IGCSE · 1 · extended response
Choosing a hoist from an energy audit
Motion, forces and energy · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 3
- Answer
- Complete
Electrical input during the rise
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Input power / W
Horizontal axis (x): Time / s
Read the exact data as a table
| Time / s | Input power / W |
|---|---|
| 0 | 300 |
| 5 | 300 |
| 10 | 300 |
These are the supplied values, not a worked answer. Lines join the supplied values; they are not a fitted model.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A hoist raises a 20 kg load through 5.0 m in 10 s at constant speed. Use g = 10 N kg⁻¹. A force sensor measures an upward cable force of 240 N throughout the rise, including a constant resisting force from guide rails. The electrical input power is the supplied 300 W throughout the lift. Supplied data (Time / s; Input power / W): (0, 300), (5, 300), (10, 300).
- (a)
Calculate cable work, useful gravitational-energy gain, guide-rail dissipation and overall efficiency.
3 marks - (b)
A second hoist performs the same lift in 5 s with 50% overall efficiency. Find its mean input power and explain the trade-off.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Calculate cable work, useful gravitational-energy gain, guide-rail dissipation and overall efficiency.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Cable work is Fh = 240(5.0) = 1200 J. Gravitational energy increases by mgh = 20(10)(5) = 1000 J.
- 2
At constant speed the load's kinetic energy does not change; 200 J of cable work is transferred by rail friction.
- 3
Electrical energy is the power–time area, 300(10) = 3000 J. Useful efficiency is 1000/3000 = 1/3, while 1800 J is also dissipated within the drive.
(b)
A second hoist performs the same lift in 5 s with 50% overall efficiency. Find its mean input power and explain the trade-off.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
The useful gravitational-energy gain remains 1000 J because mass and height do not change.
- 2
At 50% overall efficiency, input energy is 1000/0.50 = 2000 J; mean input power is 2000/5 = 400 W.
- 3
The faster hoist draws greater mean power yet uses less energy per lift. A supply must meet its power demand; energy cost follows energy use rather than power alone.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Cable work is Fh = 240(5.0) = 1200 J. Gravitational energy increases by mgh = 20(10)(5) = 1000 J.
- At constant speed the load's kinetic energy does not change; 200 J of cable work is transferred by rail friction.
- Electrical energy is the power–time area, 300(10) = 3000 J. Useful efficiency is 1000/3000 = 1/3, while 1800 J is also dissipated within the drive.
- The useful gravitational-energy gain remains 1000 J because mass and height do not change.
- At 50% overall efficiency, input energy is 1000/0.50 = 2000 J; mean input power is 2000/5 = 400 W.
- The faster hoist draws greater mean power yet uses less energy per lift. A supply must meet its power demand; energy cost follows energy use rather than power alone.
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