The area of piston 1 is 15 times smaller than the area of pi

The area of piston 1 is 15 times smaller than the area of piston 2. If you want to lift the car 1ft, how much you should push down piston?

Solution

Multiplication of force can be achieved by application Pascal\'s principle, which for the two pistons implies

P₁ = P_{2.........................(1)}

Where, P₁ = Pressure on smaller diameter piston 1

P₂=Pressure on larger diameter piston 2

Now,

P= Force/Area

So, eqn (1) implies

F₁/A₁=F₂/A₂

And,

A₂ = 15A₁

Therefor eqn (2) yields

F₁/F₂ = 1/15

F₂/F₁ = 15

Now, in an ideal case with no frictional loss

W_input = W_output

Work = Force x distance

F₁d₁ = F₂d₂

Where, d₁ is the distance to be pushed, d₂ distance to be lifted

Or,

d₁ = F₂d₂/F₁ = (F₂/F₁) x d₂ = 15 x 1 ft = 15 ft...................................(Ans)