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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