a. At a county fair, two children ram each other head-on while riding on the bum

Question

a. At a county fair, two children ram each other head-on while riding on the bumper cars. Jill and her car, traveling left at 2.90 m/s , have a total mass of 350 kg . Jack and his car, traveling to the right at 1.50 m/s , have a total mass of 250 kg .

Assuming the collision to be elastic, determine the speed of Jill and her car after the collision.

Determine the direction of the velocity of Jill and her car after the collision.

Determine the speed of Jack and his car after the collision.

b. How much momentum is acquired by a 77 kg skydiver in free fall in 1.6 s after jumping from the plane?

c. A 0.35 kg piece of putty is dropped from a height of 2.7 m above a flat surface. When it hits the surface, the putty comes to rest in 0.25 s .

What is the magnitude of the average force exerted on the putty by the surface?

Explanation / Answer

a.) In an elastic collision, the velocity of approach is equal to the velocity of separation.

So, if speed of Jill and her car after the collision is V1 towards the right and that of Jack and his car is V2 towards left, then

velocity of approach = velocity of separation

1.5 + 2.9 = V1 + V2

V2 = 4.4 - V1

applying conservation of linear momentum,

350 x - 2.9 + 250 x 1.5 = -250x V2 + 350 x V1

- 640 = -250 ( 4.4 - V1 ) + 350 V1

- 640 = -1100 + 250 V1 + 350

- 640 = 250 V1 -1540 + 350 V1

V1 = 0.766666667 m/s  (speed of Jill and her car towards right)

V2 = 4.4 -V1 = 4.4 -0.76666667 = 3.63333333 m/s (speed of Jack and his car towards left)

b.) velocity after 1.6 seconds , v = gt = 9.81 x 1.6 = 15.696 m/s

Momentum = mass x velocity = 77 x 15.696 = 1208.592 m/s

c.) velocity after falling through a height of 2.7 m , be v

v2 = 2gh

v = [ 2 x 9.81 x 2.7 ]1/2 = 7.278323983 m/s

Average force exerted on putty = mass x average retardation

= mass x change in velocity / time = 0.35 x (0 - 7.278323983) / 0.25 = - 10.18965358 N

negative sign because it is force of retardation which acts opposite to the direction of motion.

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