Question 7
A pulley system with an efficiency of 75% is used to vertically raise a 120 kg load a distance of 3 m. If the length of pulley rope pulled to raise the load is 8 m, the effort required is
Not quite. 330 N is the perfect-machine effort, 441 N, multiplied by 0.75. A machine that wastes energy needs more effort than a perfect one, so the efficiency has to make the effort bigger. In 2021, 14.6% of Queensland students chose (A).
Not quite. 392 N is $1176\div3$. It uses the 3 m lift as the VR and leaves out the efficiency. The VR is the 8 m of rope over the 3 m of lift. In 2021, 11.7% of Queensland students chose (B).
Not quite. 440 N is close to 441 N, the effort a perfect machine would need, $1176\div\frac{8}{3}$. It leaves out the 75%, and a real machine needs more effort than that. In 2021, 15.2% of Queensland students chose (C).
That is it. Step through the hints below to see why. In 2021, 57.9% of Queensland students chose (D).
The load is a mass, so turn it into a force. There is no diagram to count ropes on, so the VR comes from the two distances.
$$\begin{aligned}F_L&=mg=120\times9.8\\[6pt]&=1176\text{ N}\\[6pt]\text{VR}&=\frac{d_E}{d_L}=\frac{8}{3}=2.67\end{aligned}$$
Using the 3 m lift on its own as the VR leads to (B).
Rearrange the efficiency formula for MA, with $\eta$ as a decimal.
$$\begin{aligned}\text{MA}&=\eta\times\text{VR}\\[6pt]&=0.75\times\frac{8}{3}=2\end{aligned}$$
Keep the VR as the fraction $\frac{8}{3}$ and the MA comes out exactly 2. The MA is smaller than the VR, as it must be for a real machine.
Now the effort comes from the MA.
$$F_E=\frac{F_L}{\text{MA}}=\frac{1176}{2}=588\text{ N}$$
Check it against a perfect machine, which would need $1176\div\frac{8}{3}=441$ N. A 75% machine needs more effort than that, so (A) and (C) are both too small.
$$\begin{aligned}\text{MA}&=0.75\times\frac{8}{3}=2\\[6pt]F_E&=\frac{120\times9.8}{2}=588\text{ N}\end{aligned}$$
VR from the distances, MA from the efficiency, then the effort from the MA. The work check agrees: $588\times8=4704$ J in for $1176\times3=3528$ J out is 75%.
The most common wrong answer was (C), the effort for a perfect machine with the 75% left out. (A) was close behind, with the efficiency applied the wrong way. Ask whether a lossy machine should need more effort or less.
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 2021 QCAA Engineering external assessment, © State of Queensland (QCAA) 2021, 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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