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Physics Tutorial: Pascal’s Principle and Hydraulic Car Lifts

Pascal's Principle – Pressure applied to a completely enclosed fluid is transmitted undiminished to all

parts of the fluid and the enclosing walls.

(F₂/A₂) = (F₁/A₁)

Explanation - The figure displays two joined cylindrical chambers. They both have different diameters and including the connecting tube, are filled with liquid. Since the second piston is larger, it produces a larger force than the force applied to the smaller piston:

F2 = F1(A2/A1)

Applications

These ideas benefit us every day.

The hydraulic car lift relates to Pascal's Principle. It’s used in garage’s to transport a car off the ground for

repairing. A small force by a small-area piston can be converted to a large force at a large area piston. It works relatively close to a lever, where a small force passes through a great distance to transport a heavy object a short distance. The work is the same when lifting the heavy object or when applying a small force. In the case of a lever, a bar and a fulcrum convert the work-in the hydraulic lift, the fluid performs the work.

Question – A hydraulic car lift has a pump piston with radius r₁ = 0.0120 m. The resultant

piston has a radius of r₂ = 0.150 m. The total weight of the car and plunger is F₂ = 2500 m. If

the bottom ends of the piston and plunger are at the same height, what input force is

required to stabilize the car and output plunger?

Answer – We need to use the area for circular objects, A=3.14r² for both the piston and

plunger. Apply Pascal's Principle:

F₁= F₂(A₁/A₂) = F₂(3.14r²/3.14r²) = (20 500N)[(0.0120²)/(0.150²)] = 131 N

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Ajit Srinivas