Momentum Energy conservation Momentum Newtons 2 nd law

Momentum & Energy conservation

Momentum

Newton’s 2 nd law (shorthand version) F = ma change in v a = time F= m change in v time

Car truck collision Fc Fc = mc change in vc time Fc t = mc change in vc Ft Ft = mt change in vt time Ft t = mt change in vt Fc t + Ft t = mc change in vc + mt change in vt (Fc + Ft)t =change in mcvc + change in mtvt (Fc + Ft)t =change in (mcvc + mtvt)

Car truck collision Fc Ft (Fc + Ft)t =change in (mcvc + mtvt) Newton’s 3 rd law: Fc = -Ft (Fc + Ft)t = 0 0 = change in (mcvc + mtvt) mcvc + mtvt stays constant!

Momentum = mv mcvc = momentum of car this changes Mtvt= momentum of thruck this changes mcvc + mtvt = total momentum this stays constant Before = -40 After = -40 Momentum is conserved!

True for all collisions before =+20 after =+20 visit www. physicsclassroom. com/mmedia/index. html

Revisit the canoe at the dock Initial momentum canoe = 0 boy = 0 Total = 0 final momentum canoe = mcvc boy = mbvb Total = 0

Momentum is a vector: mv collision in 2 dimensions

eating Finding nemo

Billiard balls 2 before 1 ptot after 2 1 ptot

Conservation of momentum on a sub-atomic level before p ptot p proton p- meson after p p p- meson ptot

Rocket travel before P 0 after exhaust p P 0 + p

Rifle recoil m. V m V

Machine-gun granny

Work and Energy

Physicist’s definition of “work” dist∥ (n A s ot ca a lar ve ct or ) 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

Why this r o t n c definition? ve atio A qu e Newton’s 2 nd law: A eq sca ua lar tio n F=m a Definition of work + a little calculus Work= change in ½mv 2 This scalar quantity is given a special name: kinetic energy

Concept of Kinetic Energy Emilie du Châtelet (1706 -1749) Brilliant mathematician One of Voltaire’s lovers

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

Units again… Kinetic Energy = ½mv 2 work = F x dist∥ 2 m kg 2 s same! m N m =kg 2 m s =1 Joule

Work done by gravity end start 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 Workgrav in = PE-change in PE grav = -Work grav

If gravity is the only force doing work…. Work-energy theorem: -change in mgh = change in ½ mv 2 0 = change in mgh + change in ½ mv 2 change in (mgh + ½ mv 2) = 0 mgh + ½ mv 2 = constant

Conservation of energy mgh + ½ mv 2 = constant Gravitational Potential energy Kinetic energy If gravity is the only force that does work: PE + KE = constant Energy is conserved

Free fall height (reminder) t = 0 s V 0 = 0 t = 1 s 80 m 75 m V 1 = 10 m/s 60 m t = 2 s V 2 = 20 m/s t = 3 s 35 m V 3 = 30 m/s t = 4 s V 4 = 40 m/s 0 m

m=1 kg free falls from 80 m t = 0 s V 0 = 0 h 0=80 m mgh 800 J ½ mv 2 sum 0 800 J 50 J 800 J t = 1 s V 1 = 10 m/s; h 1=75 m 750 J t = 2 s V 2 = 20 m/s; h 2=60 m 600 J 200 J 800 J 350 J 450 J 800 J t = 3 s V 3 = 30 m/s; h 3=35 m t = 4 s V 4 = 40 m/s; h 4=0 0 800 J

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

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

Roller coaster

Work done by a spring Relaxed Position F=0 F x I compress the spring (I do + work; spring does -work) Work done by spring = - change in ½ kx 2

If spring is the only force doing work…. Work-energy theorem: -change in ½ kx 2 = change in ½ mv 2 0 = change in ½ kx 2 + change in ½ mv 2 change in ( ½ kx 2 + ½ mv 2) = 0 ½ kx 2 + ½ mv 2 = constant potential energy in the spring

Conservation of energy springs & gravity mgh + ½ kx 2 + ½ mv 2 = constant Gravitational spring potential energy Kinetic energy If elastic force & gravity are the only forces doing work: PEgrav + PEspring + KE = constant Energy is conserved

example grav PE Kinetic. E Spring PE

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

(-)Work done by friction heat

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

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

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

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

Units again Heat units: 1 calorie = heat energy required to raise the temp of 1 gram of H 2 O by 1 o C Kg m 2/s 2 1 calorie= 4. 18 Joules

Food Calories 1 Calorie = 1000 calories = 1 Kcalorie The Calories you read on food labels 1 Calorie= 4. 18 x 103 Joules 7 x 106 J 8 x 105 J 2 x 106 J

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

Other units 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 Power = time energy = power unit Elec companies use: x Kilowatts (103 W) x time unit = energy unit x hours (3600 s) 1 kilowatt-hour = 1 k. W-hr = 103 W x 3. 6 x 103 s = 3. 6 x 106 Ws J

on w 300 t u abo In Hawaii electrical energy costs about 25 cents /k. W-hr What is the cost in Seoul?