Power Developed Against Gravity And Friction
A cyclist of total mass 70 kg rides up a slope inclined at 30 degrees to the horizontal at a steady speed of 4 m/s, with friction negligible. Taking g as 10 m/s squared, what power does the cyclist develop against gravity?
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- power developed against gravity and friction
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
1400 W
As stated in NCERT Class 11, Chapter 6 (Work, Energy and Power), power can be computed as the rate of doing work against the component of gravity along the slope, P = (mg sin theta) × v. The gravitational force component along the incline is mg sin(30) = 70 × 10 × 0.5 = 350 N. Multiplying by the speed gives P = 350 × 4 = 1400 W. Because the cyclist moves at constant speed, the applied force exactly balances this gravity component along the slope. The option 2800 W uses the full weight without the sine factor. The option 700 W omits the speed correctly but uses half the force. The option 2424 W mistakenly uses cos(30) instead of sin(30). A magnitude check: only the slope component of weight opposes the climb, and at 30 degrees this is half the weight, so 1400 W is consistent for a steady ascent at 4 m/s.
This hard difficulty physics question is from the chapter work, energy and power, covering the topic of power developed against gravity and friction. It appeared in the 2025 exam.
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