Find the required force and the work input

Question

Problem

1. Two hydraulic cylinders maintain a pressure of 1200 kPa. One has a cross-sectional area of 0.01 m², the other 0.03 m². To deliver work of 1 kJ to the piston, how large a displacement V and piston motion H are needed for each cylinder? Neglect P_atm.

2. A linear spring, F = k_s(x - x₀) with spring constant k_s = 500 N/m, is stretched until it is 100 mm longer. Find the required force and the work input.

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.