Chapter 19, Problem 45A

In the hydraulic arrangement shown, the larger piston has an area that is 50 times that of the smaller piston. The strong man hopes to exert enough force on the large piston to raise the 10 kg that rests on the small piston. Do you think he will be successful? Explain.

To determine

To check: Whether the man is able to raise the weight that rests on the small piston.

Answer to Problem 45A

The man will not successful. Without using a large hammer or long lever, he would not move the 10 lg block

Explanation of Solution

Given:

Area of smaller piston = $x$

Area of larger piston = $50x$

Weight that rests on the smaller piston = $10kg$

Formula used:

The force and pressure can be related with each other is,

  $F=PA$

Here, P is the pressure and A is the area.

It is given in the problem that the area of large piston is 50 times that of the smaller piston.

  $A_1=50A_2$

The pressure remains same when man exerts force on large piston. This implies that,

  $\begin{array}{cc}\frac{F_1}{A_1}& =\frac{F_2}{A_2}\\ F_1& =\frac{F_2}{A_2}\left(A_1\right)\end{array}$

Substitute equation $A_1=50A_2$ in $F_1=\frac{F_2}{A_2}\left(A_1\right)$

  $F_1=\frac{F_2}{A_2}\left(50{\text{A}}_2\right)$

  $=50F_2$

  $=50\left(10\left(9.8\text{m}/{\text{s}}^2\right)\right)$

  $=4900\text{N}$

This implies that the strong man required this much amount of force (4900 N) to lift 10 kg weight which means that he would need to apply force much more than man’s weight or muscle force to do the job.

Conclusion:

Therefore, the man will not successful. Without using a large hammer or long lever, he would not move the 10 lg block.