The diameter of the piston of a hydraulic press is 30 cm. How much force is required to lift a car weighing 20,000 N on its piston if the diameter of the piston of the pump is 3 cm? Ans. (200 N)


Given:  

Diameter of the Piston of hydraulic Press  = D = 30 cm = 0.30 m

Diameter of the Piston of the Pump  = d = 3 cm = 0.03 m
Weight of the the car lifted = w₁ =  F₂ = 20,000 N


To Find:

Force required to lift a car by the pump = F₁ = ?

Solution:   

According to Pascal's Law for hydraulic press 

F₁a = F₂A

Where a=area of the smaller piston and A=area of the larger piston. These two values are also unknown so, we have the formula for the area as 

For Larger Piston: 

A =  πD²4

by putting values 

A =  3.1416 ｘ (0.30m)²4

A =  3.1416ｘ0.09m²4

A =  0.283m²4

A =  0.0707 m²

or

A = 7.07 ｘ1o⁻² m²

For Smaller Piston


a =  πd²4

by putting values 

a =  3.1416 ｘ (0.03m)²4

a =  3.1416ｘ0.0009m²4

a =  0.00283m²4

a =  0.000707 m²

or

a = 7.07 ｘ1o⁻⁴ m²

Now According to Pascal's Law for hydraulic press 

F₁a = F₂A

Or

F₁ = F₂A ｘ a

by Putting values

F₁ = 20,000N7.07ｘ1o⁻²m² ｘ 7.07 ｘ1o⁻⁴ m²

by simplifying we get

F₁ = 200 N
Thus the force applied on the piston of the pump will be 200 N

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