Work and Energy
Work and Energy Warm-up What is our everyday definition of work? Do you think it has the same meaning in physics? Name as many forms of energy as you can. How does a rollercoaster take advantage of the Law of Conservation of Energy? How does friction impact the Law of Conservation of Energy?
Work in Physics… A measure of energy transfer A force must be applied. An object must move. A component of the force must be in the same direction as movement.
Physicist’s definition of “work” dist∥ A scalar (not a vector) dist Work = F x dist∥= Fdcosq
Which requires more force, using 1 m rope or 3 m rope?
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
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
Gravitational Potential Energy GPE= mgh This is called: “Gravitational Potential Energy” (or 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
Pendulum conserves energy E=mghmax E=mghmax hmax E=1/2 m(vmax)2
Roller coaster
Work done by a spring x F Relaxed Position F=0 I compress the spring (I do + work; spring does -work) PEspring = ½ kx2
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
Mechanical Energy… The total energy of a system Conservation of Energy… MEi = MEf ½ mvi2 + mghi = ½ mvf2 + mghf
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
(-)Work done by frictionheat
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 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
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
Review Questions… https://docs.google.com/forms/d/e/1FAIpQLSdbEkua0RNqHWKgfNoDwkFLyALPOy9TAwABJ4RxNvmfyZ4gNg/viewform?usp=sf_link
Coaster Creator… Use the simulator to design and build a rollercoaster. Observe energy transformations throughout the ride. http://content3.jason.org/resource_content/content/digitallab/4859/misc_content/public/coaster.html