The motor of a crane uses power P to lift a steel beam. By what
factor must the motor’s power increase to lift the beam twice as
high in half the time?

## Answer

P = mgh / tP ‘ = mg 2h / [ t/2 ] = 4 mgh / t = 4 P

4 times

We know that Power = workdone / time = m g h / t Now P ‘ = m g h’ / t’ Given that h’ = 2 h t’ = t / 2 Therefore P ‘ = m g 2h / t/2 = 4 m g h / t = 4 P

Therefore power increases by four times of intial power

general formula–>P = mgh / tchanged power P ‘ = mg 2h / [ t/2 ] = 4 mgh / t = 4 P

hence,factor must be increased by factor 4.