A hoist powered by a 30 hp motor is used to raise a 300kg bucket of gravel to a height of 100 m.
1 HP = 745.7 W Power = work done/time 30 x 745.7 = 300 x 9.81 x 100 /t re-arranging to solve for t t = 300 x 9.81 x 100/(30 x 745.7) = 13.15 s
30 x 550 ft-lb/s = 16,500 ft-lb/s 300 kg weighs 300 (2.2) = 660 lbs 100 m = 328 ft work done = 660(328) = 216,480 ft-lbs IF the efficiency of the mechanical lift (includes motor) was 100% (not stated but should have been) then time = 216,480/16,500 = 13.1 s ANS
