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In a hydraulic press, a mass M is raised through a height of 5.0 mm by doing 500 J of work on the small piston. The large piston has diameter 10 cm and the small piston has diameter 2 cm. Determine the mass M. (Assume the press is ideal.)
- 10⁴ kg
- 10³ kg
- 100 kg
- 10⁵ kg
Correct answer: 10⁴ kg
Solution
For an ideal (frictionless, incompressible) hydraulic press, energy is conserved, so the input work equals the gravitational PE gained by M. Thus 500 = M*g*h = M*10*(5.0e-3) = M*0.05, giving M = 500/0.05 = 10000 kg = 10⁴ kg. The piston diameters are extra information here.
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