Work Energy Theorem Homework: Water Pump Power Output

[ehabmozart]

Homework Statement

A pump is required to lift 800 kg of water (about 210 gallons)
per minute from a well 14.0 m deep and eject it with a speed
of 8ms-1 (a) How much work is done per minute in lifting the
water? (b) How much work is done in giving the water the kinetic
energy it has when ejected? (c) What must be the power output of
the pump?

Homework Equations

Work Energy theorem

The Attempt at a Solution

The book attempt was that work done = mgh... Why don't we add tension as well... Or force applied by pump?

 

[tiny-tim]

hi ehabmozart!

The book attempt was that work done = mgh... Why don't we add tension as well... Or force applied by pump?

you can calculate the work done in two ways …

by integrating the tension T times the displacement, total ∫ T dh

or (applying the work energy theorem) by simply finding the difference in energy! ​

(if the acceleration is 0, so that T is constant, then T = mg, and ∫ T dh = mgh )

the whole point of these work-energy exercises is to show you how to avoid using the usual work done formula …

which would be very difficult if the acceleration wasn't 0!​