Physics

Physics

Problem

A hydraulic lift has a small piston of diameter 2 cm2\,\text{cm} and a large piston of diameter 20 cm20\,\text{cm}. What force must be applied on the small piston to raise a 15 000 N15\,000\,\text{N} car? a) 75 N75\,\text{N} b) 600 N600\,\text{N} c) 150 N150\,\text{N} d) 1 500 N1\,500\,\text{N}
Intuitive explanation

Pascal's principle tells us that pressure applied to a confined fluid spreads equally everywhere—so the pressure you create on the small piston must equal the pressure under the car. The key insight is that while pressure is the same, the areas are different, and that's where the mechanical advantage comes in. Calculate the area ratio between the two pistons, then use Psmall=PlargeP_{\text{small}} = P_{\text{large}} to find what force you need on the small side to support the large weight on the other.

Intuitive explanation

Pascal's principle tells us that pressure applied to a confined fluid spreads equally everywhere—so the pressure you create on the small piston must equal the pressure under the car. The key insight is that while pressure is the same, the areas are different, and that's where the mechanical advantage comes in. Calculate the area ratio between the two pistons, then use Psmall=PlargeP_{\text{small}} = P_{\text{large}} to find what force you need on the small side to support the large weight on the other.

Browse the problem library