1. Work and Energy
  2. Work
    1. Two components to scientific definition
      1. Force is applied to object
      2. Object moves
    2. Positive: force and displacement in same direction
    3. Negative: force and displacement in opposite directions
    4. Zero: force at right angles to displacement
  3. Example: Bicycle on Hill
    1. Draw diagram labeling forces
    2. Analyze direction of displacement versus forces
  4. Direction Of Force
    1. Only the component of force in the direction of motion does work
    2. Define system so direction of motion is adjacent side
  5. Work
    1. Work = force x distance
    2. W = F (cos q) d
    3. Unit = Nm = Joule (J)
  6. Types of Work
    1. Work done against a force
      1. ex. Lifting a box against gravity
    2. Work done to change velocity
      1. ex. Stopping a moving car
  7. Energy
    1. Exact nature of energy unknown
    2. Effects are observable
    3. Can calculate amount
    4. Definition: ability to create change
    5. Unit: Joule
  8. Mechanical Energy
    1. Energy due to movement or position
    2. Work transfers mechanical energy
    3. Maybe potential or kinetic
  9. Potential
    1. Stored energy, has the potential to do work or create change
    2. Method of storage:
      1. Position: raised, stretched, etc
      2. State: stored by state of molecules
  10. Gravitational Potential Energy
    1. Due to work against gravity
    2. Equal to the work done to raise object
    3. Stored as the potential to do work
    4. Equation is derived from W=Fcosqd
      1. F is weight (mg)
      2. q is 0
      3. d is vertical displacement of object (h)
  11. Gravitational Potential Energy
    1. \PE = mgh
    2. Unit: Joule
  12. Kinetic Energy
    1. Energy of a moving object
    2. Kinetic energy = 1/2 mass x velocity2
    3. KE = 1/2 mv2
    4. Unit = Joule
  13. Work and Kinetic Energy
    1. Start with 2nd Law: F = ma
    2. Multiply by d (distance)
    3. Fd = mad
    4. For straightline motion
      1. d = 1/2at2
    5. Substitute for d
    6. Fd - ma(1/2at2)
    7. Fd = 1/2 maat2
    8. Fd = 1/2 m(at)2
      1. v = at
    9. Substitute for v
    10. Fd = 1/2 mv2
    11. Left term is work
    12. Right term is kinetic energy
  14. Work-Energy Theorem
    1. Derived from F=ma
      1. F is net force on object
    2. Net work done equals the change in kinetic energy
    3. Wnet = KEf - KEi
    4. Kinetic energy in an object equals the work needed to stop it
    5. An object has KE because work has been done on it
    6. KE of an object may do work on another object
  15. Conservation of Energy
    1. Description of how energy changes
    2. Total amount of mechanical energy in a closed system is constant
    3. ET = KE + PE
  16. Analysis of a Pendulum
    1. Still at bottom: PE = 0, KE = 0
    2. Pulled side: PE max
    3. Moving at bottom: KE max
    4. Moving in between: combination of PE and KE
  17. Analysis of a Pendulum
    1. Why does it stop?
    2. ET = KE + PE + Q
  18. Mass Energy
    1. Einstein recognized equivalence of mass and energy
    2. Only impacts at atomic level
    3. Combines conservation of energy and matter
  19. Revised formula
    1. Et = KE + PE + Q + ME + . . . .
  20. Conservative Force
    1. Work done is independent of path
    2. Ex. Gravity, elastic forces, electric force
  21. Non-Conservative Force
    1. Work varies with path
    2. Ex. Friction, air resistance, normal force, propulsive force of rocket or motor
    3. Wnc = Ef - Ei = DKE + DPE
  22. Conservation of Energy
    1. Revised formula
    2. ET = KE + PE + Q + ME + Wnc
  23. Power
    1. The speed at which work can be done
    2. Working faster does not mean more work is done
  24. Power
    1. Rate of work
    2. Power = work/time
    3. P = W/t
    4. Unit = J/s = Watt (W)
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