Chapter 13.3, Problem 25PP

To determine

To Calculate:The weight of the automobile.

Answer to Problem 25PP

The weight is $\text{8}{\text{.8×10}}^{\text{3}}\text{N}$ .

Explanation of Solution

Given data:

Force exerted on piston, $F_1=\text{55}\text{N}$

Area of cross-section of automobile, $A_2\text{= 2}\text{.4}{\text{m}}^{\text{2}}$

Area of cross-section of piston, $A_1=\text{0}\text{.015}{\text{m}}^{\text{2}}$

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,

  $\text{=}\frac{\left(\text{55}\text{N}\right)\left(\text{2}\text{.4}{\text{m}}^{\text{2}}\right)}{\text{0}\text{.015}{\text{m}}^{\text{2}}}\text{=8}{\text{.8×10}}^{\text{3}}\text{N}$

Conclusion:

The weight of the automobile is $\text{8}{\text{.8×10}}^{\text{3}}\text{N}$ .