Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 20

All force are CONSERVATIVE or NON-CONSERVATIVE

A force is conservative if: The work done by the force in going from to is independent of the path the particle follows The work done by the force when the particle goes from to around a closed path, back to, is zero. or

Non-conservative: doesn’t satisfy the above conditions

If a force can be written as the derivative of some function, that force is conservative. U(x) is called the potential energy function for the force If such a function exists, then the force is conservative 1D case:

does NOT depend on path! 1D case:

does NOT depend on path! If F x (x) is known, you can find the potential energy function as

Force of gravity: Potential energy function: Spring: Potential energy function:

A particle moves in one dimension under the influence of a single conservative force given by where  is a given constant. Take the potential energy reference to be at x i =0 such that: and calculate the potential energy function U(x).