Posted by Anonymous on Saturday, March 15, 2008 at 1:11pm.
If a mechanical system is conservative, the loss of potential energy goes into kinetic energy and any loss of kinetic energy shows up as potential energy.
In other words, the sum of potential and kinetic energy is constant in a conservative mechanical system.
If energy leaves the mechanical system, for example is conducted and radiated away as heat energy, then the sum of kinetic and potential energy in the mechanical system decreases.
An example of a conservative physics problem is a rock falling off the cliff until it hits the ground. If air resistance is ignored (note you have to say that to keep the problem conservative) any m g h lost becomes (1/2) m v^2 and the sum of potential (mgh) and kinetic (1/2)m v^2 energy is constant all the way down. at any height h we can calculate v from that relationship.
When the rock hits the ground, the whole analysis falls apart. The potential energy is gone and the kinetic enrgy is gone., both probably as heat in the earth and a slight warming of the rock.
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