Potential Energy Stored energy due to the relative position of an object In the field of a field force (i.e., gravity, electrostatic, magnetic) In relation to a “normal” configuration (i.e., compressed spring, bent ruler)

Gravitational Potential Energy Depends on the height of an object relative to an arbitrary “zero” level PE g = GPE = m x g x h (mass x acceleration of gravity x height)

Elastic (Spring) Potential Energy Depends on the distance compressed or stretched PE elastic = SPE = ½ k ( Δ x) 2 (half the spring constant x distance squared) k = “the spring constant” units of N/m “how much force is stored in how much distance” Flexible spring = low k… Stiff spring = high k

Conservation of Mechanical Energy “Conserved” means constant over time What you have at the beginning Is what you have at the end It can, however, be in a different form Conserved quantities in physics: mass, energy, momentum, charge Mechanical energy = kinetic energy + gravitational potential energy + spring potential energy

Some Equations In the absence of friction: ME i = ME f ( TME i = TME f ) KE i + GPE i + SPE i = KE f + GPE f + SPE f In the presence of friction… when “work” gets done: TME i = TME f + W KE i + GPE i + SPE i = KE f + GPE f + SPE f + W

Work is the Bridge Work is the bridge between the displacement-and-force framework for the analysis of motion and the energy framework Force x distance = Work = Change in total mechanical energy