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# Physics Question on GPE

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1. A swimming pool is 20m by 30m and contains water to a depth of 2m. What is the change in GPE of the water when the pool is drained?(Ignore any further changes after the water leaves the pool and assume it is drained by pulling a plug from the bottom of the pool. Density of water = 1000kgm^-3)

I have attempted to do this question and I found the volume which is 1200m^3
I found the mass by using p x v = m and it came out as 1.2 x 10^6. I then used the GPE equation where GPE=mgh.

Subbing in I get 1.2 x 10^6 x 9.8 x 2.
However they get the answer 5.88 MJ which I do get if I do
1.2 x 10^6 x 9.8 x 0.5.

Why is the height counted as 0.5 not 2. Please explain
2. (Original post by intesar)
A swimming pool is 20m by 30m and contains water to a depth of 2m. What is the change in GPE of the water when the pool is drained?(Ignore any further changes after the water leaves the pool and assume it is drained by pulling a plug from the bottom of the pool. Density of water = 1000kgm^-3)

I have attempted to do this question and I found the volume which is 1200m^3
I found the mass by using p x v = m and it came out as 1.2 x 10^6. I then used the GPE equation where GPE=mgh.

Subbing in I get 1.2 x 10^6 x 9.8 x 2.
However they get the answer 5.88 MJ which I do get if I do
1.2 x 10^6 x 9.8 x 0.5.

Why is the height counted as 0.5 not 2. Please explain
Your calculation to find the mass is correct.

Using ΔGPE = mgΔh is correct.

However, only the water at the surface will be falling 2 metres. I'm also confused by the answer given – the centre of mass of the body of water is 1 metre above the drain. Using mgΔh with h = 1 gives 11.76 MJ – 2x the given answer. It's probably something annoyingly obvious but it's 1 AM and I shouldn't be looking at numbers with my current level of energy.

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