Question

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?

Short answer

Power becomes 4P , that is four times.

Step-by-step solution

Given information

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

Crane lift the beam twice as high in half the time .

Explanation

We know power is defined as $P=\frac{W}{t}$

Where, W= work done and t=time taken

Now find the power with double the height in half the time

$$\begin{gathered} P_{new}=2P \\ {P}_{new}=2\frac{W}{t/2} \\ {P}_{new}=4\frac{W}{t} \\ {P}_{new}=4P \end{gathered}$$

So the power will be 4 times of initial power.