Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Account for the gravitational potential-energy rise and the equal initial/final kinetic energies.
Worked solution
(a)
Account for the gravitational potential-energy rise and the equal initial/final kinetic energies.
The load has no net kinetic-energy change, so lifting work equals Mgh=480 J.
Answer: \(480\) J
(b)
Use total lifting work divided by the specified elapsed time.
Work divided by total time gives \(160\) W.
Answer: \(160\) W
(c)
Multiply watts by seconds to recover transferred energy.
Constant power times duration gives 60 J.
Answer: \(60\) 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: Account for the gravitational potential-energy rise and the equal initial/final kinetic energies.
- 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: Average power uses the complete work and complete interval.
(b) · 2 marks
- 1 mark: Use total lifting work divided by the specified elapsed time.
- 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 substitute a starting zero speed into \(\displaystyle \frac{P}{v}\) for a whole lifting interval.
(c) · 2 marks
- 1 mark: Multiply watts by seconds to recover transferred energy.
- 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: Average power uses the complete work and complete interval.
Total: 6 marks.