A hard metal ball with a mass of 1.5 kg rolls across a table and collides elasti

Question

A hard metal ball with a mass of 1.5 kg rolls across a table and collides elastically was a hard wooden ball which has a mass of 0.5 kg. The collision is head on, i.e., one dimensional, and the balls are in contact for 3 ms. Relative to the table, the metal ball has a velocity of +1.2 ms^-1 (I.e., in the same positive x-direction) prior to the collision and the wooden ball is initially stationary. After the collision the metal ball has a velocity of +0.6 ms^-1 relative to the table.
• What is the velocity of the wooden ball relative to the table after the collision (in ms^-1)?
•What is the average force exerted on the metal ball by the wooden ball during the collision (in N)?
Thank you! A hard metal ball with a mass of 1.5 kg rolls across a table and collides elastically was a hard wooden ball which has a mass of 0.5 kg. The collision is head on, i.e., one dimensional, and the balls are in contact for 3 ms. Relative to the table, the metal ball has a velocity of +1.2 ms^-1 (I.e., in the same positive x-direction) prior to the collision and the wooden ball is initially stationary. After the collision the metal ball has a velocity of +0.6 ms^-1 relative to the table.
• What is the velocity of the wooden ball relative to the table after the collision (in ms^-1)?
•What is the average force exerted on the metal ball by the wooden ball during the collision (in N)?
Thank you! A hard metal ball with a mass of 1.5 kg rolls across a table and collides elastically was a hard wooden ball which has a mass of 0.5 kg. The collision is head on, i.e., one dimensional, and the balls are in contact for 3 ms. Relative to the table, the metal ball has a velocity of +1.2 ms^-1 (I.e., in the same positive x-direction) prior to the collision and the wooden ball is initially stationary. After the collision the metal ball has a velocity of +0.6 ms^-1 relative to the table.
• What is the velocity of the wooden ball relative to the table after the collision (in ms^-1)?
•What is the average force exerted on the metal ball by the wooden ball during the collision (in N)?
Thank you!

Explanation / Answer

Let the speed of wooden ball after collision be v m/s

by the conservation of momentum we have

m1u1 + m2u2 = m1v1 + m2v2

1.5*1.2 + 0 = 1.5*0.6 + 0.5v2

v2 = 1.8 m/s

velocity of wooden ball relative to the table = 1.8 m/s

average force = dp/dt

= (0.5*(1.8-0) / 0.003)

= 300 N

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