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Potential Energy Calculations

**Please see attachment for complete questions


a) Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find ... {see attachment}

b) Consider the force exerted by a spring that obeys Hooke's law. Find {see attachment}

c) Finally, consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and direction of such a force are given by Newton's law of gravity: {see attachment}