Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Combine opposing forces before applying the mass relation.
Worked solution
(a)
Combine opposing forces before applying the mass relation.
Driving force minus resistance is \(\displaystyle 29-9=20 N\).
Answer: \(20\) N
(b)
Apply resultant=mass×acceleration to the whole horizontal force balance.
The resultant 20 divided by mass 5 gives \(\displaystyle \frac{4m}{s^{2}}\).
Answer: \(4\) \(\displaystyle \frac{m}{s^{2}}\)
(c)
Multiply mass by the new specified acceleration.
The required resultant is \(\displaystyle 5\times 7=35 N\).
Answer: \(35\) 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: Combine opposing forces before applying the mass relation.
- 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 resultant force after subtracting resistance.
(b) · 2 marks
- 1 mark: Apply resultant=mass×acceleration to the whole horizontal force balance.
- 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: Do not divide by weight instead of mass.
(c) · 2 marks
- 1 mark: Multiply mass by the new specified acceleration.
- 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 resultant force after subtracting resistance.
Total: 6 marks.