Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use the downward acceleration sign in the vertical force equation.
Worked solution
(a)
Use the downward acceleration sign in the vertical force equation.
Upward-positive acceleration is −3, so \(\displaystyle R=Mg\)−Md=42 N.
Answer: \(42\) N
(b)
Convert the measured support force using the stated scale calibration.
The calibrated display is \(\displaystyle \frac{R}{g}=\)\(\displaystyle \frac{21}{5}\) kg. The actual mass remains 6 kg.
Answer: \(\displaystyle \frac{21}{5}\) kg
(c)
Use Newton’s third law for the block-floor pair, keeping the recipient explicit.
The floor interaction partner has the same magnitude 42 N, directed downward on the floor.
Answer: \(42\) 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 the downward acceleration sign in the vertical force equation.
- 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: An upward-moving lift can have downward acceleration.
(b) · 2 marks
- 1 mark: Convert the measured support force using the stated scale calibration.
- 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: The scale reading can change while the actual block mass does not.
(c) · 2 marks
- 1 mark: Use Newton’s third law for the block-floor pair, keeping the recipient explicit.
- 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: An upward-moving lift can have downward acceleration.
Total: 6 marks.