A 4.5-g object moving to the right at 22 cm/s makes an elastic head-on collision

Question

A 4.5-g object moving to the right at 22 cm/s makes an elastic head-on collision with a 9-g object that is initially at rest.

What is the velocity of the 4.5-g mass after the collision?
Hint: (Apply conservation of energy and conservation of momentum.)


What fraction of the initial kinetic energy was transferred to the 9-g block?

Explanation / Answer

4.5 x 22 = 4.5 v1 + 9 v2 99 = 4.5 v1 + 9 v2 1/2x 4.5 x 22^2 = 0.5x 4.5 x v1^2 + 0.5 x 9 x v2^2 2.25 x v1^2 + 4.5 x v2^2 = 1089 =>2.25 x v1^2 + 4.5 x ((99-4.5v1)/9)^2 = 1089 => 2 v1^2 - 49.5 v1 -540.5 = 0 v1 = 32.95 , -8.20 32 .95 is not possible as increase in net energy is not possible so right solution would be 8.20 to left velocity of 9 g mass would be 15.1 to right so enegry is 0.5 x 9 x 15.1^2=1026.045 gm-cm^2/s^2 initial energy is = 0.5 x 4.5 x 22^2 = 1089 gm-cm^2/s^2 fraction of energy transfered = 0.9421

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