Question 5
This crane vertically lifts a load a distance of 20 m using a pulley system. What distance must the main winch cable move during the vertical lift?
Not quite. 100 m counts five strands. The main winch cable leaves the last pulley and runs along the jib to the winch, so it does not hold up the hook block. In 2021, 6.9% of Queensland students chose (A).
That is it. Step through the hints below to see why. In 2021, 66.5% of Queensland students chose (B).
Not quite. 20 m would be right for a single fixed pulley with a VR of 1. Here four strands hold the hook block, and every one of them has to shorten by 20 m. In 2021, 11.8% of Queensland students chose (C).
Not quite. 5 m divides the lift by the VR. When the VR is above 1 the effort end always moves further than the load, so you multiply. In 2021, 14.5% of Queensland students chose (D).
Draw a boundary round the hook block and count the strands of cable that cross it. Two come down from the pulleys and two from the small block between them.
$$\text{VR}=4$$
The main winch cable runs along the jib, so it does not count. The four slings under the hook only hang the load from the hook. They are not part of the pulley system.
The winch cable is the effort end and the load rises 20 m. Rearrange the VR formula for the effort distance.
$$\begin{aligned}\text{VR}&=\frac{d_E}{d_L}\\[6pt]d_E&=\text{VR}\times d_L\\[6pt]&=4\times20=80\text{ m}\end{aligned}$$
Check it with the rope. Each of the four strands is 20 m shorter at the end of the lift, so the winch has to wind in all of that cable.
$$4\times20\text{ m}=80\text{ m}$$
Any answer below 20 m, like (D), would have the winch end moving less than the load. That only happens when the VR is below 1.
$$d_E=\text{VR}\times d_L=4\times20=80\text{ m}$$
Four strands hold the hook block, so the VR is 4 and the winch cable moves four times as far as the load.
The most common wrong answer was (D), from dividing the 20 m by the VR. The effort end of a pulley system with a VR above 1 always moves further than the load.
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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