How long will it take a 634 hp motor to lift a 450 kg beam d

How long will it take a 6.34 hp motor to lift a 450 kg beam directly upward at constant velocity from the ground to a height of 30.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

A) 45 seconds B) 21 seconds C) 16 seconds D) 28 seconds E) 63 seconds

Solution

Power P = 6.34 hp

              = 6.34 x 746 W

              = 4729.64 W

Mass of the beam m = 450 kg

Height h = 30 m

We know P = work / time

                  = mgh / t

From this time t = mgh / P

                        = (450 x9.8x 30 ) / (4729.64)

                        = 27.97 s

                        = 28 s        ( two significant figures)