Work Done By Variable Force
A force F = 2x + 3 (in Newtons) acts on a body, where x is the displacement in meters. What is the work done when the body moves from x = 0 to x = 4 m?
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- work done by variable force
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
28 J
- Variable Force Formula: For a force that varies with position x, work is the integral of force over the path: W=∫x1x2F(x)dx.
- Set up Integral:
- W=∫04(2x+3)dx.
- Integration:
- W=[x2+3x]04.
- Evaluation:
- W=(42+3×4)−(02+0).
- W=(16+12)=28 J.
- Result: Total work done is 28 Joules.
This hard difficulty physics question is from the chapter work, energy and power, covering the topic of work done by variable force. It appeared in the 2025 exam.
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