A 5 kg ball collides without friction with an unknown ball at rest. The 5 kg bal

Question

A 5 kg ball collides without friction with an unknown ball at rest. The 5 kg ball was moving at +7 m/s. After the collision, the 5 kg ball has a velocity of - 1 m/s and the unknown ball has a velocity of +1 m/s.

a) What is the momentum of the 5kg ball before the collision? (magnitude and direction)

b) What is the momentum of the other ball before the collision? (magnitude and direction)

c) What is the momentum of the system that is made of the two balls? (magnitude and direction)

d) What is the momentum of the 5kg ball after the collision? (magnitude and direction)

e) What is the mass of the unknown ball?

Explanation / Answer

Let 'm' be the velocity of the unknown ball

Applying conservation of momentum,

(5*7) + (m*0) = (5*(-1)) + (m*1)

=> 35 + 0 = -5 + m

=> m = 40 kg

a) momentum of the 5kg ball before the collision = (5*7) = 35 kgm/s (+ve x-direction)

b) momentum of the other ball before the collision= 0, since it is at rest

c) momentum of the system that is made of the two balls = 35kgm/s + 0 kgm/s = 35 kgm/s

d) momentum of the 5kg ball after the collision = (5*(-1) = -5 kgm/s

Therefore, magnitude = 5 kgm/s and direction = -ve x-direction

e) mass of the unknown ball = 40 kg

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