Question 8
A fibreglass swimming pool has a potential energy of 98 kJ when raised 20 m from the ground by a crane. The mass of the swimming pool is
That is it. Step through the hints below to see why. In 2024, 88.9% of Queensland students chose (A).
Not quite. $98\,000\div20=4900$ leaves out $g$. Rearranging $\text{PE}=mgh$ for $m$ divides by both $g$ and $h$. In 2024, 6.6% of Queensland students chose (B).
Not quite. $98\,000\div9.8=10\,000$ leaves out the 20 m. The pool only has this energy because of its height, so the height has to appear. In 2024, 2.1% of Queensland students chose (C).
Not quite. $98\,000\times9.8\div20=48\,020$ multiplies by $g$ instead of dividing. In $mgh$ the $g$ is multiplied by $m$, so it moves to the bottom along with $h$. In 2024, 2.1% of Queensland students chose (D).
Convert the energy to joules first, so the mass comes out in kilograms.
$$\text{PE}=98\text{ kJ}=98\,000\text{ J}$$
Skip this and every route gives a mass a thousand times too small. None of the options comes from that slip, so you would know something had gone wrong.
The formula book gives $\text{PE}=mgh$. Divide both sides by $gh$ to get the mass on its own.
Divide by only one of $g$ and $h$ and you land on (B) or (C).
Put your mass back into the formula. It should give the 98 kJ you started with.
$$500\times9.8\times20=98\,000\text{ J}$$
Every other option fails this check by a long way. It takes ten seconds on the calculator.
Read $\text{PE}=mgh$ in reverse. Convert the kilojoules, then divide by both $g$ and the height.
The most common wrong answer was (B), from leaving out $g$. Only about one student in nine went wrong here, and the check in hint 3 catches every one of those slips.
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 2024 QCAA Engineering external assessment, © State of Queensland (QCAA) 2024, 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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