If 60 lbs of force must be applied to the valve for it to open, how much upward force must push rod X apply for the valve to open?

It must push 40 lbs of force to open the valve.

Step-by-step explanation:

The momentum at one end of the pivot must be equal to the momentum at the other end. Assuming the 60 lbs of force (F1) is applied at 2 inches from the pivot (d1) and the upward force (F2) is applied at 3 inches from the pivot (d2), then:

F1*d1 = F2*d2

Solving for F2 we get:

F2 = F1*d1/d2

F2 = 60*2/3 = 40 lbs of force

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