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 

`\frac {F₁}{a}` = `\frac {F₂}{A}`

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 =  `\frac {Ï€ D²}{4}`

by putting values 

A =  `\frac {3.1416 ï½˜ (0.30 m)²}{4}`

A =  `\frac {3.1416 ｘ 0.09 m²}{4}`

A =  `\frac {0.283 m²}{4}`

A =  0.0707 m²

or

A = 7.07 ï½˜1o⁻² m²

For Smaller Piston


a =  `\frac {Ï€ d²}{4}`

by putting values 

a =  `\frac {3.1416 ï½˜ (0.03 m)²}{4}`

a =  `\frac {3.1416 ｘ 0.0009 m²}{4}`

a =  `\frac {0.00283 m²}{4}`

a =  0.000707 m²

or

a = 7.07 ï½˜1o⁻⁴ m²

Now According to Pascal's Law for hydraulic press 

`\frac {F₁}{a}` = `\frac {F₂}{A}`

Or

F₁ = `\frac {F₂}{A}` ｘ a

by Putting values

F₁ = `\frac {20,000 N}{7.07 ｘ1o⁻² m²}` 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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