The motor of a crane uses power p to lift a steel beam.

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 / t

P ‘ = 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 / t
changed power P ‘ = mg 2h / [ t/2 ] = 4 mgh / t = 4 P
hence,factor must be increased by factor 4.

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