Answer to Question #150620 in Physics for olawumi abdulrahmon

Question

A machine of efficiency 80% is used to raise a load of a body of mass 76kg through a vertical height of 3m in 30s. Calculate the power input (g=10ms²)

Answer 1

In order to raise a load the machine should deliver the following power:

$$P_d = \dfrac{mgh}{t}$$

where $m = 76kg$ is the mass of the load, $g = 10m/s^2$ is the gravitational acceleration, $h = 3m$ is the vertical height, and $t = 30s$ is the time of raising. Since the machine is 80% efficient, The input power should be:

$$P_i = \dfrac{P_d}{0.8} = 1.25 \dfrac{mgh}{t}\\ P_i = \dfrac{76\cdot 10\cdot 3}{30} = 76\space W$$

Answer. 76 W.