Question

If you double the size of the larger pad of a hydraulic system, how much less force do you need to apply to the smaller pad to achieve the same result?

A. 1/4 the force
B. 1/2 the force
C. 1/3 the force
D. The same amount of force

Answer 1

A - ¼ of the force

Step-by-step explanation:

According to Pascal’s principle, there's an equation that relates the force to area ratios in hydraulic systems, provided that the pistons will be at the same vertical height and that the friction in the given hydraulic system is negligible. This formula is;

F1/A1 = F2/A2

Thus;

F1/F2 = A1/A2

Where F is the applied force and A is area of pad.

Now, we are told that the size of the pad is doubled. Thus;

If the initial radius is r, then the new radius is 2r

Thus;

F1/F2 = (πr²)/(π(2r)²)

F1/F2 = r²/4r²

F1/F2 = ¼

F1 = ¼F2

Thus, the answer is ¼ of the force