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?

Power is the rate of doing work.
∴ power=work-done /time taken

For a load been lifted up,
work-done = mass×gravity×height
=mgh

so, power = mgh/t
where t⇒time

When h is doubled and t is halved, the new power will be

Power-2 = mg2h ÷ 0.5t
= 4(mgh/2)

That is to say, power-2(new power) is four time the initial power.

The motor's power should increase with factor 4.

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batolisis batolisis · Answer 2 · 2022-03-10T11:41:55+01:00

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.

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