2023HSCShort answer

Q12 (c) (i)

2 marks

Question

An object of mass $m$ slides down a smooth inclined plane. The plane makes an angle $\theta$ with the horizontal. The normal reaction is $\mathbf R$ , gravity is $\mathbf g$ with magnitude $g$ , and $\mathbf i,\mathbf j$ are unit vectors parallel and perpendicular to the plane. Show that the resultant force is $\mathbf F=-(mg\sin\theta)\mathbf i.$

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Solution

Criteria	Marks
Provides correct proof	2
Attempts to resolve a force into two perpendicular components or writes $\vec F=\vec R+m\vec g$ , or equivalent merit	1

Sample answer:

Resolving parallel and perpendicular to the slope gives
$\vec R-mg\cos\theta\,\vec j=0$
and
$\vec F=-(mg\sin\theta)\,\vec i=0$
$\therefore\text{ Resultant force is }\vec F=-(mg\sin\theta)\,\vec i$

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Syllabus alignment

Mechanics

Modelling motion without resistanceApply forces, Newton's laws and calculus to model straight-line motion without resistance.

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