Machines and mechanisms

1. 1Read the velocity ratio from the geometry. This is the only step that changes with the machine. The six recipes are in Part 3.
2. 2Find the mechanical advantage with $\text{MA} = \eta \times \text{VR}$, using $\eta$ as a decimal. At 100% efficiency, write the sentence “MA = VR when 100% efficient”. It earns its own mark.
3. 3Find the missing force with $F_L = \text{MA} \times F_E$, or $F_E = F_L \div \text{MA}$.
4. 4Find the missing distance with $d_E = \text{VR} \times d_L$. Convert millimetres to metres first, if you have not already.
5. 5Find the work with $W = Fs$, using a force and a distance from the same side of the machine. Then $P = W \div t$. From here Game plan 3 takes over.

1. 1Find the ratio of each stage on its own, driven over driver.
2. 2Multiply the stage ratios: $\text{VR}_{\text{total} } = \text{VR}_1 \times \text{VR}_2 \times \dots$ An idler gear reverses the direction but leaves the overall ratio unchanged.
3. 3Multiply the stage efficiencies: $\eta_{\text{total} } = \eta_1 \times \eta_2$. Two stages at 90% and 80% give $0.9 \times 0.8 = 0.72$, which is 72%.
4. 4Run Game plan 2.1 with the overall VR and the overall efficiency.

The overall efficiency is lower than either stage, and it is never the average of the two. 2020 Q20b turns on this. Neither multiplying rule is in the formula book.

1. 1Find the circumference of the wheel or drum in metres, $\pi d$ or $2\pi r$. Check the diagram to see whether you were given a diameter or a radius.
2. 2One revolution moves the load by one circumference, so $\text{revolutions} = \text{distance} \div \pi d$.
3. 3Cross the drive to the other shaft. Multiply or divide by the ratio, depending on which way you are travelling.
4. 4Check the direction of your answer. When the ratio is above 1, the driver turns more times than the driven.

In 2021 Q22b a 500 mm drum has $\pi d = 1.571\ \text{m}$, so lifting 2 m takes $2 \div 1.571 = 1.27$ drum revolutions. The motor drives a 15-tooth gear and the drum carries a 100-tooth gear, so the motor turns $\frac{100}{15} \times 1.27 = 8.5$ times.

1. 1Name the machine and the part that gives it its advantage, such as the fulcrum of a crowbar or the two gears of a bicycle.
2. 2Sketch it. Label the effort force and the load force, or the effort distance and the load distance. Marking the fulcrum or axle and drawing arrows that show direction are good practice, but no mark guide has given them a mark of their own.
3. 3Write a sentence saying how the machine reduces the effort force needed to move the load, and what increases that effect, such as a longer effort arm or more ropes supporting the load.
4. 4Define VR in words as the distance moved by the effort divided by the distance moved by the load.
5. 5Answer the rest of the question in its own terms. When 2023 Q12 asked about work done on the pedals, the marks went to saying the work stays the same because a smaller force moves through a greater distance.

The split of marks has changed from year to year. In the 2024 crowbar question, three of the four marks were for the wording and one was for the sketch. In the 2022 pulley question, the sketch carried three of the five marks. Learn the definitions and draw a fully labelled sketch.

Go to Game plan 7 for the response shape before you write this one.

QCAA’s 2025 syllabus revision report lists the definition of MA and VR as reduced subject matter in Unit 4. Expect fewer marks for the definitions, but make sure you can write them.