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

(all forces which do work are conservative)

Substitution into (1) gives