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# Elastic and Inelastic Collisions and Momentum

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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?

https://brainmass.com/physics/conservation-of-momentum/elastic-and-inelastic-collisions-and-momentum-29418

#### Solution Preview

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.

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