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?

The power factor required to lift the beam twice as high in half the original time is : 4

Given that :

Power ( P ) = Work done / time  -- ( 1 )

Also work done for a lifted load

Work done = mgh  ( mass * gravity * height   )

Back to equation ( 1 )

Power ( p )  = mgh / time  --- ( 2 )

Considering the conditions given

When;  h = 2 * h  and t = 1/2 * t

Power becomes

New Power = m*g*2h / 1/2* t

             = 4( m*g*h / 2

Therefore we can conclude that The power factor required to lift the beam twice as high in half the original time is : 4.

Learn more about power factor : link

second mirror gathers light from a faraway object and reflects it to another mirror. - a.