A billiard ball rolling across a table to the right at 1.4 m/s makes a head-on e

Question

A billiard ball rolling across a table to the right at 1.4 m/s makes a head-on elastic collision with an identical ball. The mass of a billiard ball is 34 g. If the second ball is initially at rest, what is the velocity of the first ball after the collision? If the second ball is initially at rest, what is the velocity of the second ball after the collision? If the second ball is initially moving to the left with a velocity of -0.7 m/s, what is the velocity of the first ball after the collision? If the second ball is initially moving to the left with a velocity of -0.7 m/s, what is the velocity of the second ball after the collision?

Explanation / Answer

a) If the second ball is initially at rest

by conservation of momentum and KE,

0.034*1.4 = 0.034*u1 + 0.034*u2

0.5*0.034*1.4*1.4 = 0.5*0.034*u1*u1 + 0.5*0.034*u2*u2

solving

velocity of first ball = 0 m/s

velocity of second ball = 1.4 m/s to right

b)If the second ball is initially moving to the left with a velocity of -0.7 m/s:-

0.034*1.4 - 0.034*0.7= 0.034*u1 + 0.034*u2

0.5*0.034*1.4*1.4 + 0.5*0.034*0.7*0.7 = 0.5*0.034*u1*u1 + 0.5*0.034*u2*u2

velocity of first ball = 0.7 m/s to left

velocity of second ball = 1.4 m/s to right

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