Chapter 6: Momentum and Collisions Problems and Questions
Section 6-1 (Read Section 6-1, then answer the following problems and questions.)
1. A compact car has a mass of 725 kg, and is moving at 23.0 m/s. What is its momentum in kgm/s? 16700 kgm/s
2. What is the velocity of a 2200 kg car with the same momentum as the car in the previous problem? 7.6 m/s,
3. Explain why momentum is a relative quantity.
4. Distinguish between inertia and momentum.
5. A 0.145 kg baseball is pitched at 42.0 m/s. The batter hits the ball horizontally back towards the pitcher at 57.0 m/s. What is the change in momentum of the ball? How much impulse does the ball experience?
(be careful: consider the total change in velocity of the ball) -14.4 kgm/s, -14.4 kgm/s
6. If the ball is contact with the bat for 4.50 x 10-4 seconds, what is the average force that acted on the ball? -31900 N
7. A car weighing 15800 N and moving at 22.0 m/s is acted upon by a constant 6500 N frictional force (exerted by the road on the tires) until it is brought to a halt. What is its initial momentum? 35400 kgm/s
8. What is the change in the momentum of the car? How much impulse does the car experience?
9. How long does the braking force act on the car to bring it to a halt? 5.5 seconds
10. How far does the car travel before it stops? (hint: using the work-energy theorem is much easier than using kinematic equations) 60 m
11. Distinguish between impact and impulse.
12. Does impulse equal momentum or does it equal a change in momentum?
13. If you are riding a bicycle at full speed and you apply the brakes, why do you have to push hard on the handlebars?
14. How do airbags and seatbelts reduce the force of impact in a collision?
15. Why would it be more dangerous if automobiles were designed with extremely rigid frames so that they remained completely intact and simply bounced off other objects in a collision?
Section 6-2 (Read Section 6-2, then answer the following problems and questions.)
16. A 35 g bullet moving at 475 m/s strikes a 2.5 kg wooden block. The bullet passes through the block, leaving at 275 m/s. If the block was initially at rest, how fast is it moving when the bullet leaves? +2.8 m/s
17. Jesse and his bumpercar have a combined mass of 215 kg. Tonya and her bumpercar have a combined mass of 195 kg. Jesse is moving at 1.52 m/s and collides head-on with Tonya, who is moving in the opposite direction at 1.29 m/s. Tonya moves backward at 0.34 m/s after the collision. What is Jesse’s velocity after the collision? Hint: be careful with +/- signs! -0.042 m/s
18. A Kootenai man needs to check on his horses on Wildhorse Island. He gets out of his stationary canoe by jumping onto the shore. He has a mass of 74 kg and moves forward at 1.48 m/s. As he jumps off the canoe, it moves backward at 1.27 m/s. What is the mass of the canoe? 86 kg
19. Explain or show why Newton’s third law of motion and the “impulse-momentum theorem” require that the total momentum must be conserved in a collision or similar interaction?
20. A rocket operating in space pushes exhaust gases backwards from the engine nozzle. How does this make the rocket accelerate forward?
21. As a cone falls from a Ponderosa Pine, it accelerates downward and constantly increases its momentum. Why does this not violate the law of conservation of momentum? Explain! Hint: consider the objects that are interacting!
22. Does the amount of force during an impact constant throughout a collision?
23. A bug splatters on the windshield of a fast-moving car. Which of the following pairs are equal: (a) the forces of impact on the bug and car, (b) the impulses on the bug and car, (c) the changes in speed of the bug and car, (d) the changes in momentum of the bug and the car? More than one pair may be equal!
24. A neutron collides with an atom in a particle accelerator. The atom absorbs the neutron, but an alpha-particle is emitted from the atom. The alpha-particle is observed to move in the same direction that the neutron was moving, but at a lower speed (about ¼ as fast). What must be true about the relative masses of the neutron and the alpha particle? An alpha particle is a helium nucleus with 2 protons and 2 neutrons.
Section 6-3 (Read Section 6-3, then answer the following problems and questions.)
25. Distinguish between an elastic collision and a perfectly inelastic collision.
26. While playing billiards, Dakota notices that when the white “cue-ball” collides with the stationary ball “eight-ball,” the cue-ball stops and the eight-ball moves off at the original speed of the cue-ball. Both balls have the same mass, so this makes sense. However, Dakota wonders why both balls don’t move at half the original speed of the cue-ball, still conserving momentum. Explain why this DOES NOT occur (hint: think about another value that must be conserved).
27. While heading to Arlee, Joe notices a fox next to the road. Unfortunately, he doesn’t notice that the car in front of him has slowed down. Joe’s 1875 kg car traveling at 23 m/s rear-ends the 1025 kg car that is moving at 17 m/s. If the cars stick together, what is their combined speed immediately after the collision? +21 m/s
28. Tarzan swings down on his vine and grabs stationary Jane just before she is eaten by a crocodile. Tarzan has a mass of 95 kg, Jane has a mass of 58 kg, and their speed is 3.2 m/s right after Tarzan grabs Jane. What was Tarzan’s speed just before he grabbed Jane? 5.2 m/s
29. A 0.76 kg model airplane moving at 12 m/s explodes into a hundred pieces due to a “technical malfunction.” What is the momentum of the model airplane before the collision? What is the sum of the momenta of all the pieces after the explosion? 9.1 kgm/s, 9.1 kgm/s
30. Consider a perfectly inelastic collision head-on collision between a small car and a large truck traveling at the same speed. Which vehicle has a greater change in kinetic energy as a result of the collision? Explain.