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