Physics: Impulse / Momentum Problem Set

Transcription

1 Physics: Impulse / Momentum Problem Set A> Conceptual Questions 1) Explain two ways a heavy truck and a person on a skateboard can have the same momentum. 2) In stopping an object, how does the time of impact effect the magnitude of the force used to stop the object? 3) What is the relationship between an impulse on an object and the change in momentum of that object? 4) For a constant force, if the time the force is applied to an object doubles, the impulse will. 5) From question #4, by how much is the object s momentum changed? 6) In a car crash, what is the advantage of an air bag in terms of impulse/change in momentum? 7) Why is the impulse greater on a falling object that bounces instead of an equally massive object that doesn t bounce? 8) Explain why a tossed egg can be caught with a sagging sheet but not a piece of plywood? 9) A bug and the windshield of a moving car collide. Indicate which of the following statements are TRUE. a. The impact force on the bug and the car are the same magnitude. b. The impulse on the bug and the car are the same magnitude. c. The change in momentum of the bug and the car are the same magnitude. d. The change in velocity of the bug and the car are the same. 1) Not moving; truck really slow skateboard really fast. 2) Small time; big force 3) The impulse is equal to the change in momentum. 4) double 5) double 6) Change in momentum takes place over a longer time period. 7) The bouncing object has two changes in momentum instead of one for the one that doesn t bounce. 8) Change in momentum takes longer therefore a smaller force. 9) a. True b. True c. True d. False B> Problems 1) A compact car, mass = 725 kg, is moving at 100. km/h. a) What is the momentum of the car? b) At what velocity must a larger car, mass = 2175 kg, be traveling in order to have the same momentum? 2) A force of 6.0 N acts on a 3.0 kg object for 10.0 s. a) What is the object's change in momentum? b) What is the new velocity of the object if it started at rest? 3) An kg car moves at 22.0 m/s. Neglecting friction, what breaking force is needed to stop the car in 20.0 s? 4) A net force of N acts on a rocket of mass kg. How long must the force be applied in order to increase the rocket's velocity from 10.0 m/s to m/s? 5) A snow scooter has a mass of 250 kg. A constant force acts upon the scooter for 1.0 minute. The scooter's velocity changes from 6.0 m/s to 28 m/s. a) What change in momentum occurs? b) What is the magnitude of the force acting on the scooter? 6) A car weighing 15,680 N and moving at a speed of 20. m/s is slowed to a stop by a constant force of 640 N. a) What is the initial momentum of the car? b) How long must the breaking force be applied to the car? 7) A constant force of 300. N acts on a kg mass for 68 s. The initial velocity of the mass is 10.0 m/s. The direction of the force and the velocity is the same. What is the final velocity of the mass? 8) A rocket of mass 2.0 x 10 4 kg starting from rest is accelerated by a net force of 1.5 x 10 5 N for 15.0 s. What is the final velocity of the rocket?

2 9) A snowmobile has a mass of 250 kg. A constant force acts for 1.0 minute changing the velocity from 28.0 m/s to 6.0 m/s. What is the magnitude and direction of the force? 1) kg m/s; 9.26 m/s 2) 60 kg m/s; 20. m/s 3) 1210 N 4) 95 s 5) a) 5500 kg m/s (b) 92 N 6) 32,000 kg m/s; 50. s 7) 44 m/s 8) 113 m/s 9) 92 N, backwards C> Conservation of Momentum: 10) A 95 kg fullback, running at 8.2 m/s, collides in midair with a 128 kg defensive tackle moving in the opposite direction. Both players end up with zero speed. (a) What as the fullback s momentum before the collision? (b) What as the change in the fullback s momentum? (c) What was the change in the tackle s momentum? (d) What was the tackle s original momentum? (e) How fast was the tackle moving originally? 11) Marble A, mass 5.0 g, moves at a speed of 20.0 cm/s. It collides with a second marble, B, mass 10.0 g, moving at 10.0 cm/s in the same direction. After the collision, marble A continues with a speed of 8.0 cm/s in the same direction. (a) Calculate the marbles momenta before the collision. (b) Calculate the momentum of marble A after the collision. (c) Calculate the momentum of marble B after the collision. (d) What is the speed of marble B after the collision? 12) A kg puck moving at 48 m/s is caught by a stationary 75 kg goalie. With what speed does the goalie with the puck slide on the ice? 13) A 35.0 g bullet strikes a 5.0 kg stationary wooden block and embeds itself in the block. The block and bullet fly off together at 8.6 m/s. What was the original velocity of the bullet? 14) A 35.0 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 originally at rest, with what velocity is the block moving after the bullet leaves? 15) A 0.50 kg ball traveling at 6.0 m/s collides head on with a 1.00 kg ball moving in the opposite direction at 12.0 m/s. The 0.50 kg ball bounces back with a velocity of 14.0 m/s after the collision. What is the velocity (magnitude & direction) of the 1.00 kg ball after the collision? 16) A green ball (m = 10.0 g) moving with a velocity of 20.0 cm/s catches up to and collides with a red ball (m = 20.0 g) moving along the same line with a velocity of 10.0 cm/s. After the collision, the green ball is still moving in its original direction with a velocity of only 8.0 cm/s. Determine the final velocity of the red ball. 17) A 700. kg car traveling at 20.0 m/s collides with a stationary 1400 kg truck. The two vehicles interlock and travel together. What is the final velocity of the car? 18) A 40.0 kg projectile leaves a kg launcher with a velocity of 800. m/s. What is the recoil velocity of the launcher? 19) Upon launching, a model rocket expels 50.0 g of fuel from its exhaust at an average velocity of 600. m/s. If the rocket moves upward at 7.5 m/s, what is the mass of the rocket? 20) Two campers dock a canoe. One camper (80.0 kg) steps onto the dock moving at 4.0 m/s. The canoe and other camper move backwards at 2.9 m/s. If the second camper s mass is 75.0 kg, what is the mass of the canoe?

3 21) Two students (90.0 kg and 60.0 kg) on roller skates face-to-face push against each other. The 90.0 kg student moves at 5.0 m/s just after their hands lose contact. (a) What is the velocity of the other student? (b) What average force was exerted on each student if they were in contact for s? 10) (a) 779 kg m/s (b) 779 kg m/s (c)+ 779 kg m/s (d) -779 kg m/s (e) -6.1 m/s 11) (a) 100 g cm/s (b) 40 g cm/s (c) 160 g cm/s (d) 16 cm/s 12) m/s 13) 1200 m/s 14) 2.8 m/s 15) 2.0 m/s opposite direction 16) 16 cm/s 17) 6.7 m/s 18) 16 m/s backwards 19) 4.0 kg 20) 35 kg (a) 7.5 m/s backwards (b) 1.5 x 10 5 N D> Elastic & Inelastic Collisions: 22) In an inelastic collision, is/are conserved. 23) In an elastic collision, is/are conserved. 24) A kg marble moving to the right at 22.5 cm/s collides with a kg marble moving to the left at 18.0 cm/s. After the collision, the first marble moves to the left at 18.0 cm/s. (a) What is the final velocity of the second marble after the collision? (b) Is the collision elastic or inelastic? 23) A 0.25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target. a) What is the final velocity of the combined mass? b) What is the decrease in kinetic energy? 22) momentum 23) momentum and kinetic energy 24) (a) 22.5 cm/s to the right (b) elastic 25) (a) 0.43 m/s (b) J MOMENTUM SHORT ANSWER QUESTIONS 1. To bring a supertanker to a stop, its engines are typically cut off about 25 km from port. Why is it so difficult to stop or turn a supertanker? 2. Why is a punch more forceful with a bare fist than with a boxing glove? 3. A boxer tires more readily when he misses his opponent than when he hits him. Why is this so? 4. A fully dressed person is at rest in the middle of a perfectly frictionless iced over pond and must get to shore. How? 5. Why is it so difficult for a fire fighter to hold a hose that ejects large amounts of water at high speed? 6. If you throw a ball horizontally while standing on a pair of roller skates, you roll backwards with a momentum that matches the ball. Will you roll backwards if you go through the motions of throwing the ball and then hold it?

4 MOMENTUM CONCEPT QUESTIONS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The momentum of an object is defined as the object's a. mass times its velocity. b. force times the time interval. c. force times its acceleration. d. mass times it acceleration. e. velocity times the time interval. 2. Which has more momentum, a large truck moving at 30 miles per hour or a small truck moving at 30 miles per hour? a. Both have the same momentum. b. The small truck c. The large truck 3. Compared to a sports car moving at 30 miles per hour, the same sports car moving at miles per hour has a. twice as much momentum. b. four times as much momentum. c. the same momentum. 4. If the momentum of an object changes and its mass remains constant, a. it is accelerating (or decelerating). b. there is a force acting on it. c. its velocity is changing. d. all of the above 5. The momentum change of an object is equal to the a. impulse acting on it. b. velocity change of the object. c. force acting on it. d. force acting on it times its velocity. e. object's mass times the force acting on it. 6. In order to increase the final momentum of a golf ball, we could a. increase the force acting on it. b. follow through when hitting the ball. c. increase the time of contact with the ball. d. swing as hard as possible. e. all of the above 7. The reason padded dashboards are used in cars is that they a. look nice and feel good. b. decrease the impulse in a collision. c. increase the force of impact in a collision. d. decrease the momentum of a collision. e. increase the time of impact in a collision.

5 8. A table tennis ball launcher is fired. Compared to the force on the ball, the force on the launcher is a. larger. b. the same. c. smaller. 9. A table tennis ball launcher is fired. Compared to the impulse on the ball, the impulse on the launcher is a. smaller. b. larger. c. the same. 10. A collision is considered elastic if a. there is no lasting deformation. b. the objects don t stick together. c. the objects that collide don't get warmer. d. after the collision, the objects have the same shape as before the collision. e. all of the above 11. Suppose a girl is standing on a pond where there is no friction between her feet and the ice. In order to get off the ice, she can a. bend over touching the ice in front of her and then bring her feet to her hands. b. walk very slowly on tiptoe. c. get on her hands and knees and crawl off the ice. d. throw something in the direction opposite to the way she wants to go. e. all of the above will work 12. Which of the following has the largest momentum? a. A large truck parked in a parking lot b. A tightrope walker crossing Niagara Falls c. The science building at your school d. A pickup truck traveling down the highway e. A dog running down the street 13. A freight train rolls along a track with considerable momentum. If it were to roll at the same speed but had twice as much mass, its momentum would be a. zero. b. unchanged. c. quadrupled. d. doubled. 14. A cannon recoils from launching a cannonball. The speed of the cannon's recoil is small because the a. impulse on the cannon is less than the impulse on the cannonball. b. cannon has far more mass than the cannonball. c. momentum of the cannon is unchanged. d. force against the cannon is relatively small.

6 15. Suppose a cannon is made of a strong but very light material. Suppose also that the cannonball is more massive than the cannon itself. For such a system a. conservation of momentum would not hold. b. conservation of energy would not hold. c. the target would be a safer place than where the operator is located. d. the force on the cannonball would be greater than the force on the cannon. e. recoil problems would be lessened. 16. Two objects, A and B, have the same size and shape, but A is twice as heavy as B. When they are dropped simultaneously from a tower, they reach the ground at the same time, but A has a higher a. acceleration. b. momentum. c. speed. d. all of the above 17. In order to catch a ball, a baseball player moves his or her hand backward in the direction of the ball's motion. Doing this reduces the force of impact on the player's hand principally because a. the time of impact is decreased. b. the time of impact is increased. c. the velocity of the hand is reduced. d. the momentum of impact is reduced. 18. A car traveling along the highway needs a certain amount of force exerted on it to stop. More stopping force may be required when the car has a. less stopping distance. b. more momentum. c. more mass. d. all of the above 19. A cannon fires a cannonball. The speed of the cannonball will be the same as the speed of the recoiling cannon a. if the mass of the cannonball equals the mass of the cannon. b. because momentum is conserved. c. because velocity is conserved. d. because both velocity and momentum are conserved. 20. When you jump off a step, you usually bend your knees as you reach the ground. By doing this, the time of the impact is about 10 times more what it would be in a stiff-legged landing, and the average force on your body is reduced by a. less than 10 times. b. about 10 times. c. more than 10 times. 21. Recoil is noticeable if you throw a heavy ball while standing on roller skates. If instead you go through the motions of throwing the ball but hold onto it, your net recoil velocity will be a. small but noticeable. b. the same as before. c. zero.

7 22. A moving freight car runs into an identical car at rest on the track. The cars couple together. Compared to the velocity of the first car before the collision, the velocity of the combined cars after the collision is a. zero. b. one half as large. c. the same. d. twice as large. e. More information is needed to say. 23. Two gliders having the same mass and speed move toward each other on an air track and stick together. After the collision, the velocity of the gliders is a. twice the original velocity. b. one half the original velocity. c. zero. d. the same as the original velocity. e. There is not enough information to say. 24. A piece of putty moving with 2 units of momentum strikes and sticks to a heavy bowling ball that is initially at rest. After the putty sticks to the ball, both are set in motion with a combined momentum that is a. less than 2 units. b. 2 units. c. more than 2 units. d. There is not enough information to say. 25. The force that accelerates a rocket into outer space is exerted on the rocket by a. the exhaust gases. b. Earth's gravity. c. atmospheric pressure. d. rocket's wings. 26. If all people, animals, trains and trucks all over the world began to walk or run towards the east, then a. Earth would spin a bit slower. b. Earth's spin would not be affected at all. c. Earth would spin a bit faster. 27. Suppose an astronaut in outer space wishes to toss a ball against a very massive and perfectly elastic concrete wall and catch it as it bounces back. If the ball is as massive as the astronaut, then a. the astronaut's time between catches will decrease as the game progresses. b. the astronaut will never catch the first bounce. c. the astronaut will catch one bounce only. d. none of the above 28. Superman is at rest in space when he throws an asteroid that has more mass than he does. Which moves faster, Superman or the asteroid? a. Superman b. The asteroid c. They both move at the same speed.

8 29. A cannonball shot from a long-barrel cannon travels faster than one shot from a short-barrel cannon because the cannonball receives a greater a. force. b. impulse. c. both A and B d. neither A nor B 30. A small economy car (low mass) and a limousine (high mass) are pushed from rest across a parking lot, equal distances with equal forces. The car that receives the greater impulse is the a. limousine. b. small economy car. c. neither A nor B (same for each). d m/s 31. A ball is moving at 6.0 m/s and has a momentum of 24.0 kg m/s. What is the ball's mass? a. 0.3 kg b. 4.0 kg c kg d kg