=0.05312 v2=0.05256 Yes, we can launch the cart consistently. Because Trial 2: v1=0.05657 v2=0.05691 the speeds are so Trial 3: v1=0.05310 v2=0.05308 consistent, yes it would be reasonable to use an average speed.

Physics 7A Collisions lab, v. 5.0 p-3of8 Inelastic collision In this experiment, the launch cart collides with a stationary 2nd cart sitting near the photogates. By orienting the carts so that their Velcro ends collide, you can make them stick together. The stuck-together carts then pass through the photogates, allowing you to calculate the post-collision velocity, v, Don’t do the experiment until making predictions! 2. (Prediction) Using any technique you'd like, solve for o, in terms of v,. Is v half of vy, or three quarters of v, or what? Both carts have the same mass. That m should cancel out of your answer. Assuming energy is conserved, vf is the square root of half of vO because m2 is 2m1 1/2 m1 vOA2 = 1/2 m2 vir2 m2=2m1 1/2 vON2 = vir2 (1/2)M/2 v0 = vf 4 Making sure the Velcro end of the 2nd cart faces the launch cart, do the experiment. Find v, in terms of v,. Is it (approximately) half of v, three quarters of v;, or what? Data, calculations, and results: V1 =0.737 Vi is approximately half of VO V2 =0.368 V2 =0.49932157 V1

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Physics 7A Collisions lab, v. 5.0 p-4of8 3. Was kinetic energy conserved during the collision? Show your work. No, kinetic energy was not conserved during the collision. KEO =/= KEf KEO: 1/2m (0.737)"2 = 0.2715845 m1 KEf: 1/2 m (0.368)"2 = 0.066612 m2 0.2715845 =/= 0.135424 4. How can you reconcile energy conservation with the results of this experiment? The energy was lost from the cart-cart system in the form of friction and in sticking together via velcro.

Physics 7A Collisions lab, v. 5.0 p-5of8 5. Ifyou didn't use momentum conservation in question 2, use it now to predict o; in terms of v,. Does this prediction agree with the experimental results? p=mv pO = pf mivl = m2v2 mivi =2m1iv2 1/2v1 =v2 This agrees with the experimental results. Momentum was conserved Elastic collision This is just like the previous experiment, except now you will orient the carts so that the magnetic ends face each other. As a result, the carts bounce off each other perfectly, instead of sticking together. 6. Prediction: What will be the post-collision speeds of both carts? Show your reasoning. The post-collision speed will be half of the initial speed. p=mv pO = pf mivl = m2v2 mivl =2m1iv2 1/2v1 =v2

Physics 7A Collisions lab, v. 5.0 p.-60of8 ¢ Now run the experiment. Data, calculations, and results: T1: C1v=0.645 C2v=0.226 0+12mv2=1/2mv*2 +1/2mvi2 vOA2 =v2/2 + 0 (0.645)"2 =/= (0.226)"2 Experimental error: Cart 1 still has some velocity after the collision and does not immediately come to rest. However, this velocity cannot be measured because it comes to rest before reaching the photogate to measure that velocity every trial. (a) Was kinetic energy conserved during the collision (to within experimental error)? No, the kinetic energy is not conserved because there is thermal energy being released and there is friction (b) Was momentum conserved? p=mv pO = pf mivl + m1v2 = m2v2 0.645 =/=0.226 8. From the results of all these experiments, formulate general rules about collisions that specify when momentum is conserved, and when kinetic energy is conserved. Inelastic Collisions: KE is not conserved, but momentum is conserved Ideal Elastic Collisions: KE and momentum are conserved Experimental Elastic Collisions: KE and momentum are not conserved

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Physics 7A Collisions lab, v. 5.0 p-70f8 Different masses In the following experiments, the carts have different masses. 9. Prediction: Suppose you double the mass of the launch cart, but continue to launch it using the same plunger setting as before. Let v, denote the cart’s speed immediately after it launches. Using whatever technique you'd like, calculate the new launch velocity, v,, in terms of the “old” launch velocity, 7, Is v, equal to v,? Half of o)? If you can’t figure it out, take an intuitive guess. Same KE so 1/2m1 v1A2 =m1 v2/2 vf = sqrt(1/2) vO Same momentum m1 vl =m2v2 m1 vl =2m1v2 (172) vi=v2 Likely 1/2 ¢ Test your prediction. The metal bars have the same mass as a cart. So, placing a bar on top of the cart doubles its mass. If the prediction was wrong, try to explain why. Data, calculations, results: v1:0.772 v2 =0.566 v1 v2:0.437 Explanation for why results disagreed with predictions, if they disagreed: The results are close but disagreed slightly likely due to energy lost to friction and air resistance.

Physics 7A Collisions lab, v. 5.0 p-8of8 10. Prediction: If the double-mass launch cart undergoes a Velcro collision with the stationary 2nd cart, what will be the final speed of the two carts after they stick together? Show your work. The 2nd cart has the same mass as it did before. p=mv PO = pf v2=2/3v1 half ¢ Test your prediction, and explain what's going on if your prediction was wrong. Data, calculations, results: v1:0.521 v2:0.343 Prediction is correct v2 = 2/3 v1 11. Now let's think about the case where the double-mass launch cart undergoes a perfectly bouncy collision with the 2nd cart. (a) (Prediction) After the collision, does the launch cart move forward, move backward, or come torest? Answer intuitively, with no calculations, and briefly justify your response. It will come to rest if it is perfectly bouncy because all of the kinetic energy and momentum will be transferred in the bounce, so the first cart will have no kinetic energy or momentum and will come to rest while the second cart will move forward with the total amount of momentum and kinetic energy from the first cart.

Physics 7A Collisions lab, v. 5.0 p-90of8 (b)** Calculate the post-collision speed of the 2nd cart, in terms of v,. (If you lack time to finish the calculation, do the experiment before the lab ends. You can finish the calculation at home.) 1/2m1 viA2 + 1/2 m2 v2A2 = 1/2 m1 v1fA2 + 1/2 m2 v2fA2 1/2 (2m) viA2 + 0 =0 + 1/2 (m) v2fr2 vef = p=p 2mvi =mv2 v2=2v1 # Test your prediction about the post-collision speed of the 2nd cart. Data, calculations, results (continue on back if needed): v0 =0.244 v2 =0.546 About double

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