Question 5
A pump transfers water vertically up to a cylindrical water tank sitting on a platform 7 m above the ground. The tank is 3 m deep and holds 20 kL when full.
Given that 1 L of water has a mass of 1 kg, the potential energy of the full tank at its vertical midpoint relative to a water outlet 1 m above ground level is
That is it. Step through the hints below to see why. In 2022, 33.1% of Queensland students chose (A).
Not quite. 1.67 MJ measures the midpoint from the ground, 8.5 m. The stem asks for the energy relative to the outlet, which is 1 m up, so the height is 7.5 m. In 2022, 19.2% of Queensland students chose (B).
Not quite. 1.76 MJ uses 9 m, the top of the tank above the outlet. The stem asks for the vertical midpoint, 1.5 m above the platform. Only the surface water is at the top, and the midpoint is the average height of all of it. In 2022, 33.8% of Queensland students chose (C).
Not quite. 1.86 MJ uses 9.5 m. It adds the outlet’s 1 m to the 8.5 m midpoint instead of subtracting it. A reference level above the ground makes the height smaller. In 2022, 12.2% of Queensland students chose (D).
20 kL is 20 000 L, and each litre of water is 1 kg.
$$m=20\,000\text{ kg}$$
Every option uses this mass and $g=9.8$. The four options differ only in the height, so the whole question is choosing $h$.
The stem tells you to measure at the tank’s vertical midpoint. For a full tank that is the centre of mass of the water, halfway up the 3 m.
$$7+\tfrac{3}{2}=8.5\text{ m above the ground}$$
Split the water into a top half and a bottom half. The top half sits around 9.25 m and the bottom half around 7.75 m, and the average is 8.5 m. Using the top of the tank treats all the water as if it were at the surface, which gives (C).
Potential energy is measured from a reference level. The stem names it: the outlet, 1 m above the ground. Subtract it.
$$h=8.5-1=7.5\text{ m}$$
Measuring from the ground gives (B). Adding the 1 m gives (D).
Find the height of the midpoint, subtract the height of the outlet, then use $\text{PE}=mgh$.
The most popular answer was (C), at 33.8% against 33.1% for the key. It measures to the top of the tank instead of the midpoint the stem names. This is one of three multiple choice questions from 2021 to 2025 where a distractor drew more students than the key.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording and any figures are from the 2022 QCAA Engineering external assessment, © State of Queensland (QCAA) 2022, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.
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