What is the depth of the well from which, with the help of a gate with an efficiency of 90%

What is the depth of the well from which, with the help of a gate with an efficiency of 90%, a bucket of water weighing 9 kg is raised while doing work of 3000 J?

m = 9 kilograms is the mass of a bucket of water that is lifted from the well;

n = 90% = 0.9 – gate efficiency;

A = 3000 Joules – the work spent on lifting a bucket of water with a gate;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine h (meter) – the depth of the well.

The useful work spent on raising the water is equal to:

Ap = n * A = 0.9 * 3000 = 2700 Joules.

Then the depth of the well will be:

h = Ap / F = Ap / (m * g);

h = 2700 / (9 * 10) = 2700/90 = 270/9 = 30 meters.

Answer: the depth of the well is 30 meters.