A negative work is done when an applied force F and the corresponding displacement S are
- A.perpendicular to each other.
- B.parallel to each other.
- C.anti-parallel to each other.
- D.equal in magnitude.
Correct answer
Explanation
The correct answer is C, anti-parallel to each other. Work is negative when the force acts opposite to the displacement, because the angle between them is then 180°.
Work done is W = F S cos θ, where θ is the angle between the force and the displacement. For θ = 180°, cos θ = -1, so W = -FS. Negative work takes energy away from the moving body. Examples are the work done by friction on a sliding block, by brakes on a moving car, and by gravity on a ball thrown upwards. Work is positive when θ is less than 90° and zero when θ is exactly 90°.
A is wrong: when force and displacement are perpendicular, cos 90° = 0, so no work is done, as with a satellite in a circular orbit or a porter carrying a load on level ground. B is wrong: parallel force and displacement give cos 0° = 1, the largest positive work. D is wrong: force and displacement are different quantities with different units, so comparing their magnitudes says nothing about the sign of work.
Exam tip: W = FS cos θ: θ = 0° gives maximum positive work, θ = 90° gives zero work, θ = 180° gives negative work.
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