1. Conservation of Mechanical Energy
Or the More Things Change the More They Stay the Same

2. Conservation of Mechanical Energy
Mechanical Energy includes kinetic energy, gravitational potential energy and elastic potential energy.
Mechanical Energy is conserved for a single object or system when there are no outside forces or when the outside forces are elastic gravitational or some other conservative (action at a distance) force.
ME conserved for elastic collisions, objects in freefall, objects sliding or rolling down inclined plane or roller coaster, pendulums, and masses on springs.

3. Elastic Collisions
Both momentum and mechanical energy are conserved in elastic collisions
ME is conserved for system of objects involved in collision
Energy only expressed as kinetic energy throughout collision=> no deformation or sound
E.G. Newton’s cradle, atomic, molecular and subatomic particle collisions

4. Objects in Freefall
Neglecting air resistance gravity is only outside force so ME is conserved.
ME conserved for single object in freefall
As object moves upward KE is transformed into PE g. As move down PE g is transformed into KE
All ME is PE g at top of trajectory and KE at bottom of trajectory=> PE g at top = KE at bottom

5. Pendulums
Neglecting friction and air resistance, tension and gravitational force are outside forces. Tension acts perpendicular to motion so does no work=> ME conserved for the bob
As bob moves upward KE is transformed into PEg. As move down PE g is transformed into KE
All ME is PE g at top of swing and KE at bottom of swing=> PE g at top = KE at bottom

6. Horizontal Mass on Spring
Neglecting friction and air resistance for mass on horizontal spring only outside forces are spring and gravity. Later acts perpendicular to motion => ME conserved for mass
When spring is extending KE is transforming into PE elastic. When relaxing PE elastic transforms into KE.
ME is all KE at equilibrium position and all PE elastic at extremes
PE elastic at extreme = KE at equilibrium

7. Inclined Planes and Roller Coasters
Neglecting air resistance and friction outside forces are gravity and normal force. Normal force is perpendicular to motion leaving only parallel gravitational component=> ME conserved.
As object moves downward PE g transformed into KE. As moves upward KE transforms into PE g.
ME is all PE at top and KE at bottom=> PE top = KE at bottom.

8. Conservation Laws Compared
System
Mechanical Energy Conservation
Linear Momentum Conservation
Elastic Collision X
Inelastic Collision
Explosion
Free Fall and Pendulums,
Inclined Planes and Roller Coasters
Mass on Spring Systems