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Work and Energy Physics 100 Chapt 5

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**Physicist’s definition of “work”**

dist∥ A scalar (not a vector) dist Work = F x dist∥

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**Atlas holds up the Earth**

But he doesn’t move, dist∥ = 0 Work= Fx dist∥ = 0 He doesn’t do any work!

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**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

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**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

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**the Work-Energy Theorem**

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

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

same! =1Joule m s2 N m =kg m

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**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

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**Gravitational Potential Energy**

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

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**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

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**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

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

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**m=1kg free falls from 80m mgh ½ mv2 sum t = 0s V0 = 0 h0=80m 800J 0**

750J J V1 = 10m/s; h1=75m 800J t = 2s V2 = 20m/s; h2=60m J J J t = 3s V3 = 30m/s; h3=35m J J J t = 4s V4 = 40m/s; h4= J J

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**T is always ┴ to the motion**

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

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**Pendulum conserves energy**

E=mghmax E=mghmax hmax E=1/2 m(vmax)2

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Roller coaster

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**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

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**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

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**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

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**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

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example grav PE KineticE Spring PE

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**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

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**(-)Work done by frictionheat**

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**Thermal atomic motion Heat energy= KE and PE associated with Air solid**

the random thermal motion of atoms

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**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)

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**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

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**Energy conversion while skiing**

Potential energy Potential energykinetic energy Friction: energy gets converted to heat

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**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

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**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

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**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

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**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

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**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

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Physics Section 5.2 Define and apply forms of mechanical energy. Energy is the ability to do work. Kinetic energy is the energy of an object due its motion.

Physics Section 5.2 Define and apply forms of mechanical energy. Energy is the ability to do work. Kinetic energy is the energy of an object due its motion.

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