Momentum Problems

(From Merrill Principles and Problems with some changes)

  1. A compact car with a mass of 725 kg is moving at 100 Km/hr.
  2. Find its momentum
  3. What would the velocity of a larger car of mass 2175 kg have to be to have the same momentum as the smaller car?
  4. The brakes exert a 640 N force on a car weighing 15,680 N that is moving at 20 m/s, causing it to stop.
  5. What is the car’s mass?
  6. What is the car’s initial momentum?
  7. What is the change in the car’s momentum?
  8. How long does the braking force take to stop the car?
  9. A 0.06 kg ball is dropped from a height of 4.0 meters above the floor. Ignoring air resistance, find the momentum of the ball just before impact.
  10. The figure below shows the force exerted by a ball that collides with a box at rest versus time.
  11. Find the impulse given to the box by the ball.
  12. If the box has a mass of 24 kg, what velocity did it have after the collision?
  1. A 35 gram bullet moving at 475 m/s strikes a stationary 2.5 kg wooden block and passes through the block, exiting at a speed of 275 m/s. How fast is the block moving after the bullet passes through it?
  2. Two campers dock a canoe, and the camper with an 80 kg mass steps out onto the dock at 4 m/s. With what speed and direction do the canoe (50 kg) and the other camper (70 kg) move?
  3. A colonial gunner sets up his 225 kg cannon at the edge of the flat top of a high tower. It shoots a 4.5 kg cannon ball horizontally that hits the ground 215 meters from the base of the tower. The cannon recoils on frictionless wheels, falling off the back of the tower, landing on the ground.
  4. What is the horizontal distance of the cannon’s landing, measured from the base of the tower?
  5. Why do you not need to know the width of the tower?
  6. A 1325 kg car moving north at 27 m/s collides with a 2165 kg car moving east at 17 m/s, and they stick together. In what direction and with what speed do they move off together afterward?
  7. A stationary life raft of mass 180 kg carries two swimmers of mass 50 kg (on the right) and 80 kg (on the left), who jump off in opposite directions, each with a horizontal speed of 3 m/s. What speed and direction does the raft have afterward?
  8. A car moving at 10 m/s crashes into a barrier and stops in 0.25 meters.
  9. Find the time to stop the car.
  10. If a 20 kg child were to be stopped in the same time as the car, what average force must be exerted?
  11. Approximately what is the mass of an object whose weight equals the force from part “b”? Cold you lift such a mass?
  12. What does your answer to part “c” say about the wisdom of holding an infant on your lap instead of using a separate infant restraint seat?
  13. An animal rescue plane flying due east at 36 m/s drops a bale of hay from an altitude of 60 meters. If the bale of hay weighs 175 N, what is the momentum of the bale the moment it strikes the ground?
  14. A 10 kg lead brick fall froma height of 2 meters.
  15. Find its momentum as it reaches the ground
  16. What impulse is needed to bring the brick to rest?
  17. The brick falls onto a carpet that is 1 cm thick. Assuming the force stopping it is constant, find the average force on the carpet exerts on the brick.
  18. If the brick falls onto a 5 cm foam rubber pad, what constant force is now needed to bring it to rest?
  19. A 60 kg dancer leaps 0.32 meters high.
  20. With what momentum does the dancer reach the ground?
  21. What impulse is needed to make her stop at the ground?
  22. As the dancer lands, the knees bend, lengthening the stopping time to 0.05 sec. Find the average force exerted on the body.
  23. Compare the average stopping force to the dancer’s weight.
  24. A 50 kg woman, riding on a 10 kg cart is moving east a 5 m/s. She then jumps off the cart and hits the ground a 7 m/s eastward relative to the ground. Calculate the velocity of the cart after she jumps off.
  25. Two students on roller blades stand face-to-face, then push each other away. One student has a mass of 90 kg, the other a mass of 60 kg. Find the ratio of the velocity of the larger student to the velocity of the smaller student after they push off.
  26. A 92 kg fullback, running at 5 m/s attempts to dive across the goal line for a touchdown. Just as he reaches the goal line, he is met head-on in midair by two 75 kg linebackers, on moving at 2 m/s and the other at 4 m/s. If they all become entangled as one mass, with what velocity do they travel? Doe the fullback score?
  27. Ball A, rolling west at 3 m/s has a mass of 1 kg, and stationary ball B has a mass of 2 kg. After colliding with ball B, ball A moves south a 2 m/s. Calculate the momentum and velocity of ball B after the collision.
  28. A 0.05 kg stone moving north at 4 m/s collides with a 4 kg lump of clay moving west a 1 m/s. The stone becomes embedded in the clay. What is the speed and direction of the composite body after the collision?
  29. The nucleus of a hydrogen atom is a single proton of mass 1.67 x 10-27 kg. The mass of the electron which circles the proton at a radius of about 0.51 x 10-10m is 9.1 x 10-31 kg. Find the center of mass of the proton-electron system as measured from the proton.
  30. Using the graph from problem 3, assume that the initial velocity of the object was -20 m/s and find the final velocity.
  31. What force, acting for one millisecond, will change the velocity of a 100 gram baseball from 30 m/s eastward to 40 m/s westward?
  32. A ball of mass 3 kg, moving a 2 m/s eastward, strikes a 1 kg ball moving westward at 4 m/s.
  33. If the balls stick together, what is their combined speed and direction after the collision?
  34. If the balls rebound, with the 3 kg ball moving westward at 1 m/s after the collision, what is the speed and direction of the 1 kg ball after the collision?
  35. One way of measuring the muzzle velocity of a bullet (mass of 50 grams) is to fire it horizontally into a massive wooden block on (mass of 15 kg) on a wheeled cart (mass of 5 kg). After the shot, a stopwatch determines that the combined system moves 8 meters in 0.4 seconds. What was the original velocity of the bullet?
  36. A 100 gram bullet is fired into a ballistic pendulum block of mass 10 kg and the combined mass swings up to a height of 5 cm above the block rest position.
  37. What was the initial speed of the bullet-block combination immediately after penetration?
  38. What was the initial speed of the bullet?
  39. A circus cannon fires a 200 gram banana horizontally at a speed of 70 m/s at a 10 kg monkey hanging from a rope at rest. The monkey catches the banana. To what height does the monkey swing?
  40. A 50 gram bullet is fired into a ballistic pendulum block of mass 10 kg, and exits the block at a speed of 100 m/s, leaving the block to rise to a height of 7 cm. What was the initial speed of the bullet?
  41. A 40 kg cart traveling north at 30 m/s collides inelastically with a 20 kg cart traveling west at 40 m/s. What is their combined speed and velocity after the collision?
  42. Find the center of mass of the earth-moon system as measured from the earth’s center. The center-to-center distance between them is 3.84 x 108 meters. The mass of the earth is 5.98 x 1024 kg, and that of the moon is 7.38 x 1022 kg.
  43. Find the center of mass of the carbon monoxide molecule as measured from the center of the oxygen atom. The mass of the carbon atom is 12 u and the mass of the oxygen atom is 16 u. Their centers are 2 x 10-9 meters apart.
  44. A 6 kg object A moving at 3 m/s east collides with a 6 kg mass object B at rest. After the collision, A moves off in a direction 40 degrees to the left of its original direction and B moves off in a direction 50 degrees to the right of A’s original direction.
  45. Determine the momenta of the both objects after the collision.
  46. Determine the velocity of each object after the collision
  1. A stationary ball with a mass of 0.17kg is struck by an identical ball moving at 4 m/s. After the collision, the second ball moves off at 60 degrees to the left of its original direction, and the stationary ball moves of at 30 degrees to the right of the second ball’s original direction. What is the velocity of each ball after the collision?
  2. A 48.5 kg cart traveling at 4.48 m/s overtakes and collides with a 27.9 kg cart traveling at 2.63 m/s in the same direction. What is the final velocity of the second cart if the first one continues in its original direction at 1.5 m/s?
  3. A 31.2 kg cart traveling at 4.4 m/s has a head-on collision with a 19.4 kg cart traveling at 1.63 m/s in the opposite direction. What is the final velocity of the first cart if the second one rebounds with a speed of 30 m/s?
  4. An astronaut is motionless in outer space,. Upon command, the propulsion unit strapped to his back ejects some gas at a velocity of 14 m/s, and the astronaut recoils with a speed of 0.5 m/s in the opposite direction. After the gas is ejected, the mass of the astronaut is 160 kg. What is the mass of the gas?
  5. Adolf and Ed are wearing harnesses and are hanging from the ceiling by means of ropes attached to them. They are face to face and push off against one another. Adolf has a mass of 110 kg, and Ed has a mass of 73 kg. Following the push, Adolf swings upward to a height of 0.3 meters above his starting point. How high does Ed swing above his starting level?
  6. Batman (mass of 91 kg) jumps straight down from a bridge into a boat (mass of 510 kg). The velocity of the boat is initially 11 m/s. What is the velocity of the boat after Batman lands in it?
  7. A 2.5 gram bullet, traveling a 425 m/s strikes a 0.2 kg wooden block of a ballistic pendulum. How high does the bullet/block combination swing?
  8. A person stands in a stationary canoe and throws a 5.0 kg stone with a velocity of 8 m/s at an angle of 30o above the horizontal. The person and canoe have a combined mass of 105 kg. Ignoring air and water resistance, find the horizontal recoil velocity of the canoe.
  9. A 1.5 kg soccer ball moving at 30 m/s west is kicked so that it moves at 40 m/s east after the kick. The foot is in contact with the ball for 0.2 seconds. How much force did the foot apply to the soccer ball?
  10. A 3 kg cat is dropped from a height of 5 meters onto a trampoline and rebounds to a height of 4 meters. What impulse acted on the cat?

Answers:

  1. 2.04 x 104 kgm/s, 33 km/hr
  2. 1600 kg, 32,000kgm/s, -32,000 kgm/s, 50 sec
  3. 0.53 kgm/s
  4. 1430 Ns, 59.6 m/s
  5. 2.8 m/s
  6. -2.7 m/s, time of fall doesn’t depend on when the cannon leaves the tower.
  7. 4.3 m
  8. 14.7 m/s at 44.2o N of E
  9. 0.5 m/s in the direction the 50 kg kid went.
  10. 0.05 sec, -4000N, 410 kg, No WAY!
  11. 888 kgm/s at 43.6o from the horizontal
  12. 63 kgm/s, 63 Ns, 20,000 N, 4000N
  13. 150 kgm/s, 150 Ns, 3000N, 5 times
  14. 5.0 m/s west
  15. 0.67 times
  16. 0.041 m/s
  17. 3.6 kgm/s, 1.8 m/s at 34o N of W
  18. 0.994 m/s at 63.4o W of N
  19. 2.78 x 10-14 meters
  20. 39.6 m/s
  21. -7000N

22. 0.5 m/s east, 3 m/s east

23. 8020 m/s

24. 99.98 m/s

25. 9.6 cm

26. 334.3 m/s

27. 24 m/s at 33.7o W of N

28. 4.68 x 106 meters

29. 8.57 x 10-10 meters

30. 14 kgm/s & 2.3 m/s, 12 kgm/s & 2.0 m/s

31. 3.5 m/s and 2.0 m/s

32. 7.81 m/s

33. -15.67 m/s

34. 5.7 kg

35. 0.66 m

36. 9.3 m/s

37. 1.41 meters

38. -0.33 meters.

39. -525 N

40. -56.26 Ns