A 2.0-g particle moving at 6.2 m/s makes a perfectly elastic head-on collision w

Question

A 2.0-g particle moving at 6.2 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object.

(a) Find the speed of each particle after the collision.

(b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g.

(c) Find the final kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b).

In which case does the incident particle lose more kinetic energy?

case (a) case (b)    

Explanation / Answer

I think you have already solved the three parts (a),(b) and (c), because you have already mentioned the answers.

So, I am solving the last part.

Case(a)

Initial kinetic energy = 0.5*2*10^-3*6.2^2 + 0 = 38.44 x 10^-3 J

Final kinetic energy = 0.5*2*10^-3 * 1^2 + 0.5*1*10^-3*2^2 = 3 x 10^-3 J

Loss in kinetic energy = 38.44 x 10^-3 J - 3 x 10^-3 J = 35.44 x 10^-3 J

Case(b)

Initial Kinetic energy = 0.5*2*10^-3*6.2^2 + 0 = 38.44 x 10^-3 J

Final kinetic energy = 0.5*2*10^-3 * 3^2 + 0.5*10*10^-3*4^2 = 9 x 10^-3 + 80 x 10^-3 J = 89 x 10^-3 J

Loss in kinetic energy = 38.44 x 10^-3 J - 89 x 10^-3 J = - 50.56 x 10^-3 J

So, loss in kinetic energy in case(a) is more.

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