A mass of 3.81 kg moving at 24 m/s in the x direction collides inelastically wit

Question

A mass of 3.81 kg moving at 24 m/s in the x direction collides inelastically with a mass of 12 kg initially at rest. How much kinetic energy is lost, in Joules, before and after the collision? Note that if you calculated this correctly, the change in kinetic energy should be negative, but I'm asking how much is lost, so the answer here should be positive. In other words, if you lose $10 from your wallet, the difference of total money in your wallet is -$10, but you say you lost $10, not you lost -$10.

Explanation / Answer

as we know in the absence of external force, linear momentum of the system remains conserved which can be shown as -

initial momentum = 3.81*24 + 12*0 = 91.44

if they move together after collision then-

final momentum = [3.81+ 12] v

15.81 v = 91.44

v = 5.78 m/sec

initial kinetic energy = 0.5*3.81*24*24 = 1097.28 Joule

final kinetic energy = 0.5*[3.81+12]*5.782 = 264.09 joule

so loss in kinetic energy = 1097.28 - 264.09

= 833.19 joule

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