A hydraulic lift used in garages and workshops works based on which fundamental principle of fluid mechanics?

Introduction / Context:
Hydraulic lifts are widely used to raise heavy vehicles and loads with relatively small applied forces. They use an incompressible fluid and different piston areas to multiply force. The basic principle underlying their operation is a key law of fluid mechanics that relates pressure in an enclosed fluid. Recognising this principle is important for understanding many hydraulic devices such as brakes, jacks, and presses.

Given Data / Assumptions:
• The device is a hydraulic lift, using a fluid in a closed system. • A small force is applied on a small piston, generating pressure in the fluid. • This pressure is transmitted to a larger piston supporting a heavy load. • The fluid is assumed incompressible and at rest (no significant flow).

Concept / Approach:
Pascal's law states that when pressure is applied to a confined fluid, that pressure is transmitted undiminished in all directions throughout the fluid and to the walls of the container. In a hydraulic lift, a small input force on a small-area piston produces a pressure P = F1 / A1. This same pressure acts on a larger-area piston, generating a larger output force F2 = P * A2. Because A2 is much greater than A1, F2 can be much larger than F1, enabling the lift to raise heavy loads with relatively little effort. This is the exact working principle of hydraulic machines.

Step-by-Step Solution:
Step 1: Use Pascal's law: pressure applied to an enclosed fluid is transmitted equally in all directions. Step 2: For the input piston, pressure P = F1 / A1, where F1 is the applied force and A1 is the piston area. Step 3: The same pressure P is transmitted through the fluid to the output piston. Step 4: On the output piston, the force is F2 = P * A2 = (F1 / A1) * A2. Step 5: If A2 > A1, then F2 > F1, providing mechanical advantage and allowing heavy loads to be lifted. Step 6: This use of pressure transmission and force multiplication is exactly the application of Pascal's law.

Verification / Alternative check:
Real-world hydraulic systems such as car jacks, brake systems, and industrial presses all rely on the same principle: fluid pressure is transmitted uniformly. If Newton's laws alone were sufficient, the fluid step of equal pressure transmission would be missing. Engineers design hydraulic systems by choosing suitable piston areas so that Pascal's law leads to the required force multiplication. This confirms that Pascal's law is the foundation of hydraulic lifts.

Why Other Options Are Wrong:
Option a (Newton's law): While Newton's laws describe motion and forces generally, they do not specifically explain the pressure transmission in fluids that hydraulic lifts rely on. Option c (Archimedes' principle): This principle deals with buoyant force on bodies immersed in a fluid and does not explain force multiplication in hydraulic machines. Option d (Joule's law): This relates to heat produced by electric current in a conductor and is unrelated to hydraulics. Option e (Bernoulli's principle): Bernoulli's principle applies to moving fluids and relates pressure to fluid speed and elevation; hydraulic lifts involve mostly static fluids.

Common Pitfalls:
Students sometimes confuse Archimedes' principle with Pascal's law because both concern fluids. A simple way to distinguish them is: Archimedes' principle explains why objects float or sink (buoyancy), while Pascal's law explains how pressure in a confined fluid is transmitted and used to multiply forces. For hydraulic lifts, always think of Pascal's law and equal pressure transmission.

Final Answer:
A hydraulic lift works on Pascal's law, which states that pressure applied to a confined fluid is transmitted equally in all directions.