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

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.

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

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

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

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

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.

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