Editor

Explain the working of a hydraulic press.

OR

A small force applied on the smaller piston results in a large force on the larger piston. Why?

Difficulty: Medium

Hydraulic Press:
A hydraulic press is a machine that works on Pascal's law. It consists of two cylinders of different cross-sectional areas. They have fitted with pistons of cross-sectional areas a and A. 


The object to be compressed is placed over the piston of a large cross-sectional area A. The force $F_{1}$ is applied to the piston of the small cross-sectional area a. The pressure P produced by the small piston is transmitted equally to the large piston and a force $F_{2}$ acts on A which is much larger than $F_{1}$. 
Pressure on the piston of the small area a is given by 


P = $\frac{(F_{1})}{a}$ 
Applying Pascal's law, the pressure on the large piston of area A will be the same as on the small piston. 
P  =$\frac{(F_{2})}{A}$ 


Comparing the above equations, we get
$\frac{(F_{1})}{a}$ = $\frac{(F_{2})}{A} 
F_{2}$ = $A \times \frac{(F_{1})}{a}$ 
Or, $F_{2}$ = $F_{1} \times\frac{(A)}{a}$  ………………..(i)


Notes: Since the ratio $\frac{(A)}{a}$ is greater than 1, hence the force $F_{2}$ that acts on the larger piston is greater than the force $F_{1}$ acting on the smaller piston. Hydraulic systems working in this way are known as force multipliers.

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