Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use the stated datum, allowing a negative initial height.
Worked solution
(a)
Use the stated datum, allowing a negative initial height.
Mg times the signed initial height gives 0 J.
Answer: \(0\) J
(b)
Multiply Mg by the change of vertical height.
The vertical rise is 6 m, giving increase 540 J.
Answer: \(540\) J
(c)
Use the opposite sign to the gravitational potential-energy change.
Gravity does minus the potential-energy increase, namely -540 J.
Answer: \(-540\) J
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 stated datum, allowing a negative initial height.
- 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 vertical height rather than the distance along an incline.
(b) · 2 marks
- 1 mark: Multiply Mg by the change of vertical height.
- 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 changed datum affects absolute energies, not their differences.
(c) · 2 marks
- 1 mark: Use the opposite sign to the gravitational potential-energy change.
- 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 vertical height rather than the distance along an incline.
Total: 6 marks.