ConservationOfEnergy lecture notes part 1.docx

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Conservation of Energy 1 of 8 Conservation of Energy The important conclusions of this chapter are: · If a system is isolated and there is no friction (no non-conservative forces), then KE + PE = constant (Our text uses the notation K +U = constant) · If there is friction, then KE + PE + E therm = constant. (E therm = thermal energy) · Two examples of PE (potential energy) PE grav = mgh PE elastic = (1/2)kx 2 Potential Energy So, how do we define potential energy, PE, and get PE grav = mgh ? If a force involves no dissipation (no friction), then it can be a special type of force called a con- servative force. The defining property of a conservative force is that the work done by the force depends only the initial and final positions, not on the path taken. We showed in a previous con- cept test that gravity is a conservative force. The force of friction is not a conservative force, be- cause the work done depends on the path taken: the longer the path the more work is done by friction. Conservative forces include: · gravity (F = mg) · the spring force, or elastic force (F = kx) · the normal force The normal force is something of a special case. The work done by the normal force is always zero, so the normal force is "trivially" path-independent: the work is zero, regardless of path, and regardless of initial and final positions.
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Conservation of Energy 2 of 8 Associated with every conservative force is a kind of energy called potential energy (PE or U). PE is a kind of stored energy. If a configuration of objects has PE, then there is the potential to change that PE into other kinds of energy (KE, thermal, light, etc ). The definition of the PE as- sociated with a conservative force involves the work done by that force. If a force F (such as gravity) is a conservative force, then we define the PE associated with that force by In words: the change in potential energy is the negative of the work done by the conservative force and it is therefore the positive of the work done by an external force opposing the conser- vative force. Only changes in PE are physically meaningful. We are free to set the zero of potential energy wherever we want. . In this formula, the height h is the height above (h+) or below (h ) the h=0 level. So h is really . So I should really write the formula as . If I choose to set PE i = 0 at h i = 0, then the formula becomes or simply, In the previous chapter, we showed that the work done by an external force to stretch or com- press a spring by an amount x is W ext = +(1/2)kx 2 .
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