Question 6
A cyclist exerts an effort force of 125 N on the pedal of a bicycle. The load force on the rear wheel is 500 N. The velocity ratio of the bicycle is 5.
What is the efficiency of the bicycle?
Not quite. 125% is $\text{VR}\div\text{MA}=5\div4$, the efficiency upside down. No machine gives out more work than you put in, so an efficiency above 100% is always wrong. In 2024, 4.7% of Queensland students chose (A).
That is it. Step through the hints below to see why. In 2024, 89.9% of Queensland students chose (B).
Not quite. 8% is a decimal slip. $\text{MA}\div\text{VR}=4\div5=0.8$, and 0.8 as a percentage is 80%. In 2024, 2.1% of Queensland students chose (C).
Not quite. 5% comes from turning the MA upside down, $125\div500=0.25$, then dividing by the VR of 5. The MA is the load over the effort. In 2024, 3.0% of Queensland students chose (D).
Both forces are given in newtons, so the mechanical advantage comes straight from the stem. It is the load over the effort.
$$\text{MA}=\frac{F_L}{F_E}=\frac{500}{125}=4$$
Turning it upside down gives 0.25 and leads to (D).
The formula book gives the efficiency as the MA over the VR.
$$\begin{aligned}\eta&=\frac{\text{MA}}{\text{VR}}\times100\%\\[10pt]&=\frac{4}{5}\times100\%=80\%\end{aligned}$$
The $\times100\%$ turns 0.8 into 80%. Moving the decimal only one place gives (C).
Check it with work. A VR of 5 means the pedal moves 5 m for every 1 m the load moves.
$$\frac{W_{\text{out}}}{W_{\text{in}}}=\frac{500\times1}{125\times5}=\frac{500}{625}=0.8$$
A real machine always loses some work to friction, so the efficiency is below 100%. That rules out (A).
$$\begin{aligned}\eta&=\frac{F_L\div F_E}{\text{VR}}\times100\%\\[10pt]&=\frac{500\div125}{5}\times100\%\\[10pt]&=80\%\end{aligned}$$
Find the MA from the two forces, then divide it by the VR.
The most common wrong answer was (A), the efficiency upside down. If an efficiency ever comes out above 100%, you have divided the wrong way. Flip it before you move on.
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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