1. Conservation of Energy Or the More things change the more they stay the same.

2. Conservation Laws Momentum Conserved for all collisions Conserved when no outside forces Mechanical Energy Conserved for elastic collisions only Conserved when no outside forces Conserved when outside forces are due to gravity and springs Not conserved when friction and air resistance act.

3. Example: Elastic Collisions KE is being directly transferred w/o loss between objects involved in collision Energy is conserved only in elastic collisions – Inelastic collisions lose some energy due to deformation energy becoming thermal energy – Momentum is conserved in all collisions KE before = KE after Newton’s cradle explanation

4. Example: Freefall Gravity only major force acting if ignore air resistance PE top = KE bottom – mg  h top =1/2 mv bottom 2 – Mass has no effect since divides out

5. Example Pendulum Gravity is only major force acting if ignore friction of bearing and air resistance on bob PE greatest at top KE and v greatest at bottom F net and acceleration in direction of motion greatest at top mg  h top = ½ mv bottom 2

6. Example: Sliding Down an Inclined Plane or Roller Coaster Gravity only force acting on if ignore friction PE greatest at top KE, v greatest at bottom mg  h top =1/2 mv bottom 2 Comparing inclined planes – Same distance – Same starting height – Same starting and end height

7. Roller Coaster Physics Mechanical energy is combination of kinetic and gravitational potential energy – Sum of two is always the same (conserved) – KE and v maximum at lowest point – PE maximum at highest point – Equal heights result in equal speeds – First hill always the highest

8. Conservation Laws CaseMomentum Conservation Energy Conservation Elastic CollisionYes Inelastic CollisionYesNo Falling ObjectNoYes Sliding down incline (no friction) NoYes PendulumNoYes Mass on a springNoYes

9. Example: Spring Systems Spring only force acting if ignore deformation forces in stretch KE max at equilibrium, minimum at max stretch or compression, opposite for PE Vertical spring – 1/2 kx bottom 2 =mg  h top =1/2 mv equilibrium 2 Horizontal Spring – 1/2 kx fully extended 2 =1/2mv equi 2

10. Conservative Forces and Energy Conservation Like momentum, energy is always conserved when no outside forces act But unlike momentum, energy can also be conserved when only conservative forces act. – Conservative forces are those that vary with distance and allow PE to completely transform into KE w/o loss – Examples include gravity, springs, electric force, magnetic force, NOT friction or air resistance For first semester will use conservation of mechanical energy (KE+ PE elastic + PE gravity stays the same).

11. Conservation of Mechanical Energy Mechanical energy is conserved when there are no outside forces and when the only outside forces are due to gravity and springs. – True for elastic collisions, falling bodies, pendulums, inclined planes and roller coasters if ignore friction and air resistance. – Not true for systems where friction and air resistance are too large to ignore High speed flying Large friction bearings