Work and Energy

Physicist’s definition of “work” dist∥ A scalar (not a vector) dist Work = F x dist∥

Atlas holds up the Earth But he doesn’t move, dist∥ = 0 Work= Fx dist∥ = 0 He doesn’t do any work!

Garcon does work when he picks up the tray but not while he carries it around the room dist is not zero, but dist∥ is 0

This scalar quantity is given a special name: kinetic energy Why this definition? A vector equation Newton’s 2nd law: F=m a Definition of work + a little calculus A scalar equation Work= change in ½mv2 This scalar quantity is given a special name: kinetic energy

the Work-Energy Theorem Work = change in KE This is called: the Work-Energy Theorem

Units again… Kinetic Energy = ½mv2 m2 s2 kg work = F x dist∥ =1Joule m same! =1Joule m s2 N m =kg m

change in vertical height Work done by gravity end start dist dist∥ change in vertical height W=mg Work = F x dist∥ = -mg x change in height = -change in mg h

Gravitational Potential Energy Workgrav = -change in mgh This is called: “Gravitational Potential Energy” (or PEgrav) change in PEgrav = -Workgrav Workgrav = -change in PEgrav

If gravity is the only force doing work…. Work-energy theorem: -change in mgh = change in ½ mv2 0 = change in mgh + change in ½ mv2 change in (mgh + ½ mv2) = 0 mgh + ½ mv2 = constant

Conservation of energy mgh + ½ mv2 = constant Gravitational Potential energy Kinetic energy If gravity is the only force that does work: PE + KE = constant Energy is conserved

Free fall (reminder) height t = 0s 80m V0 = 0 75m t = 1s V1 = 10m/s

m=1kg free falls from 80m mgh ½ mv2 sum t = 0s V0 = 0 h0=80m 800J 0 750J 50J V1 = 10m/s; h1=75m 800J t = 2s V2 = 20m/s; h2=60m 600J 200J 800J t = 3s V3 = 30m/s; h3=35m 350J 450J 800J t = 4s V4 = 40m/s; h4=0 0 800J 800J

T is always ┴ to the motion pendulum T W=mg Two forces: T and W T is always ┴ to the motion (& does no work)

Pendulum conserves energy E=mghmax E=mghmax hmax E=1/2 m(vmax)2

Roller coaster

Work done by spring = - change in ½ kx2 Work done by a spring Relaxed Position F=0 x F I compress the spring (I do + work; spring does -work) Work done by spring = - change in ½ kx2

Spring Potential Energy Workspring = -change in ½ kx2 This is the: “Spring’s Potential Energy” (or PEspring) Workspring = -change in PEspring change in PEspring = -Workspring

If spring is the only force doing work…. Work-energy theorem: -change in ½ kx2 = change in ½ mv2 0 = change in ½ kx2 + change in ½ mv2 change in ( ½ kx2 + ½ mv2) = 0 ½ kx2 + ½ mv2 = constant

Conservation of energy springs & gravity mgh + ½ kx2 + ½ mv2 = constant Gravitational potential energy spring potential energy Kinetic energy If elastic force & gravity are the only force doing work: PEgrav + PEspring + KE = constant Energy is conserved

example grav PE KineticE Spring PE

Two types of forces: “Conservative” forces “Dissipative” forces forces that do + & – work Gravity Elastic (springs, etc) Electrical forces … “Dissipative” forces forces that only do – work Friction Viscosity …. -work  heat (no potential energy.) -work  change in PE

(-)Work done by frictionheat

Thermal atomic motion Heat energy= KE and PE associated with Air solid the random thermal motion of atoms

Work-energy theorem (all forces) Workfric = change in (PE+KE) Work done dissipative Forces (always -) potential energy From all Conservative forces Kinetic energy -Workfric = change in heat energy Workfric = -change in heat energy -change in Heat Energy = change in (PE+KE)

Work – Energy Theorem (all forces) 0 = change in Heat Energy + change in (PE+KE) 0 = change in (Heat Energy+PE+KE) Heat Energy + PE + KE = constant Law of Conservation of Energy

Energy conversion while skiing Potential energy Potential energykinetic energy Friction: energy gets converted to heat

1 calorie = heat energy required to raise the Units again Heat units: 1 calorie = heat energy required to raise the temp of 1 gram of H2O by 1o C Kg m2/s2 1 calorie= 4.18 Joules

Food Calories 1 Calorie = 1000 calories = 1Kcalorie The Calories you read on food labels 1 Calorie= 4.18x103 Joules 7 x 106 J 8 x 105 J 2 x 106 J

electrical energy each second to produce light Power amout of energy elapsed time Rate of using energy: Power = Joule second Units: 1 = 1 Watt A 100 W light bulb consumes 100 J of electrical energy each second to produce light

Other units 1 Horsepower = 750 Watts Over a full day, a work-horse can have an average work output of more than 750 Joules each second 1 Horsepower = 750 Watts

HECO charges us about 15 cents /kW-hr Kilowatt hours energy time Power =  energy = power x time  power unit x time unit = energy unit Kilowatts (103 W) hours (3600 s) Elec companies use: x 1 kilowatt-hour = 1kW-hr = 103 W x 3.6x103 s = 3.6x106 Ws J HECO charges us about 15 cents /kW-hr