**EXAMPLE 3: POTENTIAL ENERGY**

Mass *m* is released from rest at *A* and
moves on the smooth collar from *A* to *B* under the
action of the spring and gravity. Calculate the speed of the particle
before it hits *B*. The spring has an initial length of .

**Solution:**

Force analysis:

*mg*is conservative- is conservative
*N*is perpendicular to the path at all points from A to B, so it does no work.

Balance of work and energy:

Starts from rest at A

Substitution into (1) gives