Question

An input force is applied to a 2 cm diameter piston. The piston compresses oil and is connected to a 4 cm diameter output piston. The force on the output piston is ________ the force on the input piston. (Select all that apply.)

Answer 1

Answer:

4 times

Explanation:

Given:

diameter of the input piston, $d_i=2\ cm=0.02\ m$

diameter of the output piston, $d_o=4\ cm=0.04\ m$

In such mechanical arrangements the fluid acts as an incompressible link and the pressure remains uniform throughout the fluid bulk.

Then, by the Pascal's law:

$\frac{F_i}{A_i} =\frac{F_o}{A_o}$

where:

$F_i\ \&\ F_o$ are the input and the output forces respectively.

$A_i\ \&\ A_o$ are the input and the output area of pistons respectively.

$\frac{F_i\times 4}{\pi.d_i^2} =\frac{F_o\times 4}{\pi.d_o^2}$

$\frac{F_i}{d_i^2} =\frac{F_o}{d_o^2}$

$\frac{F_o}{0.04^2}=\frac{F_i}{0.02^2}$

$F_o=4\times F_i$