Tutorial Section 6.1 - Vector nature of momentum The goal of this experiment is to demonstrate the vector nature of momentum. Use the photogates to calculate the gtiders' speeds before and after the collision. If the gliders move too quickly they can jump in the track, which we don't account for in our analysis. Photogate A Photogate B Glider D (heavier) Air Track Consider the following experiment conducted by colliding two gliders on a flat air track: glider D is twice as massive as glider C, glider D is initially at rest and glider C initially moves with speed v. 1. Do you expect the momentum of the system of two gliders to be constant? Why or why not? Hint: Review the law of conservation of momentum. What must be true for the momentum of the system to be constant? 2. Remember to only allow the gliders to collide with a hard edge of one glider contacting the soft edge of the other (never two hard edges colliding). Run the experiment described above. Add weights one of the gliders to double its mass (to 400 g). The gliders should collide between the two photogates so that you can measure the initial and final speed of glider C using photogate A and the final speed of glider D using photogate B2. Experimental Initial photogate (No data since D Final photogate Photogate time data time for C initially at rest) time for C for D Calculated Initial momentum Initial momentum Final momentum Final momentum results for C for D C 4. Calculate the change in momentum for the system. Does the momentum of the system change based on your calculations? 5. Is momentum a vector or a scalar? Consider your calculations above. Are the momenta you wrote for gliders C and D vectors or scalars? Tutorial Section 6.2 - Momentum conservation, force, and impulse Use this description to answer the first set of questions. An Before collision After collision experiment is conducted on a frictionless air track in which glider C is launched toward Va V. =0 VN = ? glider D, which is initially at rest. Gate A Gate B Gate A Gate B The air track is level. Ignore air C D C D X resistance. Glider D is free to Air Track Air Track move and glider C rebounds Note: arrows here show direction of velocity only, their lengths do not (moves backwards after the indicate relative speed. collision) in this case. The collision takes place during a time interval At. 1. Draw separate free-body diagrams for each glider and for the system S (both gliders) at an instant during the collision.While the gliders are in contact, how does the net force on glider C compare to the net force on glider D? Discuss both magnitude and direction, and explain how you figured out your answer. Consider the force of glider C on glider D, and the force of glider D on glider C, just as the collision is starting. How do the magnitudes of these two forces compare? Now consider the force of glider C on glider D, and the force of glider D on glider C as glider C is changing direction. How do the magnitudes of these two forces compare to one another? How do the magnitudes of these forces compare to the magnitudes of the forces in the last question (an instant earlier)? Think about your answer to the last question. During the time when the gliders are in contact, does the instant for which you draw the free body diagram matter in order to determine the relative directions and magnitudes of the horizontal forces? Compare, for example, the instant the gliders first touch to the instant in which glider C changes direction. Explain. Consider the small time interval (At) when the gliders are touching. Compare (1) the product of ) (m0). _, the average net force and time for C (I? ) (Ato) to (2) the same product for D (F av net, C cw net. D Discuss both magnitude and direction. Explain. 7. In the last question you calculated F At. Now apply this to Newton's Second Law (F Ap net net At -) for each glider to compare the change in momentum (Ap) of each glider during the collision. Discuss both magnitude and direction. Explain. 8. The momentum of a system containing multiple objects can be defined to be the sum of the momenta of the constituent objects. Use this definition to write an equation for the change in momentum of system S in terms of the change in momentum of glider C and of glider D. 3 Each object in the system.9. Draw and label vectors to represent the initial momentum, the final momentum, and the change in momentum of the gliders and system. glider C: [37 p? A; glider D: p; 5?, a; system: ET, pi A'p' |:lCheckpoint. Please continue working. 10. Which quantity: bfw A17, or none of these is consistent with the direction of the net force, shown in your free-body diagrams for each case? Consider whether there is a net force, and the direction of the net force. 11. Review your answers about Emilt0 and A]; for each glider. What physical quantity is EnetAtO ? How does this physical quantity relate to A17? What is the name of the principle your work demonstrates? 12. Review your answers about IF;l {Mo and A17 for the system 8. Does the physical principle you named in the last question still hold for looking at these choices of systems: 8, glider C, and glider D? 13. a. Write an equation for the change in velocity for glider C. b. Is the equation for the final velocity of glider C the same as the equation for the final speed of glider C? Explain