Chapter 13.3, Problem 24PP

To determine

To Calculate:The force applied to the smaller piston to lift the chair.

Answer to Problem 24PP

The force is $\text{80}\text{N}$ .

Explanation of Solution

Given data:

Weight of chair, ${\text{F}}_{\text{1}}\text{=1600}\text{N}$

Area of cross-section of smaller piston, ${\text{A}}_{\text{2}}\text{=72}{\text{cm}}^{\text{2}}$

Area of cross-section of piston, ${\text{A}}_{\text{1}}\text{=1440}{\text{cm}}^{\text{2}}$

Formula used:

According to Pascal's law:

  $P\text{ =}\frac{F_1}{A_1}= \frac{F_2}{A_2}$

Therefore, the force  $F_2$  is larger than  $F_1$  by multiplying factor  $\frac{A_2}{A_1}$ .

Force Exerted by Hydraulic Lift, $F_2\text{ =}\frac{F_1{A}_2}{A_1}$

Calculation:

Now, by using formula, $F_2\text{ =}\frac{F_1{A}_2}{A_1}$

By putting all the values in above formula,

  $\text{=}\frac{\left(\text{1600}\text{N}\right)\left(\text{72}{\text{cm}}^{\text{2}}\right)}{\text{1440}{\text{cm}}^{\text{2}}}\text{=}\text{80}\text{N}$

Conclusion:

The force applied to the smaller piston to lift the chair is $\text{80}\text{N}$ .