Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use Fd cos θ and retain the sign of cosine.
Worked solution
(a)
Use Fd cos θ and retain the sign of cosine.
The along-displacement component times displacement gives \(-104\) J.
Answer: \(-104\) J
(b)
Resolve the force along the actual displacement direction.
\(\displaystyle F \cos \theta =\)\(\displaystyle - \frac{52}{5}\) N.
Answer: \(\displaystyle - \frac{52}{5}\) N
(c)
Resolve the perpendicular component without treating it as work-producing here.
\(\displaystyle F \sin \theta =\)\(\displaystyle \frac{39}{5}\) N; θ lies above the horizontal axis in the stated range.
Answer: \(\displaystyle \frac{39}{5}\) N
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Use Fd cos θ and retain the sign of cosine.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Use the angle between the force and displacement, not an unrelated angle on the diagram.
(b) · 2 marks
- 1 mark: Resolve the force along the actual displacement direction.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep negative work when the along-displacement component opposes the motion.
(c) · 2 marks
- 1 mark: Resolve the perpendicular component without treating it as work-producing here.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Use the angle between the force and displacement, not an unrelated angle on the diagram.
Total: 6 marks.