Bad news! When Marcel finds the distance L from the previous part, it turns out

Question

Bad news! When Marcel finds the distance L from the previous part, it turns out to be greater than Lend, the distance from the pivot to the end of the seesaw. Hence, even with Jacques at the very end of the seesaw, the twins Gilles and Jean exert more torque than Jacques does. Marcel now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is at height h above the pivot. (Figure 3)

With what force in the rightward direction, Fx, should Marcel push? If your expression would give a negative result (using actual values) that just means the force should be toward the left.

Express your answer in terms of W, Lend, w, L2, L3, and h.

Explanation / Answer

lets assume that each twin has weight=w

The torques should balance. The clockwise torquesare:   wL2 + wL3

The ccw torques are:    WLend   +   F h

So:    WLend  +   F h   = wL2 +wL3

Or:       F = (1/h)( wL2 + wL3   -WLend   )

For this, F is to the left, so it is the negative ofFx. So the final answer is:

    Fx = - (1/h)( wL2 + wL3   -WLend )

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