# Maximum separation between blocks on spring

1. Feb 3, 2015

### henry3369

1. The problem statement, all variables and given/known data
Two blocks, each of mass m, are connected on a frictionless horizontal table by a spring of force constant k and equilibrium length L.

Find the maximum and minimum separation between the two blocks in terms of their maximum speed, vmax, relative to the table. (The two blocks always move in opposite directions as they oscillate back and forth about a fixed position.)

2. Relevant equations
Conservation of energy

3. The attempt at a solution
Ki + Ui = Kf + Uf
Ki = Uf
(1/2)mvmax2 = (1/2)kx2
Solve for x and the (1/2) cancel.
So:
x = sqrt(mvmax/k)
This gives the amount the string has stretched, so the distance between the blocks would be x + L which would result in:
Max Seperation = sqrt(mvmax/k) + L.
When I type in the solution I get a message that his is incorrect because the maximum separation does not depend on vmax.

2. Feb 3, 2015

### BvU

Re-check the step (1/2)mvmax2 = (1/2)kx2, So: x = sqrt(mvmax/k)

For example with a dimension check.

And: what exactly is vmax if there are two blocks ? Is the centre of the spring fixed to the table ? Don't you have two half springs that way ?

3. Feb 3, 2015

### haruspex

In addition to BvU's comments, there are two blocks to store KE but only one spring to store PE.