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).

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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:

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The magnitude of F2 is the sum of both the weight of the car and the platform, and F1 is the force applied by the operator. Substituting the givens of the problem statement:

Make sure that you include units in your results. In his case we have used the SI unit of length (m).

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