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.

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

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.