# Elastic and Inelastic Collisions and Momentum

For the attached problem set, the answers are included. The solution therefore should provide the work - how were the answers calculated?

7. The linear momentum of a runner in a 100-m dash is 7.5 * 10 kg * m/s. If the runner's speed is 10m/s, what is his mass?

13. A 15.0-g rubber bullet hits a wall with a speed of 150m/s. If the bullet bounces straight back with a speed of 120 m/s, what is the change in momentum of the bullet?

15. If a 0.50-kg ball is dropped from a height of 10 m, what is the momentum of the ball (a) 0.75 s after being released and (b) just before it hits the ground?

21. A loaded tractor-trailer with a total mass of 5000 kg traveling at 3.0 km/h hits a loading dock and comes to a stop in 0.64 s. What is the magnitude of the average force exerted on the truck by the dock?

31. An automobile with a linear momentum of 3.0 * 10 kg * m/s is brought to a stop in 5.0 s. What is the magnitude of the average braking force?

35. A volleyball is traveling toward you. (a) Which action will require a greater force on the volleyball, your catching the ball or your hitting the ball back? Why?

(b) A 0.45-kg volleyball travels with a horizontal velocity of 4.0 m/s over the net. You jump and hit the ball back with a horizontal velocity of 7.0 m/s. If the contact time is 0.040 s, what was the average force on the ball?

39. A 0.35-kg piece of putty is dropped from a height of 2.5 m above a flat surface. When it hits the surface, the putty comes to rest in 0.30 s. What is the average force exerted on the putty by the surface?

41. In a simulated head-on crash test, a car impacts a wall at 25 mi/h (40 km/h) and comes abruptly to rest. A 120-lb passenger dummy (with a mass of 55 kg), with-out a seat belt, is stopped by an air bag, which exerts a force on the dummy of 2400 lb. How long was the dummy in contact with the air bag while coming to a stop?

49. In a pairs figure-skating competition, a 65-kg man and his 45-kg female partner stand facing each other on the skates on the ice. If they push apart and the woman has a velocity of 1.5 m/s eastward, what is the velocity of her partner (Neglect friction.)

51. A 100-g bullet is fired horizontally into a 14.9-kg block of wood resting on a horizontal surface, and the bullet becomes embedded in the block. If the muzzle velocity of the bullet is 250 m/s, what is the speed of the block immediately after the impact? (Neglect surface friction.)

55. A 1200-kg car moving to the right with a speed of 25 m/s collides with a 1500-kg truck and locks bumpers with the truck. Calculate the velocity of the combination after the collision if the truck is initially (a) at rest, (b) moving to the right with a speed of 20 m/s, and (c) moving to the left with a speed of 20 m/s.

57. A 1600-kg (empty) truck rolls with a speed of 2.5 m/s under a loading bin, and a mass of 3500 kg is deposited in the truck. What is the truck's speed immediately after loading?

65. If a rubber ball hits a wall and bounces back with the same speed, is the collision elastic or inelastic? Explain.

67. A ball with a mass of 0.10 kg is traveling with a velocity of 0.50 m/s in the direction + x-direction and collides head on with a 5.0-kg ball that is at rest. Find the velocities of the balls after the collision. Assume that the collision is elastic.

73. A car traveling east and a minivan traveling south collide in a completely inelastic collision at a perpendicular intersection. (a) Right after the collision, will the car and minivan move toward a general direction (1) southeast, (2) north of west, or (3) either due south or due east? Why?

(b) If the initial speed of the 1500-kg car was 90.0 km/h and the initial speed of the 3000-kg minivan was 60.0 km/h, what is the velocity of the vehicles immediately after collision?

75. A fellow student states that the total momentum of a three-particle system (m = 0.25 kg, m = 0.20 kg, and m = 0.33 kg) is initially zero, and he calculates that after an inelastic triple collision, the particles have velocities of 4.0 m/s at 0 degrees, 6.0 m/s at 120 degrees, and 2.5 m/s at 230 degrees, respectively, measured from the +x-direction. Do you agree with his calculations? If not, assuming the first two answers to be correct, what should be the momentum of the third particle so the total momentum is zero?

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#### Solution Preview

7. Answer: 75 kg

Linear momentum = m*v = 750 = m*10 --> m = 750/10 = 75 kg.

13. Answer: 4.05 kg * m/s in direction opposite to initial velocity

u = 150 m/s; v = -120 m/sec (since it is in the opposite directions to initial velocity)

Change in momentum = m*(v-u) = .015*(-120-150)* = -4.05 kg*m/s

Or 4.05 kg*m/s inn direction opposite to initial velocity.

15. Answer: (a) 3.7 kg * m/s down, (b) 7.0 kg * m/s down

a) v = u + g*t = 0 + 9.81*0.75 = 7.3575 m/s

momentum = m*v = o.5*0.73575 = 3.68 kg*m/s down

b) velocity when it hits the ground, v, is obtained by conservation of energy.

mgh = (1/2)m*v^2

v = sqrt(2gh) = sqrt(2*9.81*10) = 14 m/s

mv = 7.0 kg*m/s down

21. Answer: 6.5 * 10 N

m*v = F*t

F = 5000*3000/0.64/3600 = 6,510 N

31. Answer: 6.0 * 10 N

m*v = F*t

F = 3.0*10^4/5 = 6,000 N

35. Answers: (a) hitting it back. When a ball changes its direction, the change in momentum is greater.

2

(b) 1.2 * 10 N in direction opposite to v

o

a) Change in momentum = Force*time

To hit the ball back, we need to send it back with a velocity which is in the negative direction to that of ...

#### Solution Summary

This solution provides calculations for each question.