Question

A hydraulic lift raises a 2 000-kg automobile when a 500-N force is applied to the smaller piston. If the smaller piston has an area of 10 cm2, what is the cross-sectional area of the larger piston

Answer 1

The cross-sectional area of the larger piston is 392 cm²

Step-by-step explanation:

Given;

output mass of the piston, m₀ = 2000 kg

input force of the piston, F₁ = 500 N

input area of the piston, A₁ = 10 cm² = 0.001 m²

The output force is given by;

F₀ = m₀g

F₀ = 2000 x 9.8

F₀ = 19600 N

The cross-sectional area of the larger piston or output area of the piston will be calculated by applying the following equations;

`(F_i)/(A_i) = (F_o)/(A_o) \\\\A_o= (F_o A_i)/(F_i) \\\\A_o = (19600*0.001)/(500) \\\\A_o = 0.0392 \ m^2\\\\A_o = 392 \ cm^2`

Therefore, the cross-sectional area of the larger piston is 392 cm²