Question

The small piston of a hydraulic lift (see figure below) has a cross-sectional area of 2.70 cm², and its large piston has a cross-sectional area of 199 cm². What downward force of magnitude F₁ must be applied to the small piston for the lift to raise a load whose weight is F_g = 14.0 kN?

Answer 1

This question is without the image required but I think I get what we are asked to find. The pressure applied on the small piston is going to be the same that pushes the large piston up. So, to life a load that exerts 14 kN downward force, we need to atleast supply the larger piston with the same force upwards.

It is clear that is the pressure on the small and the large piston respectively. Pressure, as we know, is force per unit area. So, if the pressure on both pistons has to be the same, then,

Which is an ingenius bit of physics as we don't actually have to apply 14 kN of force, we can just make sure the pressure is same by reducing the area. So, the by applying a smaller force on the smaller piston, we can get the same pressure as a larger force on a larger piston.