A hydraulic jack is used to lift a load of weight 4000 N. The load-bearing cylinder has a radius of 4 cm, and the other piston has a radius of 1 cm. What force must be exerted on the smaller piston to support the load?

Question

Quizplus · Accepted Answer

The pressure in the liquid is the same throughout the two cylinders because they are connected. Therefore, the force exerted on the load-bearing piston is equal to the force exerted on the smaller piston. Using the formula F1/A1 = F2/A2, where F1 is the force on the load-bearing piston (4000 N), A1 is the area of the load-bearing piston (πr1^2 = π(0.04m)^2 = 0.00502 m^2), F2 is the force on the smaller piston, and A2 is the area of the smaller piston (πr2^2 = π(0.01m)^2 = 0.000314 m^2), we can solve for F2. 
F2 = F1 * (A2/A1) = 4000 N * (0.000314 m^2 / 0.00502 m^2) ≈ 250 N. 
Therefore, the force that must be exerted on the smaller piston to support the load is 250 N.

A Hydraulic Jack Is Used to Lift a Load of Weight