Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Subtract the upward applied force from the weight.
Worked solution
(a)
Subtract the upward applied force from the weight.
Vertical balance gives \(\displaystyle R=Mg-P=60 N\), which is positive.
Answer: \(60\) N
(b)
Do not change gravitational force when the support reaction changes.
The weight remains \(\displaystyle Mg=100 N\).
Answer: \(100\) N
(c)
Recalculate vertical balance with the explicitly doubled applied force.
The new balance gives \(\displaystyle Mg-2P=20 N\), still positive.
Answer: \(20\) 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: Subtract the upward applied force from the weight.
- 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: A support reaction cannot be negative in this contact model.
(b) · 2 marks
- 1 mark: Do not change gravitational force when the support reaction changes.
- 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: Include every applied vertical force before deciding whether \(\displaystyle R=Mg\).
(c) · 2 marks
- 1 mark: Recalculate vertical balance with the explicitly doubled applied force.
- 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: A support reaction cannot be negative in this contact model.
Total: 6 marks.