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Work, Energy, and Power


Gravitation is often the context for conservation of energy problems on comprehensive exams. The work a conservative force performs on an object in moving it from A to B is does not depend on the path. Gravity is a conservative force. With gravitation, the work does not depend on the path taken. It depends only on the end points of the motion.

Let's talk about an important consequence. If the work performed were not path independent, a circular path could be conceived which would dissipate energy, but on the contrary, because gravity is a conservative force, any path which ends in the same initial position must necessary result in no change in potential energy state. This means that for an isolated gravitational system, the total energy must be be the same everywhere. And because or an initial state has both kinetic and potential energy, this total energy value gives the total of the kinetic energy plus the potential energy for all other possible states, regardless of the path between states, as long as only gravitational force is involved.

Work, Energy, and Power


Like gravitational systems, potential energy and kinetic energy also interconverts within electrostatic systems, although you need to be careful as to whether the MCAT passage refers to an ideal or approximately ideal system before you apply strict conservation of energy.

In other words, the passage may make it clear whether or not dissipation of energy through electromagnetic radiation is occuring, in which case the system may be losing energy to its environment as radiation.

Nevertheless, as with gravitational systems, it is absolutely true that the electrostatic potential energy depends on the relative position of the charges, not the specific path through which the charges have moved in the past. However, a change within a purely electromagnetic system may not be completely reversible due to emission of radiation. This is a somewhat advanced point really, and the MCAT would be probably give you some clues to coax you to think along these lines.

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