How high can you raise a kilogram of sugar with 1 kWh of electrical energy? (To 2 s.f in kilometres)
The first thing to recognise is that the terms 'sugar' and 'electrical' are there to confuse you - the substance raised and the type of form of energy used to raise it are not important to the question.
This is ultimately a question of equating energies, Ep as potential energy of the sugar and Ee the electrical energy used to raise it. We know that the gravitational energy of the sugar after raising it will be equal to 1 kWh, so we look to express this in a unit that is more useful, Joules.
1 kWh is the energy output of 1000 Watts of power for 1 hour (6060 seconds). As 1 Watt is 1 Joule / second, we find that:Ee = (1000)(60)(60) = 3,600,000 J
The potential energy of the sugar after raising it to a height h is: E = mg*h
We have m = 1kg and g = 9.8 m/s/s .
Therefore with Ep = Ee we have:
3,600,000 = (9.81)*hh = 367.3469... km
To 2 s.f this is rounded to: h = 370 km
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