Marc is getting bored of marking the midterms and decides to entertain himself w

Question

Marc is getting bored of marking the midterms and decides to entertain himself with two objects and a spring (only a physicist could be entertained with two objects and a spring...). Marc puts the spring between the two objects and forcefully holds the two objects together which compresses the spring. He then lets go and the spring pushes the two objects apart, pushing the objects in opposite directions, free of the spring. The mass of object A is 2.00 times the mass of B. If the total energy stored in the spring was 60 J and has negligible mass what are the kinetic energies of (a) object A and (b) object B, assuming that there was a perfect transfer of potential energy?

Explanation / Answer

Let us suppose M as the mass of B
So, 2M is the mass of A.

Again, conservation of momentum applies,
call V the velocity of B
then V/2 is the velocity of A

Now, com-on the kinetic energy -

KE = ½mv²
total KE of system = 60 = ½(2M)(V/2)² + ½(M)(V)²
(2M)(V/2)² + (M)(V)² = 120
=> 2MV²/4 + MV² = 120
=> MV²(1 + 2/4) = 120
=> MV²(6/4) = 120
=> MV² = 80

(b) Kinetic energy of B = ½MV² = 40.0 J
(a) Kinetic energy of A = 60 - 40 = 20.0 J

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