Question 4
A simple pulley and belt driving system is shown.
The velocity ratio of the system is
Not quite. $200\div500=0.40$ has both diameters right but divides the wrong way. The ratio for a belt drive puts the driven pulley on top. In 2023, 40.2% of Queensland students chose (A).
Not quite. $200\div250=0.80$ makes two errors. It reads the 250 mm radius as a diameter, then divides driver by driven. In 2023, 14.2% of Queensland students chose (B).
Not quite. $250\div200=1.25$ divides the right way but reads the 250 mm as a diameter. That arrow runs from the centre dot to the rim, so it is a radius and the driven diameter is 500 mm. In 2023, 12.0% of Queensland students chose (C).
That is it. Step through the hints below to see why. In 2023, 33.4% of Queensland students chose (D).
Look at what each arrow spans before you read its number. The 200 mm arrow runs between two dashed lines that touch the top and bottom of the driver, so it is a diameter. The 250 mm arrow starts at the centre dot and stops at the rim, so it is a radius.
$$d_{\text{driven}}=2\times250=500\text{ mm}$$
Measure both pulleys the same way. That rules out (B) and (C), which both treat 250 mm as a diameter.
The 2026 formula book gives the belt drive ratio with the driven pulley on top. The 2019 book the 2023 cohort sat with did not print it, so they had to recall it.
$$\text{VR}=\frac{d_{\text{driven}}}{d_{\text{driver}}}=\frac{500}{200}=2.50$$
The driver is the pulley QCAA labelled, the small one on the left.
A small driver turning a large driven pulley has to turn more than once for every turn of the big one. The effort side moves further than the load side, so the VR must be above 1.
$$\frac{\pi\times500}{\pi\times200}=2.5$$
One turn of the driven pulley takes 2.5 turns of the driver. That rules out (A) and (B). Run this check every time you divide two pulleys or two gears.
$$\begin{aligned}\text{VR}&=\frac{d_{\text{driven}}}{d_{\text{driver}}}\\[10pt]&=\frac{2\times250}{200}\\[10pt]&=2.50\end{aligned}$$
Turn the radius into a diameter so both pulleys are measured the same way, then divide driven by driver.
The most common wrong answer was (A), and more students chose it than the key. It has the radius converted correctly and then divides driver by driven. Label the driver and the driven pulley on the diagram before you divide anything.
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 2023 QCAA Engineering external assessment, © State of Queensland (QCAA) 2023, 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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