Question

1. In a car lift, compressed air exerts a force on a piston with a radius of 5.00 cm.

This pressure is transmitted to a second piston with a radius of 15.0 cm.

 

a. How large a force must the compressed air exert to lift a 1.33 × 104 N car?

b. What pressure produces this force? Neglect the weight of the pistons.

Answer 1

a. Find the mechanical advantage:

$$n=\frac{A_\text{large}}{A_\text{small}}=\frac{r^2_\text{large}}{r^2_\text{small}}.$$

The required force:

$$F=\frac{W}{n}=W\frac{r^2_\text{small}}{r^2_\text{large}},\\\space\\ F=1.33·10^4·\frac{0.05^2}{0.15^2}=1478\text{ N}.$$

b. This force of 1478 N produces the pressure of

$$p=\frac{F}{A_\text{small}}=\frac{F}{\pi r^2_\text{small}}=752.74\text{ kPa}.$$