energy2

# energy2 - Physics 53 Energy 2 Things are more like they are...

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Physics 53 Energy 2 Things are more like they are now than they ever were before. — Dwight D. Eisenhower Conservative forces In general the work done by a force depends on the path taken from the initial position to the Fnal one, as well as on the location of those points. But, as we have seen, there are some forces for which the work depends only on the endpoints, not on the path. These are called conservative forces . Consider a trajectory which ends where it began, forming a closed curve. The work done by a conservative force for such a path must be zero. We therefore have two equivalent ways to deFne a conservative force: Conservative force: two deFnitions F d r 1 2 is independent of path F d r = 0 In the second case, the small circle around the integral sign denotes a line integral following a closed curve , one that ends where it began. Potential energy Suppose a conservative (net) force moves a particle from point 1 to point 2, during which time it does positive work, so the kinetic energy increases. Now suppose the same force then moves the particle back to point 1. The work done in this part must be exactly the negative of the other, because the total work done by a conservative force in a round trip is zero. The particle's kinetic energy thus decreases back to its original value. Is kinetic energy “created” by the force in the trip from 1 to 2 and then “destroyed” in the return trip? It seems more useful, since this process could be repeated indeFnitely, to imagine that the “lost” kinetic energy during the trip from 2 to 1 is stored somewhere and can be returned to the particle during its next trip from 1 to 2. PHY 53 1 Energy 2

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The idea of storing energy is the basis of potential energy . It is one of the most important concepts in physics. It is called “potential” because it has the possibility of being converted back into kinetic energy. Where is the energy stored? That turns out to be a very deep question, to which we will return when we discuss the gravitational Feld. Potential energy, denoted by U , is associated with the conservative force, i.e., with the interaction between the particle and its environment. It is a property of the system of interacting objects . It is not (like kinetic energy) a property of any single particle. To make the idea quantitative, we introduce a deFnition:
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energy2 - Physics 53 Energy 2 Things are more like they are...

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