2020HSCShort answer

Q12 (a) (i)

2 marks

Question

A 50-kilogram box is initially at rest. The box is pulled along the ground with a force of $200$ newtons at an angle of $30^\circ$ to the horizontal. The box experiences a resistive force of $0.3R$ newtons, where $R$ is the normal force, as shown in the diagram. Take $g=10\,\mathrm{m/s^2}$ .

(i) By resolving the forces vertically, show that $R=400$ .

Uncropped source page 7 for question 12.a.i; requires human review and cropping — Reviewed visual · source page 7

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Solution

Criteria	Marks
Provides correct solution	2
Correctly obtains the vertical component of the 200 newton force, or equivalent merit	1

Sample answer:

Resolving vertically,

200\sin30^\circ+R=mg

\therefore R=50\times10-200\times\frac12=400\text{ newtons}

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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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