Finding the maximum compression of a spring

[kappakeepo]

Homework Statement

A block of mass m1 slides along a frictionless table to the right with a speed of v1. A second mass M2 slides in the same direction with a speed of v2 such that it will collide with m1 which is in front of m2. Say that a spring of stiffness k is attached to one of the masses such that it compresses when the two masses finally collide. Find the maximum compression of the spring.

Homework Equations

It sounds like momentum to me so I guess F=dp/dt will be relevant here.

The Attempt at a Solution

Now I think max compression occurs when velocity of mass 1 relative to mass 2 is zero. But that's the only thing I could really figure out. I don't know what to proceed next. Can anyone help me?

 

[Simon Bridge]

What sort of physical laws will be relevant here? "something to do with momentum"? ... what laws do you know about momentum? Are there any other laws you know about that could apply?

Can you describe, qualitatively, what happens during the collision?

 

[kappakeepo]

What sort of physical laws will be relevant here? "something to do with momentum"? ... what laws do you know about momentum? Are there any other laws you know about that could apply?

Can you describe, qualitatively, what happens during the collision?

I'm thinking centre of mass might be relevant here but I don't know how. It's a gut feeling. Also definitely F=-kx during collision.
During the collision, momentum from the left mass is transferred to the right mass. I believe this is an elastic collision.

 

[Jason Healy]

Is there anything else you know about the blocks while they're in motion? Any other properties they have that you could use?

 

[kappakeepo]

Is there anything else you know about the blocks while they're in motion? Any other properties they have that you could use?

Well. There's no horizontal force obviously since a = 0. Since it is in motion, there has to be kinetic energy and momentum (relative to that frame of reference to be exact)

 

[Simon Bridge]

Do you know any laws about the energy?
Center of mass may be a promising approach, especially if you have just done a lot of coursework on center f mass problems - can you describe the motion in the com frame?

@Jason Healy: welcome to PF

 

[kappakeepo]

Do you know any laws about the energy?

@Jason Healy: welcome to PF

Yes but I think my professor wants me to do this question using centre of mass thinking or momentum thinking or both. But I'm not sure using laws of energy is a must here.

 

[Simon Bridge]

Laws of energy are always available - right now you are collecting your ideas.
Center of mass may be a promising approach, especially if you have just done a lot of coursework on center of mass problems - can you describe the motion in the com frame?

 

[kappakeepo]

Laws of energy are always available - right now you are collecting your ideas.
Center of mass may be a promising approach, especially if you have just done a lot of coursework on center of mass problems - can you describe the motion in the com frame?

Well. Since both bodies have no acceleration(no horizontal force), then the centre of mass of both bodies must have a=0. Also V of com is moving right. The collision occurs at the final centre of mass obviously.

 

[Simon Bridge]

While the spring is being compressed - don't the bodies accelerate?
Can you think of a general principle for energy and momentum that may hold for the interaction here?

Describe the motion in the center of mass frame.