Jumping box with a spring and mass inside

[Zeor137]

Homework Statement

Inside a mass M box, over a horizontal floor, there are a massless spring of elastic constant k, fixed to a body of mass m. That body is trapped to a wire in the bottom of the box. After the wire breaks the box will jump with which deformation b of the spring?

Homework Equations

F=m.g
F=k.b

The Attempt at a Solution

I know the answer is that below but i just can't think how would I get to it.
b > (M + 2m)g/k.

 

[NascentOxygen]

Hi Zeor137. I think what happens is that in the situation shown, the spring is stretched. When the wire is cut, the mass m accelerates upwards until the spring becomes compressed by almost as much as it had been stretched (less an allowance for the weight of m).

I haven't worked it out, so I can't be certain that that's the right way to view it.

 

[berkeman]

Homework Statement

Inside a mass M box, over a horizontal floor, there are a massless spring of elastic constant k, fixed to a body of mass m. That body is trapped to a wire in the bottom of the box. After the wire breaks the box will jump with which deformation b of the spring?

Homework Equations

F=m.g
F=k.b

The Attempt at a Solution

I know the answer is that below but i just can't think how would I get to it.
b > (M + 2m)g/k.

Welcome to the PF. Please use NO's hint to help you work this problem. We do not allow posts here where you do not show your work toward a solution.