# Does spring continue to stretch?

1. Apr 1, 2015

### Calpalned

1. The problem statement, all variables and given/known data
It was stated that the block separates from the compressed spring when the spring reached its equilibrium length of x=0. Explain why separation doesn't take place before (or after) this point.

I understand how this works, intuitively. What I don't understand is my textbook's answer guide. "Until the x = 0 point, the spring has a positive acceleration and is accelerating the block, and therefore will remain in contact with it. After the x = 0 point, the spring begins to slow down, but (in the absence of friction), the block will continue to move with its maximum speed and will therefore move faster than the spring and will separate from it."

2. Relevant equations
N/A

3. The attempt at a solution
How can the spring begin to slow down after x=0? At x=0, the spring is at its natural uncompressed/unstretched length. If it begins to slow down after x=0, that means that it stretches beyond its original length, but this can't be true.

2. Apr 1, 2015

### rude man

Why not? Think of a spring with the mass m permanently attached. You compress the spring and then let go. Energy must be conserved at any time. So when the spring reaches the relaxed point x=0 all the initial potential energy 1/2 kxinitial2 must be changed to kinetic energy 1/2 mv2. The spring would stretch as far as it was initially compressed ( xmax = -xinitial with xinitial < 0.
I think a better answer is: after the spring is relaxed the force exerted by the spring can only be in the negative direction, but since the mass is not attached this negative force is not exerted on the mass so it stays at the x=0 speed and keeps going at that speed forever.

3. Apr 1, 2015

### Calpalned

Thanks for your explanation, but here's a better way for me to phrase my question. Let's assume a spring has an un-stretched length of five feet. One side is bolted to a wall and the other side touches a block of mass m. I push on the block and thus compress the spring two feet (so now the block is two feet from the wall instead of five feet). When I let go, the block will stop moving at a distance greater than five feet from the wall right? Once the spring stretches back to its original length of five feet, it won't go further right?

4. Apr 1, 2015

### rude man

Why would the block stop at 5 ft? There are no more forces acting on the block at the 5 ft point so Newton says it will go on forever.
The spring will expand beyond the 5 ft point because it has velocity at the 5 ft point. It's a bit difficult to explain the behavior of the massless spring with no mass attached. Think of a very small mass attached to the spring in addition to the loose mass. This mass will start to slow down at the 5 ft point because the spring force on it is now in the negative direction. So the distance between the small mass and the loose mass will start to increase forever.