Question

In a hydraulic machine, the two pistons are of area of cross section in the ratio 1:10. What force is needed on the narrow piston to overcome a force of 100N on the wider piston?

Answer 1

Hint: Pressure in a hydraulic machine is always constant. So wider the pistol more you would require to do work. Equipment such as cranes, forklifts, jacks and fall arrest safety harnesses use hydraulics to operate objects. Their panels are controlled by the hydraulic mechanisms.

Formula used:
$\dfrac{F}{A}=\dfrac{f}{a}$

Complete answer:
The amount of force applied per unit area is known as pressure.

Hydraulic machine uses the force of liquid to lift heavy stuff. Heavy building automobiles are a common example. In this type of machinery, hydraulic fluid is pushed through various hydraulic motors and hydraulic cylinders throughout the machine and becomes pressurized according to efficiency of work to be done. Pascal's law states that the pressure in an enclosed fluid is distributed in all directions uniformly. The hydraulic systems work under this principle. The product of pressure and area gives us the force applied.

Let us consider F and f as the force applied by the wider and the narrower piston respectively. Similarly, A and a are the area of the wider and the narrower piston respectively.
F = 100N
A = 10 ${{m}^{2}}$
f = x N
a = 1 ${{m}^{2}}$

Pressure is constant
Hence, P=$\dfrac{F}{A}=\dfrac{f}{a}$
$\Rightarrow \dfrac{100}{10}=\dfrac{x}{1}$
x = 10N
So the amount of force required by a narrow piston to overcome a force of 100N is 10N

Note:
Advantages of hydraulic systems include power, accuracy, efficiency, ease of maintenance and scoop of technological advancement. They also have disadvantages. They can leak, which makes them messy, and the fluids inside them are often harmful to paint and some seals.