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Alex_Xolod [135]
3 years ago
13

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.
Physics
1 answer:
boyakko [2]3 years ago
6 0

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.

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