Tonya crashes into Nancy while they are practicing their figure skating routines

Question

Tonya crashes into Nancy while they are practicing their figure skating routines. Tonya's mass

is 60 kg and Nancy's mass is 50 kg. Just before the collision occurs, Tonya's velocity is 5 m/s

and Nancy's velocity is 6 m/s in the opposite direction. During the collision, Tonya exerts an

average force of 1000 N against Nancy.

a. How big is the average force Nancy exerts against Tonya during the collision?

b. If this is the only horizontal force acting on each skater during the collision, what average

horizontal acceleration does each skater experience during the collision?

c. If the collision is perfectly inelastic, how fast and in what direction will Tonya and Nancy

be moving immediately after the collision?

answers:

a. 1000 N in the opposite direction of the force

Tonya exerts on Nancy.

b. Tonya will accelerate 16.67 m/s2 in the direc-

tion of the 1000 N force that Nancy exerts

on her. Nancy will accelerate 20 m/s2 in the

opposite direction.

c. 0 m/s

PLEASE PROVIDE WORKOUT STEPS

Explanation / Answer

Part A)

This is just a concept question

Newton's Third Law says That for Every Action there is and Equal and Opposite Reaction. So if Nancy exerts 1000 N on Tonya, then Tonya exerts the same force on Nancy, but in the opposite direction. Thus, the answer is 1000 N in the opposite direction

Part B)

Apply F = ma

1000 = 60(a)

a = 16.7 m/s^2 for Tonya

1000 = 50(a)

a = 20 m/s^2 for Nancy

Part C)

Apply conservation of momentum

mv + mv = (m + m)(v)

(60)(5) + (50)(-6) = 110(v)

v = 0 m/s

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