# Mass Colliding With a Spring (Fixed Speed)

1. Apr 5, 2014

### checkmatechamp

1. The problem statement, all variables and given/known data

A 2.77 kg mass is sliding across a frictional surface. It then encounters a happy little spring, as shown in the figure. By how much will the mass compress the spring? (The mass is moving at 3 meters per second, and the spring constant is equal 50 N/m)

2. Relevant equations

F = ma
F = kx
F*t = m*v (Possibly?)

3. The attempt at a solution

If the mass was accelerating at 3 m/s^2, the problem would be straightforward. (Just use the acceleration to calculate the force exerted by the mass on the spring, and then divide by the spring constant). But since the mass is moving at a constant speed, you can't do that.

If the speed is constant, acceleration is 0, but that would imply that the spring doesn't compress at all once the mass hits it, which obviously makes no logical sense. I don't think the friction plays any real role (presumably, the mass is traveling at 3 m/s at the instant it hits the spring), and they don't give the coefficient of friction anyway.

The only thing I can think of is if the momentum were calculated, and then divided by the amount of time it takes to compress the spring. But the time isn't given either. (Actually, there's a second part to this question where it asks how long it would take for the spring to compress)

2. Apr 5, 2014

### AlephZero

You didn't attach the figure, but from the question I guess you can assume the spring has no mass, and the other end of the spring is fixed. So conservation of momentum isn't relevant here.

What other types of motion have you studied that involve a mass and a spring?

Or if that doesn't help, what other quantities might be conserved, as well as momentum?

Also did you mean a "frictional surface", or is that a typo for a "frictionless surface"?

3. Apr 5, 2014

### checkmatechamp

Yes, the spring has no mass, and the other end is fixed.

I copied and pasted the question, but since he didn't give any coefficient of friction, I'm going to assume he meant frictionless.

The total energy of the system would be conserved. So I tried kx^2 = mv^2, solved for x, and got 0.706 meters (which was the correct answer).

But then I'm not sure what to do for the second part (where I try calculating how long it would take for the spring to compress). I was initially going to use F = kx, solving for F, and then using F*t = m*v to calculate the time it takes to compress the spring, but I tried that, and the program said the answer was wrong.

Then I tried solving for the acceleration (or deceleration, rather), using ma = kx, and then substituting it into the formula x = vit + 0.5at^2, but that didn't work.

Last edited: Apr 6, 2014