# Pascal's law - Hydraulic lift

Problem statement:

A hydraulic lift such as the one shown in the figure below is used to lift cars of up to 3500 kg of mass. The platform of the lift has a mass of 500 kg. The smaller cylinder has a diameter of d1 = 25 cm. If the maximum force that the operator can apply on this cylinder is F1 = 100 N, find the diameter of the larger cylinder (g = 10 m/s2). Knowledge is free, but servers are not. Please consider supporting us by disabling your ad blocker on YouPhysics. Thanks!

Solution:

To solve this problem we are going to apply Pascal’s law. Since pressure is transmitted throughout the fluid, the force applied on the left side by the operator is multiplied on the right side.

Pressure on each side of the lift is defined as the force per unit area: According to Pascal’s law, both pressures must be equal. Solving for the largest cylinder we have: On the other hand, the base area of a cylinder is given by: Now, expressing both areas as a function of their diameter:  