Question

A 12000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil with a density of and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of and the narrower arm has a radius of The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised? For purposes of this problem, neglect the weight of the pistons.

Answer 1

Answer:

$f \geq 12000(\frac{r}{R})^2$

Explanation:

Let R be the radius of the wider arm of the U-tube, and r be the radius of the narrower arm of the U-tube. Let A be the pressurized area of the wider arm of the U-tube and a be the pressurized area of the narrower arm.

$A = \pi R^2$

$a = \pi r^2$

Let f be the force applied on the smaller piston and F be the force applied at the larger piston. Since the 2 are at the same level, their pressure, or force per unit area, must be the same

$F/A = f/a$

In order to lift the car, f must be:

$f \geq F\frac{a}{A}$

$f \geq F\frac{\pi r^2}{\pi R^2}$

$f \geq 12000(\frac{r}{R})^2$