Question

A 10,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. 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 initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons.

Answer 1

Weight of the car = W = 10000 N

Radius of the wider arm of the U tube = R₁ = 18 cm = 0.18 m

Radius of the narrower arm of the U tube = R₂ = 5 cm = 0.05 m

Area of the wider arm of the U tube = A₁

A₁ = $\pi$R₁²

Area of the narrower arm of the U tube = A₂

A₂ = $\pi$R₂²

Force applied on the piston in the narrower arm of the U tube = F

Both the pistons are at the same level.

The pressure on both sides is same

$\frac{W}{A_{1}} = \frac{F}{A_{2}}$

$\frac{W}{\pi R_{1}^{2}} = \frac{F}{\pi R_{2}^{2}}$

Ri R

10000 (0.18)2 ー (0.05)2

F = 771.6 N

Initial force that must be applied to the smaller piston to start lifting the car = 771.6 N