Physics Tutorial
Conservative Forces and Conservation of Energy (Proof)
Intro
In this short section we will
a) define conservative forces and
b) prove that such forces conserve a quantity we call energy for constant mass systems.
A conservative force is defined as:
(1)
Where is a function of the coordinates.Now we multiply both sides by
. We get:
(2)
Where we used Newton’s second law in the first equal sign. It is left to the reader to prove:
(3)
Where is the velocity. Using the equations above we have:
(4)
Defining energy to be the sum of the kinetic energy and the potential energy
we have:
(5)
In other words , the standard conservation of energy.
Sample Problem
Solution
For the first equality we have:
For the second equality we have:
(1)
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