Lab6 100 Collisions & Momentum OL

Physics 100 Lab 6 Collisions and Momentum Each group should complete and submit a copy of the lab so it is important that all group members agree with the answers to the questions. Group Member (print) _________________________________________________ Group Member (print) _________________________________________________ Group Member (print) _________________________________________________ For this lab, you will need the following items: 2 m track book(s) to raise track lap top smart cart with rubber stopper and bumper dumb cart two 0.5 kg blocks + electrical tape balloons scale ( instructor’s table ) Overview In the past, we have explored the motion of an object when a constant force is applied to it. We have also explored how multiple objects interact with one another. However, in all of these cases, the applied force has remained constant. What happens when the applied force is not constant?!? In this lab, we will investigate what happens to objects when a force is applied to them, but the force is not constant. That is, it changes over time. In particular, we will observe what happens when a large force is applied over a short period of time – this is called a ‘collision’. 1

To understand what happens when an object undergoes a collision, we must introduce some new terms. First, we will introduce the idea of momentum. Momentum p is defined as: p = m v (1) where m is the mass and v is the velocity of the object. Recall Newton’s second law, which states: F net = m a (2) We can rewrite this using our new term momentum. We know that: a =  v /  t (3) So we can rewrite Newton’s second law as: F net = m(  v /  t) = (m  v )/  t (4) We can also rewrite the momentum equation as:  p = m  v , since mass is constant (5) Substituting equation 5 into equation 4, we can see that: F net = (m  v )/  t =  p /  t (6) So, the net force is related to the change in momentum over time. The change in momentum is given by:  p = p f – p i (7) Where p i is the momentum immediately before the collision and p f is the momentum immediately after . Another important concept when dealing with collisions is the idea of an impulse . The impulse combines the applied force and the time interval over which it is applied. Looking at a force vs time graph, you can see that the impulse is defined as the product of the force times the length of time that the force is applied. Impulse = F  t The symbol that we use to represent the impulse is J . Therefore, we can rewrite the equation above as: 2

10. From the force vs time graph, measure the impulse by finding the area under the graph. Expand the time axis to open up the force spike. Highlight the force spike and use the ‘ Display area under active data ’ tool to determine the area ( using the tool without highlighting the force spike yields erroneous results ). 11. Use the statistics tool to determine the maximum force and record all data in table I. 12. Determine v i and v f from the velocity graph using the ‘ Coordinates ’ tool and then calculate p i and p f . Be careful in determining the initial and final velocities of the collision. For your data to be comparable, starting position of the cart should be the same in each run . 13. Repeat this experiment 3 times to make sure your results are reproducible. Make sure that each time you release the cart from exactly the same spot so your data will be comparable. Data table I mass of the cart ______________________________ # v i [m/s] v f [m/s] p i [kgm/s] p f [kgm/s ]  p [kgm/s ] J [Ns] ( area under curve )  p & J % diff [%] F max [N] 1 2 3 QUESTION 1-1: From your measurements, you should have two different methods of determining the change in momentum for the cart ( from the velocity vs time and force vs time graphs ). Do they agree? Why or why not? Explain how you calculated the change in momentum. 4

14. Repeat the experiment with a 0.5 kg block placed on top of the cart. It is helpful to tape the block to the cart to keep it from bouncing around during the collision. Data table II mass of the cart + block ____________________ # v i [m/s] v f [m/s] p i [kgm/s] p f [kgm/s ]  p [kgm/s ] J [Ns] ( area under curve )  p & J % diff [%] F max [N] 1 2 3 QUESTION 1-2: From your measurements, you should have two different methods of determining the change in momentum for the cart. Do they agree? Why or why not? How do your results in data table II compare to your results in data table I? 15. Replace the hard surface with a soft surface by wedging a balloon between the end of the track and the wall. Pull back the track just enough to accommodate the balloon and gently hold the balloon in place during impact. Repeat your experiment with the 0.5 kg block still in place on the cart, but replace the cart’s rubber stopper with the cart bumper ( failure to use the bumper will yield erroneous results ). Enter your results in the tables below: 5

Investigation 2: Conservation of Momentum Momentum in an isolated system will always be conserved. That is: p f = p i Where p i is the total momentum of the system just before the collision and p f is the total momentum of the system just after the collision. Activity 2-1 – Inelastic Collisions 1. Place the track on the table and use a cart to check for level. If the cart moves, adjust by adding paper under the low end of the track. The cart should not move if the track is level. 2. Place the dumb cart ( cart 2 ) about half way down the track and orient it so that it will stick via velcro to the smart cart ( cart 1 ) when they collide. 3. Measure the mass of each of the carts and record your data in table IV. 4. Push cart 1 slowly so that it will collide and stick to cart 2. Record a velocity vs time graph. 5. Repeat this process until you get a good collision where both carts move stuck together afterward. 6. Determine the momentums of carts 1 and 2 just before the collision using the magnitude of the velocity found from your graph ( don’t use negative velocities ). 7. Determine the momentum of ( cart 1 + cart 2 ) just after the collision using the velocity found from your graph. 8. Repeat your experiment 3 times to make sure your results are reproducible ( not necessarily the same because the velocities you give cart 1 will not be exactly the same ) and record your data in table IV below. 7

Data table IV Cart 1 ( smart cart ) mass ________________________ Cart 2 ( dumb cart ) mass ________________________ Cart 2 initial velocity ( v 2_i ) _____________________ Cart 2 initial momentum ( p 2_i ) ___________________ # v 1_i [m/s] p 1_i [kgm/s] p system_i [kgm/s] v system_f [m/s] p system_f [kgm/s] p system_i & p system_f % diff [%] 1 2 3 Q uestion 2-1: How does the total momentum of the system prior to the collision compare to the total momentum of the system after the collision? Does this prove that momentum is conserved? Why or why not? 8

10. Switch the two 0.5 kg blocks from cart 2 to cart 1 and repeat the experiment. Data table VI Cart 1 ( smart cart ) mass ________________________ Cart 2 ( dumb cart ) mass ________________________ Cart 2 initial velocity ( v 2_i ) ______________________ Cart 2 initial momentum ( p 2_i ) ___________________ # v 1_i [m/s] p 1_i [kgm/s] p system_i [kgm/s] v system_f [m/s] p system_f [kgm/s] p system_i & p system_f % diff [%] 1 2 3 QUESTION 2-4: Is the momentum conserved when the first cart is heavier? Explain. 10