Two pulleys and same masses - velocity?

[riverguardian]

Homework Statement

If two equal masses are suspended as in the following, and they are both initially at rest, after they are released, what is the velocity of the leftmost mass at the instant the separation between the two masses is h ? Assume frictionless pulleys and extensionless strings.

Homework Equations

KE(i) + PE(i) = KE(f) + PE(f)

The Attempt at a Solution

Set x as the height initially. For every extension of the string immediately left, the pulley system pulls the second mass up half the distance, so the left cord will have traveled 2/3h and the right cords will have moved 1/3h, for a total separation of h.

mgx + mgx = mg(x+1/3h) + mg(x-2/3h) + 1/2*m*v1^2 + 1/2*m*v2^2

We don't know what the velocity of each mass is, correct? We also know that each of the tensions a/b/c or T, and there's a gravitational force downwards with magnitude mg.

 

[riverguardian]

The answer, apparently is v = sqrt(8/15gh)

 

[riverguardian]

help?

 

[LawrenceC]

You know what the speed of each is relative to the other. Therefore you only have one unknown in your energy balance. Answer is correct.

 

[riverguardian]

You know what the speed of each is relative to the other. Therefore you only have one unknown in your energy balance. Answer is correct.

How are the speeds related? What do we use to determine their relation?

 

[LawrenceC]

You know how far each has traveled from its starting point...if one mass went twice as far (which you have already determined) in the same amount of time, how must their speeds relate given that the cord does not streach?