Question 5
A conveyor belt moves 1 tonne of material with an effort of 3.5 kN. What is the efficiency of the conveyor when the velocity ratio is 4?
Not quite. $1000\div3500=0.29$ uses the mass as the load and never divides by the VR. The load has to be a force, $mg=9800\text{ N}$, and the efficiency is the MA over the VR. In 2023, 5.2% of Queensland students chose (A).
That is it. Step through the hints below to see why. In 2023, 75.4% of Queensland students chose (B).
Not quite. 80% is what you get when you divide the correct MA of 2.8 by 3.5 instead of by the VR of 4. The 3.5 is the effort in kilonewtons. In 2023, 5.2% of Queensland students chose (C).
Not quite. $3.5\div4=0.875$ treats the 3.5 kN effort as if it were the MA. The MA is the load force over the effort, $9800\div3500=2.8$. In 2023, 13.7% of Queensland students chose (D).
The effort is a force in kilonewtons, so the load has to be a force too. One tonne is 1000 kg.
$$F_L=mg=1000\times9.8=9800\text{ N}$$
Dividing the bare 1000 by the effort is how you land on (A).
The mechanical advantage is the load force over the effort force. Put both in newtons.
$$\text{MA}=\frac{F_L}{F_E}=\frac{9800}{3500}=2.8$$
The 3.5 is the effort. It is never the MA, and using it as one gives (D).
Efficiency is the MA over the VR. The question gives you the VR, 4.
$$\begin{aligned}\eta&=\frac{\text{MA}}{\text{VR}}\times100\%\\[10pt]&=\frac{2.8}{4}\times100\%\\[10pt]&=70\%\end{aligned}$$
Dividing by 3.5 instead gives (C). Check that the MA came out below the VR. It must, for any real machine.
$$\begin{aligned}\eta&=\frac{\text{MA}}{\text{VR}}\times100\%\\[10pt]&=\frac{9800\div3500}{4}\times100\%\\[10pt]&=70\%\end{aligned}$$
Turn the tonne into a weight force, divide by the effort for the MA, then divide the MA by the VR.
The most common wrong answer was (D), from $3.5\div4$. It uses the effort as if it were the MA. Write $\text{MA}=F_L/F_E$ as its own line before the VR comes anywhere near your working.
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.
Spot a mistake on this page? Report it