The Falkirk Wheel is used to raise (and lower) barges between two canals separat

Question

The Falkirk Wheel is used to raise (and lower) barges between two canals separated in height by 24 m. There are two diametrically-opposed gondolas within each of which the depth of water is 2.5m, regardless of whether or not the gondola contains a boat. The surface area of each gondola (i.e. the exposed water surface area) is 200m^2. Ignoring frictional losses, how much energy is required to raise a barge of mass 5 tonnes (i.e. 5000 kg) from the lower to the upper canal, when the other gondola is empty.

Explanation / Answer

exposed water surface area = 200 m2

depth of water = 2.5 m

so Volume of water = area x depth = 200 x 2.5 = 500 m3

density of water = 1000 kg/m3

so mass of water = density x volume = 1000 x 500 = 5 x 105 kg

total mass = M = 500000 + 5000 = 505000 kg

height raised = h = 24 m

potential energy = Mgh = (505 x 103 ) (9.8) (24 )= 1.18 x 108 J

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