Question

6. Applying Concepts The area of an output

piston is 25 times greater than the area of the
input piston. If the input force is 40 newtons,
what is the output force?

helppp please

Answer 1

`1000\; {\rm N}`.

Step-by-step explanation:

By Pascal's Law, the pressure on the two pistons should be the same.

Let
`F_{\text{in}}` and
`F_{\text{out}}` denote the forces on the two pistons. Let
`A_{\text{in}}` and
`A_{\text{out}}` denote the area of the two pistons.

Divide force by area to find the pressure.

• Pressure on the input piston:
  `\displaystyle P_{\text{in}} = (F_{\text{in}}/A_{\text{in}})`.
• Pressure on the output piston:
  `\displaystyle P_{\text{out}} = (F_{\text{out}} / A_{\text{out}})`.

By Pascal's Law,
`P_{\text{in}} = P_{\text{out}}`. Therefore:

`\displaystyle \frac{F_{\text{in}}}{A_{\text{in}}} = \frac{F_{\text{out}}}{A_{\text{out}}}`.

It is given that
`F_{\text{in}} = 40\; {\rm N}` and that
`A_{\text{out}} = 25\, A_{\text{in}}`. Therefore, the equation becomes:

`\displaystyle \frac{40\; {\rm N}}{A_{\text{in}}} = \frac{F_{\text{out}}}{25\, A_{\text{in}}}`.

Rearrange to find
`F_{\text{out}}`:

`\begin{aligned}F_{\text{out}} &= \frac{(40\; {\rm N})\, (25\, A_{\text{in}})}{A_{\text{in}}} = 1000\; {\rm N}\end{aligned}`.