1Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 1Hour Exam #1• Hour Exam I, Wednesday Feb. 8, in-class• Material from March Chapters 1,2,3,4,5Griffith Chapter 7• One page of notes (8.5” x 11”) allowed• Questions are multiple choice• Scantron sheets will be used -bring #2 HB pencils and calculator• In-class review, Monday Feb. 6On-line review questions at course web siteuw.physics.wisc.edu/~rzchowski/phy107Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 2From last time…• Work = Force x Distance• Energy = an object’s ability to do work• Kinetic energy of motion: Ekinetic=(1/2)mv2• Work - energy relation:Change in kinetic energy of a single object= net work done on it by all forces.• Many types of energy, e.g.– Kinetic– Gravitational– Electromagnetic– Chemical– Solar– NuclearFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 3Today…• Potential energy– An additional form of energy– Can store energy in a system, to be extracted later.• Conservation of energy: energy is never lost,but just changes form.• Power: How fast work is done.• Measurements and applications of power.Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 4The bowling ballθhAt top of swing, velocity of ball is zero,so it’s kinetic energy is zero.At the bottom of the swing, it’s velocityis very large, so it’s kinetic energy islarge.Where did this energy come from?Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 5WorkθInitial positionFinal positionhI do mgh of work on the bowling ball.Gravity did -mgh of work on the ball.Net work = 0.No change in kinetic energy.How much work was done on the Earth?None - the Earth did not move.Work = Force x DistanceFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 6• We say that energy was stored inthe system as potential energy.• Releasing the ball lets itaccelerate and turn the potentialenergy into kinetic energy.Now release the ballh2Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 7Where’s the energy?• When I did work, I transferred energy to the ball.• But zero net work done on the ball.• Ball’s kinetic energy has not changed.• Energy is ‘stored’ as potential energy.• Can think of this as energy stored in thegravitational field.Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 8Potential energy• The potential energy of a system is the workrequired to get the system into that configuration.• A little vague– For a pendulum, it is the work required to move the bob tothe top of its swing.– For a falling apple, it is the work required to lift the apple.– For a spring, it is the work required to compress the springFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 9Storing energyWater tower and pumphouseWater is pumped into tower whenelectricity cost is lowElectrical energy transformed intopotential energy.Work is extracted when needed totransport the water to homes.Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 10Energy conservation• In Newtonian mechanics, it is found that thetotal energy defined as the sum of kinetic(visible) and potential (invisible) energies isconserved.• E = K + U = constant• Many situations become much clearer froman energy perspective.Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 11Questions about the pendulumhtop of swingbottom of swingFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 12Conservation of energy• This was an example of conservation of energy.• Energy was converted from potential to kinetic.• As the pendulum swings, energy is converted backand forth, potential to kinetic.3Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 13QuestionIf the pendulum swing has 1.0 m vertical height, whatis the kinetic energy of the 1 kg pendulum bob atthe top of its swing?A. 1 JB. 10 JC. 0 JThe velocity is zero, so thekinetic energy is zero.Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 14QuestionIf the pendulum swing has 1.0 m vertical height, whatis the kinetic energy of the 1 kg pendulum bob atthe bottom of its swing?A. 1 JB. 10 JC. 0 JConservation of energy. Kinetic =potential, potential = mgh =(1kg)x(10m/s2)x(1m)=10 JFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 15Work Done by Gravity Change in gravitational energy, Change in energy = mghtrue for any path : h, is simply theheight difference, yfinal - yinitial A falling object converts gravitationalpotential energy to its kinetic energy Work needs to be done on an objectto move it vertically up - work doneis the same no matter what path istakenFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 16Potential E independent of path• Since the gravitational force is pointed directlydownward, only the vertical distance determinesthe potential energy.• We say it is ‘independent of the path’• This is true for most ‘non-contact’ (field) forces.– Gravity– Electromagnetism– Nuclear forcesFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 17QuestionIf balls are released from the same height on thesetwo different tracks, which will have greater speedat the bottom?A. Track AB. Track BC. Both sameABFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 18Testing conservation of energy• Speed at bottom of ramp should be related to change inpotential energy.• On flat section, use timer and distance traveled todetermine speed.h4Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 19Conservation of energyYou are jumping a 600 kg motorcycle between ramps.The ramps are 10 meters high.In order to jump successfully, the car must leave theramp with a speed of 10 m/s. (Kinetic En.=30,000 J)What kinetic energy must the motorcyle have enteringthe jump?A. 30,000 JB. 90,000 JC. 60,000 JFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 20What speedWhat speed must the 600 kg motorcycle have at theramp entrance (needs 90,000 J)?A. 10 m/sB. 13.2 m/sC. 17.3 m/s(1/2)mv2 = 90,000 J(300 kg)x(v)2 = 90,000 Jv = sqrt(300) m/s = 17.32 m/sFriday, Feb. 3 Phy 107, Spr. 06 Lecture 8 21Power ! P =Worktime, Joules(J)second(s) " Watts (W)Power is the rate at which work is doneIt is measured in Watts.(also Horsepower, 1 horsepower = 750 Watts)Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 22QuestionYou run up the first flight of stairs, then walk up thesecond flight. How do the work and power compareon the two flights?A. Work same on both flights, power also sameB. Work and power both differentC. Work same of both flights, power different`Friday, Feb. 3 Phy 107, Spr. 06 Lecture 8 23Example• Suppose the engine of a car puts outa fixed power P.• How would the velocity of the car change withtime if all that power went directly to movingthe car?Power is energy transfer /
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