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Sphw1 - HOMEWORK SET 1 2.22 A car of mass 1775 kg travels...

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HOMEWORK SET 1 2.22 A car of mass 1775 kg travels with a velocity of 100 km/h. Find the kinetic energy. How high should it be lifted in the standard gravitational field to have a potential energy that equals the kinetic energy? Solution: Standard kinetic energy of the mass is KIN = ½ m V 2 = ½ × 1775 kg × 100 × 1000 3600 2 m 2 /s 2 = ½ × 1775 × 27.778 Nm = 684 800 J = 684.8 kJ Standard potential energy is POT = mgh h = ½ m V 2 / mg = 684 800 Nm 1775 kg × 9.807 m/s 2 = 39.3 m 2.29 A hydraulic lift has a maximum fluid pressure of 500 kPa. What should the piston-cylinder diameter be so it can lift a mass of 850 kg? Solution: With the piston at rest the static force balance is F = P A = F = mg A = π r 2 = π D 2 /4 PA = P π D 2 /4 = mg D 2 = 4mg P π D = 2 mg P π = 2 850 kg × 9.807 m/s 2 500 kPa × π × 1000 (Pa/kPa) = 0.146 m
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