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A person carries a briefcase at constant velocity across a level floor, so the upward force from her arm is perpendicular to the horizontal displacement. How much work does her arm do on the briefcase?
AA large positive amount, force is clearly exerted
BA negative amount, since the briefcase does not fall
CZero work, since the force is perpendicular to motion
DIt depends on how heavy the briefcase happens to be
Answer & Solution
Correct answer: C. Zero work, since the force is perpendicular to motion
1. Work depends on the component of force along the direction of displacement, W = F d cos theta.
2. When the force is perpendicular to the displacement, theta is 90 degrees and cos 90 degrees is zero, so the work done is zero regardless of how large the force is.
3. This is exactly the situation for carrying a briefcase horizontally at constant speed, since the supporting force is vertical while the motion is horizontal.
4. A large positive or negative value would require a force component along the motion, and the briefcase's weight does not change this geometric fact about the angle between force and displacement.
_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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