In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 48 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 9.0. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

Force that the output plunger applies to the car; F2 = 3888N

Explanation:

For a hydraulic device, the relationship between the force and the area using Pascal's principle is;

F1/A1 = F2/A2

Where;

F1 is force applied to the input piston

F2 is force that the output plunger applies to the car

A1 is Area of input piston

A2 is area of larger piston

We are given;

R2/R1 = 9

So, R2 = 9R1

F1 = 48N

Area of input piston;

A1 = π (R1) ²

Area of output piston;

A2 = π (9R1) ²

Since, (F1/A1) = (F2/A2)

Thus;

F1 / (π (R1) ²) = F2 / (π (9R1) ²)

If we simplify, π (R1) ² will cancel out to give;

F1 = F2/9²

Thus;

F2 = 9² x F1

Plugging in 48N for F1, we have;

F2 = 9² x 48

F2 = 81 x 48

F2 = 3888N