Question

A booster pump on a brake system designed to be used horizontally consists of two cylinders capped by pistons connected by a hose. The cylinders and hose are filled with an incompressible fluid. The system produces a mechanical advantage of three times; that is, the output force is three times as great as the input force. If the cross-sectional area of the input piston is 4.0 in2, how large must the area of the output piston be?

A) 1.0 in²
B) 4.0 in²
C) 9.0 in²
D) 12.0 in²

Answer 1

The size of the output piston's area in a hydraulic system that provides a mechanical advantage of three must be three times larger than the input piston's area. Since the input piston's area is 4.0 in², the output piston's area must be 12.0 in².

Step-by-step explanation:

The question asks us to determine the size of the output piston's area in a hydraulic system that produces a mechanical advantage of three. In hydraulic systems, the force produced is proportional to the area of the pistons, given that the pressure in the system is constant.

Since the system gives a mechanical advantage of three, the area of the output piston must be three times larger than that of the input piston to produce three times the force.

If the cross-sectional area of the input piston is 4.0 in², the output piston's area must be:

Area of output piston = Mechanical advantage × Area of input piston

Area of output piston = 3 × 4.0 in²

Area of output piston = 12.0 in²

Therefore, the correct answer is D) 12.0 in².