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Difficulty: EasyPascal's Principle and Hydraulics

In a small vehicle's hydraulic braking system, a driver applies an input force of 30 lbs30 \text{ lbs} to the master cylinder piston. The master cylinder piston has a cross-sectional area of 1 in21 \text{ in}^2. If the brake caliper piston has a cross-sectional area of 4 in24 \text{ in}^2, what is the resulting output force applied by the brake caliper piston?

Answer: 120 lbs

Answer

120
According to Pascal's Principle, pressure is transmitted equally throughout an enclosed fluid. Because the brake caliper piston has an area 4 times larger than the master cylinder piston, it will multiply the input force by a factor of 4, resulting in 120 lbs of output force.

Step-by-Step Solution

1
Calculate the fluid pressure created by the master cylinder.
P=30 lbs1 in2=30 psiP = \frac{30 \text{ lbs}}{1 \text{ in}^2} = 30 \text{ psi}
Pressure is defined as force divided by area.
2
Calculate the output force at the brake caliper using Pascal's Principle.
F2=30 psi×4 in2=120 lbsF_2 = 30 \text{ psi} \times 4 \text{ in}^2 = 120 \text{ lbs}
Pascal's Principle states that the 30 psi pressure is transmitted undiminished to the 4 sq in output piston.

Key Concept

Pascal's Principle and Mechanical Advantage in Hydraulics
Estimated Time:45s
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Topics

Pascal's Principle and Hydraulics

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