In a car lift, compressed air exerts a force `F_(1)` on a small piston having a radius of `0.5 cm`. This pressure is transmitted to a second piston of radius 10.0 cm . If the mass of the car to be lifted is 1350 kg. calculate `F_(1)`. What is the pressure necessary to accomplish this task?

Explanation

Since pressure is transmitted undiminished throughout the fluid,
`F_(1)=(A_(1))/(A_(2))=F_(2)=(pi(5xx10^(-2)m)^(2))/(pi(15xx10^(-2)m)^(2))(1350kgxx9.8ms^(-2))`
`=1470N`
`~~1.5xx10^(3)N`
The air pressure that will produce this force is
`P=(F_(1))/(A_(1))=(1.5xx10^(3)N)/(pi(5xx10^(-2))^(2)m)=1.9xx10^(5)Pa`
This is almost double the atmospheric pressure. Hydraulic brakes in automobiles also work on the same principle. when we apply a little force on the pedal with our foot the master piston moves inside the master cylider. and the pressure caused is transmitted through the brake oil to act on a piston of larger area. A large force acts on the piston and is pushed down expanding the brake shoes against brake lining. In this way, a small force on the pedal produces a large retarding force on the wheel. An important advantage of the system is that the pressure set up by pressing pedal is transmitted equally to all cylinders attached to the four wheels so that the braking effort is equal on all wheels.