Maximum Compression of a Spring in a Collision?

[planck42]

Homework Statement

An object with mass m is being held on a spring in equilibrium position with spring constant k. This system(both the object and the spring) is moving in one direction with a velocity v. The system then collides perfectly inelastically with a wall. What is the maximum compression of the spring?

Homework Equations

F=-kx
Conservation of Momentum(?)
Newton's Third Law of Motion

The Attempt at a Solution

By Newton's Third Law, the force the wall exerts on the system is equivalent in magnitude to the force the system pushes on the wall. However, the force appears incalculable. Newton's Second Law cannot really be used here because it concerns net force on an object. Therefore, it appears that the only way out is to calculate the impulse the object is experiencing and then to take the time derivative of that impulse. This does not seem to accomplish anything either, since the impulse is mv, and when one takes the time derivative of that, it comes out to be ma, which doesn't help my cause one bit. I feel at an impasse with this problem. Help would be much appreciated.

 

[Coto]

Perhaps we can use some physical intuition to find a relevant equation.

Perfectly inelastic generally means the two objects "stick" together and for most situations means that you can't rely on conservation of energy. However, in this case you could argue that the energy is completely converted into potential energy of the spring and hence we could try using conservation of energy.

With this tool at your hands, the solution is simple.

 

[planck42]

Perhaps we can use some physical intuition to find a relevant equation.

Perfectly inelastic generally means the two objects "stick" together and for most situations means that you can't rely on conservation of energy. However, in this case you could argue that the energy is completely converted into potential energy of the spring and hence we could try using conservation of energy.

With this tool at your hands, the solution is simple.

Ah! I never thought of it that way. So what you're saying is that mv²=kx² since the 1/2's cancel.

 

[Coto]

Correct. All you need to do is isolate for x then.