Chapter 14, Problem 12STP

To determine

The area of the smaller piston.

Answer to Problem 12STP

The area of the smaller piston is $0.25{\text{m}}^{\text{2}}$ .

Explanation of Solution

Given info:

The area of the hydraulic piston is $25{\text{m}}^{\text{2}}$ .

Weight of the car is $15,000\text{N}$ .

The force on the smaller piston required to lift it is $\frac{1}{100}$ of its weight.

Formula used:

Pressure is defined as the force per unit area. It can be expressed as,

  $P=\frac{F}{A}$

Where,

• $F$is the force.
• $A$is the area.

Calculation:

According to the Pascal’s principle, for a fluid, the pressure in is equal to the pressure out. The pressure is the force exerted by its particles per unit area of container and then the Pascal’s principle is written as follows.

  $\begin{array}{c}\frac{\text{Input}\text{force}\text{in}\text{N}}{\text{Input}\text{area}\text{in}{\text{m}}^{\text{2}}}=\frac{\text{Output}\text{force}\text{in}\text{N}}{\text{Output}\text{area}\text{in}{\text{m}}^{\text{2}}}\\ \frac{F_{\text{in}}}{A_{\text{in}}}=\frac{F_{\text{out}}}{A_{\text{out}}}\\ A_{\text{out}}=\frac{F_{\text{out}}\cdot A_{\text{in}}}{F_{\text{in}}}\end{array}$

Substitute the values to calculate the output force.

  $\begin{array}{c}{F}_{\text{out}}=\frac{1}{100}\times 15,000\text{N}\\ =150\text{N}\end{array}$

Substituting the value in the formula.

  $\begin{array}{c}{A}_{\text{out}}=\frac{25{\text{m}}^{\text{2}}\cdot 150\text{N}}{15,000\text{N}}\\ =0.25{\text{m}}^{\text{2}}\end{array}$

Conclusion:

Thus, the area of the smaller piston is $0.25{\text{m}}^{\text{2}}$ .