Using Pascal's Law and a hydraulic jack, you want to lift a 4,000 lbm rock. The large cylinder has a diameter of 6 inches.

a. What would the diameter of the small cylinder need to be if the amount of forceyou could apply was limited to your weight (120 lbf) ? (neglect the leveragegained by using a handle)

a diameter of D₂ = 0.183 inches would be required

Explanation:

appyling pascal's law

P applied to the hydraulic jack = P required to lift the rock

F₁*A₁ = F₂*A₂

since A₁ = π*D₁²/4, A₂ = π*D₂²/4

F₁*π*D₁²/4 = F₂ * π*D₂²/4

F₁*D₁²=F₂*D₂²

D₂ = D₁ * √ (F₁/F₂)

replacing values

D₂ = D₁ * √ (F₁/F₂) = 6 in * √ (120 lbf / (4000 lbm * 32.174 (lbf/lbm)) = 0.183 inches