Question 16
The 15-tooth gear A drives a gear train used to raise a platform a distance of 1.2 m. The teeth of gear C have a pitch of 10 mm and gear B has 30 teeth. Identify the gear train used and determine the ratio of gear A to gear C. Explain your reasoning.
[5 marks]
Every tooth that passes the rack lifts it 10 mm, so one turn of gear A lifts the platform 150 mm
This is QCAA’s figure, which is not drawn to scale, redrawn to scale with 10 mm teeth. Watch the orange tooth on each gear and count the turns while the rack climbs.
Gear A, gear B and the rack all share the same 10 mm teeth. One turn of A pushes 15 teeth through, which is 150 mm of rack. Gear B only changes the direction and the count of turns.
Build the answer one sentence at a time and see which marks it earns
Each row is one thing the marker looks for. Pick the sentence you would write. Each pick tells you whether it earns its mark and why, and the checklist ticks the marking guide criteria your answer meets.
Work through the solution one mark at a time
Try each step yourself before you reveal it. The guide opens with “explains correctly and includes”, then gives one mark for each of the five things below.
C has teeth along a straight edge, and the stem gives it a pitch rather than a tooth count. That makes C a rack and B, the gear that meshes with it, the pinion. Gear A drives the pinion.
“A gear ratio of the system is determined using the distance travelled by the rack for each revolution of the pinion gear B.”
Marker: identification of rack and pinion gears
Each tooth of B that passes the rack moves it one pitch. One turn of B passes all 30 teeth.
$$\begin{aligned}&\text{rack per turn of B}\\&=30\times10\text{ mm}=300\text{ mm}\end{aligned}$$
“The pitch of the teeth on the rack is 10 mm, which means that each revolution of the pinion gear that has 30 teeth will raise the rack by 300 mm.”
Marker: an accurate numerical relationship between linear and rotational movement of the rack and pinion gears
Use the formula book form, driven teeth over driver teeth. A is the driver.
$$\begin{aligned}\text{GR}&=\frac{\text{teeth on driven gear}}{\text{teeth on driver gear}}\\&=\frac{30}{15}=2\Rightarrow\quad 2:1\end{aligned}$$
A turns twice for every turn of B. Writing 1:2 says the opposite.
Marker: an accurate gear ratio of gear A to B
Convert 1.2 m to millimetres, find the turns of B, then cross the 2:1 pair to A.
“To lift the platform 1.2 m, the pinion gear must rotate 4 times. The gear ratio between gear A and gear B is 30 divided by 15 or 2:1. To raise the rack 1.2 metres, gear A is required to turn 8 times to turn gear B 4 times.”
Marker: evidence of mathematical reasoning
C is a rack, so it does not turn. The ratio of A to C links turns of A to distance moved by C.
$$\begin{aligned}&\text{C per turn of A}\\&=\frac{1200\text{ mm}}{8}=150\text{ mm}\end{aligned}$$
Check it a second way. One turn of A pushes its 15 teeth through the mesh, and every tooth moves the rack 10 mm, so $15\times10=150\text{ mm}$. The guide notes say “Also accept A to C = 8 rotations of A to move platform 1.2 m.”
Marker: an accurate gear ratio of gear A to C
Each phrase of the question gave you something
Everything you need is printed in the stem, and the chain is teeth times pitch, a two-gear ratio and one division. The 2020 subject report says Section 2 held six simple familiar questions and one complex familiar question worth 6 marks. This question is worth 5, so it is one of the simple familiar six. For 2026 the gear ratio formula is in the formula book and rack and pinion gears are still named in the Unit 4 dot point.
If I had to guess where you might lose marks, it would be the ratio of A to C. C does not turn, so a pure number such as 4:1 cannot describe it, and 4 is the turns of B anyway. Give turns of A against distance moved by C. The quieter loss is the first mark. It is easy to do every calculation perfectly and never write the words “rack and pinion”.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording, any figures and marking-guide steps are from the 2020 QCAA Engineering external assessment, © State of Queensland (QCAA) 2020, 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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