Question

2 kg and 4 kg are held with a compressed spring between them. If the masses are released,. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compress ?

Answer 1

54 J

Explanation:

You start from the fact that the momentum is conserved. At the beginning all is stopped so Q(tot) = 0. later the smaller mass has a momentum of
`Q= m xx v = 2 kg xx 6 m/s = 12 kgm/s`
also the bigger mass will have a momentum of 12 kgm/s but negative (-12 kgm/s) in the other verse, so the sum of the momentum is still zero (12-12=0). Its velocity will be`v= Q/v= (12kgm/s)(4kg)=3 m/s`.

Energy:
`E_(k1) = 1/2 xx m xx v^2= 1/2 xx2 kg xx (6m/s)^2 =36 J`
`E_(k2) = 1/2 xx m xx v^2= 1/2 xx4 kg xx (3m/s)^2 =18 J` the total Kinetic Energy is 36J +18J = 54 J, and (since the energy is conserved) it is also the energy in the spring