Question 3
During a race, the rear wheels of a go-kart exert a horizontal force of 100 N on the racetrack surface when the rear axle is rotating at 1000 revolutions per minute (rpm). The wheels have a diameter of 280 mm.
The power being transmitted to the track by the rear wheels is
Not quite. 88 kW forgets that rpm is per minute. $100\times0.88\times1000$ treats all 1000 revolutions as happening every second. Divide by 60 first. In 2022, 20.5% of Queensland students chose (A).
Not quite. 2.9 kW uses 0.28 m as the radius, so the circumference comes out as $2\pi\times0.28=1.76$ m, twice the real 0.88 m. The 280 mm in the stem is the diameter. In 2022, 31.1% of Queensland students chose (B).
That is it. Step through the hints below to see why. In 2022, 42.8% of Queensland students chose (C).
Not quite. 0.73 kW halves the circumference by putting the radius, 0.14 m, into $\pi d$. Use the diameter with $\pi d$, or the radius with $2\pi r$. In 2022, 4.4% of Queensland students chose (D).
Each revolution, the wheel rolls out one circumference of track. The stem gives the diameter, so use $\pi d$ with $d=0.28$ m.
$$\pi d=\pi\times0.28=0.88\text{ m}$$
Using 0.28 m as a radius doubles this and gives (B). Putting the radius into $\pi d$ halves it and gives (D).
rpm is revolutions per minute. Power is per second, so divide by 60 to get the speed of the track past the wheel. Keep the unrounded circumference, 0.8796 m.
Skip the 60 and the answer is sixty times too big. That is (A).
Power is work per second. Each second the 100 N acts along 14.66 m of track, so $W=Fs$ and $P=W/t$ combine into $P=Fv$.
$P=Fv$ is not printed in the formula book. If you need to show where it comes from, write $W=Fs$ and $P=W/t$ first.
Turn the rpm into a track speed with the circumference and a divide by 60, then multiply by the force.
The most common wrong answer was (B), from treating the 280 mm diameter as a radius. Check which measurement the stem gives you before you write $2\pi r$.
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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