# Homework Help: Finding the maximum compression of a spring

1. Feb 26, 2015

### kappakeepo

1. The problem statement, all variables and given/known data
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.
2. Relevant equations
It sounds like momentum to me so I guess F=dp/dt will be relevant here.
3. 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?

2. Feb 26, 2015

### 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?

3. Feb 26, 2015

### kappakeepo

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.

4. Feb 26, 2015

### 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?

5. Feb 26, 2015

### kappakeepo

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)

6. Feb 27, 2015

### 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

Last edited: Feb 27, 2015
7. Feb 27, 2015

### kappakeepo

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.

8. Feb 27, 2015

### 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?

9. Feb 27, 2015

### kappakeepo

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.

10. Feb 27, 2015

### 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.