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For a force doing work on an object, under what condition is the work done negative rather than positive?
AWhen the force and displacement have the same direction
BWhen the force and displacement point in opposite directions
CWhen the force is larger than the object's weight
DWhen the object is moving at constant speed
Answer & Solution
Correct answer: B. When the force and displacement point in opposite directions
1. Work is W = F d cos theta, and the sign of cos theta depends on the angle between the force and displacement.
2. When force and displacement point in the same direction, theta is 0 degrees, cos theta is positive, and the work is positive.
3. When force and displacement point in opposite directions, theta is 180 degrees, cos theta is negative one, and the work comes out negative.
4. The size of the force relative to weight and whether the object moves at constant speed do not by themselves determine the sign of the work, only the relative directions of force and displacement do.
_Source: OpenStax College Physics (CC BY 4.0), Ch 7 "Work, Energy, and Energy Resources", section 7.1 Work: The Scientific Definition_
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