Elastic potential energy of two blocks of mass

[TrippingBilly]

Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them. A cord initially holding the blocks together is burned; after this, the block of mass 3M moves to the right with a speed of 1.50 m/s.
(a) What is the speed of the block of mass M?
(b) Find the original elastic potential energy in the spring if M = 0.350 kg.

I already have the answer to a, which is obviously 4.5m/s. But, I am clueless as to part b. Please help!

 

[Hootenanny]

What factors determine the potential energy stored in a spring and how do they relate to each other?

 

[TrippingBilly]

It depends on how much is compresses or stretches, but that isn't known and as far as I know can't be calculated. It also depends on the stiffness of the spring but that isn't given either.

 

[Hootenanny]

It depends on how much is compresses or stretches, but that isn't known and as far as I know can't be calculated.

Okay, sorry a little misleading perhaps. What quantities must be conserved here?

 

[TrippingBilly]

Momentum is conserved, and kinetic energy is conserved, so that means that potential energy must be conserved too. and change in kinetic energy = - change in potential energy..

 

[Hootenanny]

Momentum is conserved, and kinetic energy is conserved, so that means that potential energy must be conserved too.

Energy is conserved, it can however, be transformed from one form to another (i.e. from potential to kinetic).

 

[TrippingBilly]

I think my problem was only calculating the kinetic energy of the smaller mass, because I thought if i calculated it for the system they would offset each other but they dont. So, KE=(.5)(.35)(.45^2) - (.5)(.35)(3)(1.5^2) = 2.3625 so potential energy is the opposite of that?

 

[Hootenanny]

I think my problem was only calculating the kinetic energy of the smaller mass, because I thought if i calculated it for the system they would offset each other but they dont. So, KE=(.5)(.35)(.45^2) - (.5)(.35)(3)(1.5^2) = 2.3625 so potential energy is the opposite of that?

Note that kinetic energy is not a vector quantity, it is scalar. You should therefore add the individual kinetic energies to obtain the potential.