Question

An object of mass 80 kg moving with velocity 2 ms hit by collides with another object of mass 20 kg moving with velocity 4 ms. Find the loss of energy assuming a perfectly inelastic collision

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Answer 1

We have loss in KE = {m1m2÷2(m1+m2)}(1-e2)(u1-u2)2

Putting m1=20 kg, m2=80 kg, u1=4 m/s, u2=2 m/s, and e=0

Loss in KE = 32 joule

Answer. Loss in energy is 32 joule.

Answer 2

It is not clear whether they are moving in the same direction or opposite direction.  After collision they stick together and move.


1) If the masses are moving in the same direction:

Apply conservation of Linear Momentum

     80 * 2 + 20 * 4 = (80+20) * v
     v = 2.40 m/s

Loss of energy:  1/2 [80*2² + 20 * 4² - 100 * 2.4² ]
                    = 32 J

Suppose they are moving in opposite directions, then,
     80* 2 - 20 * 4 = (80+20) * v
     v = 0.80 m/sec

Loss in KE = 1/2 * [ 80*2² + 20 * 4² - 100 * 0.80² ]
                   = 288 J