Question

A crane exerts a power of 11kW on an object which travels upwards for 4 seconds. The mass of the object is 100kg. The body has an acceleration of 0.1m/s². What height is the body on, and what height is the body on if the utility  η=60%

Answer 1

Given:

The power exerted by the crane is P = 11kW = 11000 W.

The time is t = 4 s.

The mass of the object is m = 100 kg.

The acceleration of the object is a = 0.1 m/s^2.

To find the height of the body, h.

Explanation:

The height of the body can be calculated by the formula

$\begin{gathered} P=\text{ }\frac{force\times displacement}{time} \\ =\frac{ma-mg\times h}{t} \\ h=\frac{Pt}{ma-mg} \end{gathered}$

On substituting the values, the height will be

$\begin{gathered} h\text{ =}\frac{11000\times4}{(100\times0.1)-(100\times9.8)} \\ =-45.36\text{ m} \end{gathered}$

Here, the negative sign indicates that the object is moving upwards.