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 18.0 m/s. (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?
Solution 91P a) Step 1: Depth of the well from where the pump lifted the water is 14 meters. Mass of the water which got lifted is 800 kg. Time taken is 1 minute. Work done is, W = force × distance = 800 kg × 9.8 m/s × 14 meters = 109760 J b) Step 2: Water ejected with a speed of 18 m/s. The final kinetic energy is, K.E = 1/2 mv = 0.5 × 800 × 18 = 129600 Initially the water is at rest so, the kinetic energy was zero. Change in kinetic energy is, K.E = 129600 0 = 129600 J . This is the work done as per the work-energy theorem. c)