A simple hydraulic lift is made by fitting a piston attached to a handle into a 3.0-cm diameter cylinder. The cylinder is connected to a larger cylinder with a 24-cm diameter. If a 50-kg woman puts all her weight on the handle of the smaller piston, what weight could the other piston lift?

Approximately (assuming that the acceleration due to gravity is .)

Explanation:

Let denote the first piston's contact area with the fluid. Let denote the second piston's contact area with the fluid.

Similarly, let and denote the size of the force on the two pistons. Since the person is placing all her weight on the first piston:

.  

Since both pistons fit into cylinders, the two contact surfaces must be circles. Keep in mind that the area of a square is equal to times its radius, squared:

By Pascal's Law, the pressure on the two pistons should be the same. Pressure is the size of normal force per unit area:

.

For the pressures on the two pistons to match:

.

, , and have all been found. The question is asking for . Rearrange this equation to obtain:

.

Evaluate this expression to obtain the value of , which represents the force on the piston with the larger diameter:

.

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