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For a constant force F acting on an object that is displaced a distance d, with theta the angle between the force and displacement vectors, how is the work done by that force defined?
AW equals F plus d, multiplied by cos theta
BW equals F divided by d, times cos theta
CW equals F times d, divided by cos theta
DW equals F times d times cos theta
Answer & Solution
Correct answer: D. W equals F times d times cos theta
1. Work is defined as the product of the component of the force in the direction of motion and the distance through which the force acts.
2. The component of the force along the displacement is F cos theta, so multiplying by the distance d gives W = F d cos theta.
3. Adding F and d, or dividing one by the other, does not reduce to a component-of-force-times-distance definition.
4. Dividing by cos theta instead of multiplying would invert how the angle between force and displacement affects the work.
_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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