Chapter SH, Problem 14.9APP

To determine

To calculate: Area of the second piston.

Answer to Problem 14.9APP

Area of the second piston is $\underset{\_}{0.01{\text{ m}}^2}$ .

Explanation of Solution

Given:

Force on first piston = $\text{7500 N}$

Area of first piston = $0.05{\text{ m}}^2$

Force on second piston = $1500\text{ N}$

Formula used:

Pascal’s Principle is given by,

  $\frac{F_{\text{in}}}{A_{\text{in}}}=\frac{F_{\text{out}}}{A_{\text{out}}}$

Where $F_{\text{in}}$is input force, $A_{\text{in}}$ is input area, $F_{\text{out}}$ is output force and $A_{\text{out}}$ is output area.

Calculation:

Area of the second piston is calculated as:

  $\begin{array}{l}\frac{F_{\text{in}}}{A_{\text{in}}}=\frac{F_{\text{out}}}{A_{\text{out}}}\\ A_{\text{out}}=\frac{F_{\text{out}}\cdot A_{\text{in}}}{F_{\text{in}}}\\ A_{\text{out}}=\frac{\left(1500\text{ N}\right)\left(0.05{\text{ m}}^2\right)}{7500\text{ N}}\\ A_{\text{out}}=0.01{\text{ m}}^2\end{array}$

Conclusion:

Area of the second piston is $\underset{\_}{0.01{\text{ m}}^2}$ .