Question

n 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.

Answer 1

Answer:

The  force on the output piston is 4 times of the force on the input piston.

Explanation:

Given that,

The diameter of the input piston, $d_1=2\ cm$

The radius of the input piston, $r_1=1\ cm$

The diameter of the output piston, $d_2=4\ cm$

The radius of the output piston, $r_2=2\ cm$

According to Pascal's law, the pressure at smaller piston is equal to the pressure at larger piston such that,

$\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}\\\\\dfrac{F_2}{F_1}=\dfrac{A_2}{A_1}\\\\\dfrac{F_2}{F_1}=\dfrac{\pi r_2^2}{\pi r_1^2}\\\\\dfrac{F_2}{F_1}=\dfrac{r_2^2}{r_1^2}\\\\\dfrac{F_2}{F_1}=\dfrac{2^2}{1^2}\\\\\dfrac{F_2}{F_1}=\dfrac{4}{1^2}\\\\F_2=4\times F_1$

So, the  force on the output piston is 4 times of the force on the input piston.