A machine of efficiency of 70% is used to raise
a body of
mass 80 kg through
a vertical distance of 3m in
40 seconds. Calculate the power input. (Take g = 10 m/s²)

Power_input = 85.71 [W]

Explanation:

To be able to solve this problem we must first find the work done. Work is defined as the product of force by distance.

where:

W = work [J] (units of Joules)

F = force [N] (units of Newton)

d = distance [m]

We need to bear in mind that the force can be calculated by multiplying the mass by the gravity acceleration.

Now replacing:

Power is defined as the work done over a certain time. In this way by means of the following formula, we can calculate the required power.

where:

P = power [W] (units of watts)

W = work [J]

t = time = 40 [s]

The calculated power is the required power. Now as we have the efficiency of the machine, we can calculate the power that is introduced, to be able to do that work.