# What physical conditions would allow for this kind of perpetual seesaw

I'm working with a simulator(Box2D) and need to create these conditions.

I have a perpetual seesaw with two objects on either side. I'd like for the following conditions to be met.

The first object will be on the seesaw and the second object will be dropped from a height. This will launch the first object and vice versa.

1. When their masses are the same, and the first object is dropped from a height, the second object should be launched to the same height.
2. If a heavier object is dropped from a height, the lighter object has to be launched higher
3. If a lighter object is dropped from a height, the heavier object has to be launched lower.

Under what conditions would this work?

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Presumably you know that perpetual motion machines don't exist :-), but for a simulator we'll allow frictionless bearings, a massless lever for the seesaw, etc. In this situation, all you need to do is calculate the kinetic energy of the first dropped object, transfer all that kinetic energy to the other object, and then calculate the height to which the second object will fly. Use the standard equations, e.g. $v = a*t$ , $KE = \frac{m*v^2}{2}$ , $s= v_0*t + \frac{a*t^2}{2}$ , to get the values of interest.