# What would happen if a spring was between two moving objects?

1. Oct 11, 2011

### lluke9

Hey people!

So, what would happen? (This is not a school question, I was just wondering!)

Say, a spring is between a totally unmoving wall and a 1 kg object. The spring pushes on the object with 1 Newton of force. The block accelerates at 1 m/s^2.

But... what if the wall WASN'T unmoving... what it it were ANOTHER object with a mass of 2 kg?
Would the spring somehow split the force 2/3 to 1/3? Or split the force evenly among the two blocks, making one accelerate at .5 m/s^2 and the other at .25 m/s^2?
What will it do!?
Can someone explain what would happen and why? I think I can imagine what would happen, but I'm not sure why.

Thanks and hi!

2. Oct 11, 2011

### Staff: Mentor

Welcome to PF!

When a spring pushes on two objects, there is essentially one force, pushing in two different directions. It doesn't matter if the objects are stationary or moving.

3. Oct 13, 2011

### lluke9

So even if the two objects had different masses, the spring would push both with the same force?
Hmm...

Then, will the spring push for a longer time on the object with less mass or more mass?
In other words, which block receives more work?
I'm THINKING it's the one with more mass, because it will accelerate slower and stay on the spring longer.
But when the lighter mass leaves the spring, won't the spring just pop into equilibrium without something to push off of? So that means the one with less mass actually receives more work...

Sorry, but can I get some more help here?

4. Oct 13, 2011

### AlephZero

The spring pushes on both masses for the same amount of time, with equal and opposite forces at each end. It doesn't "pop" into equlibrium. Both masses will leave the spring when it reaches its unstretched length and stops applying any force.

You seem to be assuming both masses are initially at rest, though you don't actually say that. Because all the forces within the system are equal and opposite, the center of mass of the complete system never moves.

So if the masses are $m_1$ and $m_2$, their final velocities will be $-p/m_1$ and $p/m_2$ where $p$ is the momentum of one mass, and the kinetic energies will by $p^2/(2m_1)$ and $p^2/(2m_2)$. So you are right, the lighter mass gets more kinetic energy.

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