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A conservative force, such as the gravitational force, is defined by what property of the work it does?
AIts work depends only on the time the motion takes
BIts work is always exactly zero over any path
CIts work depends on the exact path traveled
DIts work depends only on start and end points, not the path
Answer & Solution
Correct answer: D. Its work depends only on start and end points, not the path
1. A conservative force is defined as one for which the work done by or against it depends only on the starting and ending points of the motion.
2. This is exactly why a potential energy can be defined for a conservative force, since the work done has a single value tied only to position, not to the route taken.
3. Depending on the path traveled is instead the hallmark of a nonconservative force, and depending only on elapsed time does not match how work is defined at all.
4. The work done by a conservative force is not generally zero, since raising or lowering an object against gravity clearly does nonzero work.
_Source: OpenStax College Physics (CC BY 4.0), Ch 7 "Work, Energy, and Energy Resources", section 7.4 Conservative Forces and Potential Energy_
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