epair shop. The hydraulic pump has a constant pressure of 100 lbf/in.^2

Question

A hydraulic hoist raises a 3650 lbm car 6 ft in an auto repair shop. The hydraulic pump has a constant pressure of 100 lbf/in.² on its piston. What is the increase in potential energy of the car and how much volume should the pump displace to deliver that amount of work?

Answer 1

C.V. Car.

No change in kinetic or internal energy of the car, neglect hoist mass.

E₂ – E₁ = PE₂ - PE₁ = mg (Z₂ – Z₁)

= 3650 x 32.174 x 6/32.174

 = 21900 lbf-ft

The increase in potential energy is work into car from pump at constant P.

W = E₂ – E₁ = ∫P dV = P ∆V 

⇒ ∆V = E₂ – E₁/P = 21900/100 × 144

= 1.52 ft³