Chapter 14.2, Problem 12PP

To determine

The force needed to lift the crate.

Answer to Problem 12PP

The force needed to lift the crate is $50\text{N}$ .

Explanation of Solution

Given info:

Force applied by the crate, $F=1500\text{N}$

Area of the crate, $A=30{\text{m}}^2$

Size of the smaller piston, $a=\frac{A}{30}$

Formula Used:

Write the expression to calculate the force needed to lift the crate.

  $\begin{array}{c}\frac{F}{A}=\frac{f}{a}\\ f=\frac{F\cdot a}{A}\end{array}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}f=\frac{\left(1500\text{N}\right)\left(\frac{A}{30}\right)}{A}\\ =50\text{N}\end{array}$

Conclusion:

Thus, the force needed to lift the crate is $50\text{N}$ .