Question 2
The force required to just stop an 80 kg box from sliding down a 20° incline is
Not quite. 97 N is far below the 268 N pull of the weight down the slope. A force that small only works if friction does most of the holding, and the question gives you no coefficient of friction to count on. In 2023, 4.4% of Queensland students chose (A).
Not quite. 250 N is 18 N short of the 268 N pull down the slope, so the box would still slide. (C) is the closest option. In 2023, 6.1% of Queensland students chose (B).
That is it. Step through the hints below to see why. In 2023, 67.5% of Queensland students chose (C).
Not quite. 282 N is more than the 268 N pull down the slope. Using $\tan20^\circ$ in place of $\sin20^\circ$ gives 285 N, and (D) is the option nearest to that. In 2023, 21.1% of Queensland students chose (D).
The question gives you no coefficient of friction, so treat the incline as frictionless. Nothing else holds the box, so your force has to do all of it.
“Just stop” means the forces along the slope balance. The smallest force that does this acts straight up the slope.
The part of the weight that pulls the box down the slope is the sine component.
$$\begin{aligned}F_\parallel&=mg\sin20^\circ=80\times9.8\times\sin20^\circ\\&=268.14\text{ N}\end{aligned}$$
Check it at the extremes. A flat floor needs no holding force and a vertical wall needs the whole weight, $mg$. Only sine gives zero at $0^\circ$ and $mg$ at $90^\circ$.
Your holding force balances that pull exactly.
$$F_{hold}=F_\parallel=268.14\text{ N}$$
No option says 268 N. The nearest is (C) 265 N. (D) 282 N is further away and more than you need.
$$\begin{aligned}F&=mg\sin20^\circ=80\times9.8\times\sin20^\circ\\&=268.14\text{ N}\end{aligned}$$
With no friction given, the holding force balances the component of the weight down the slope.
QCAA’s key is 265 N, about 3 N below the 268.14 N that $g=9.8\text{ m s}^{-2}$ gives. The marking guide shows only the key, so there is no working to say where the 265 came from. It is the nearest option, and it is the answer.
The most common wrong answer was (D), 282 N. Using tan instead of sin lands nearest to it. When your answer is not printed exactly, choose the closest option and 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 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.
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