Problem about an impulse and a spring

[ubergewehr273]

Homework Statement

The attached image.

Homework Equations

Momentum conservation
Conservation of mechanical energy

The Attempt at a Solution

I tried conserving momentum,
$P=mv_{1} + Mv_{2}$
and then conserving M.E.,
P^2/(2m)=1/2$mv_1{1}^2$ + 1/2$Mv_{2}^2$
After that I can't seem to relate v1 and v2. Also can someone tell me the condition when maximum compression of spring is obtained ?

 

[Orodruin]

Also can someone tell me the condition when maximum compression of spring is obtained ?

What do you think? Can you think of an expression for how fast the compression of the spring is growing?

 

[ubergewehr273]

What do you think? Can you think of an expression for how fast the compression of the spring is growing?

I think when mass m stops moving relative to the ground is when max compression occurs.

 

[Orodruin]

I think when mass m stops moving relative to the ground is when max compression occurs.

This is not correct. Can you give an expression for the spring length as a function of the positions of the masses?

 

[ubergewehr273]

This is not correct. Can you give an expression for the spring length as a function of the positions of the masses?

If mass m moves by x1 wrt mass M and mass M moves by x2 wrt ground then spring compression will be x1-x2.

 

[Orodruin]

Right, so what is the time derivative of that expression? That would be the change in the compression per time. What does this tell you about when the compression is maximal?

 

[ubergewehr273]

Right, so what is the time derivative of that expression? That would be the change in the compression per time. What does this tell you about when the compression is maximal?

So compression is maximum when both masses have equal velocities.

 

[Orodruin]

So compression is maximum when both masses have equal velocities.

Yes. If the upper block moves faster, the string will be compressing, if it is moving slower it will be decompressing. This should give you enough information to solve your original question.