Sep. 22, 2004 Phy 107, Lecture 8HW and Exam #1• Hour Exam I, Wednesday Sep 29, in-class• Material from Chapters 1,3,4,5,6• One page of notes (8.5” x 11”) allowed• Questions are multiple choice• Scantron sheets will be used -bring #2 HB pencils and calculatorOn-line review questions added to web siteuw.physics.wisc.edu/~rzchowski/phy107HW#3Chap. 5 Concept: 22, Problems: 2, 4Chap. 6 Concept: 18, Problems: 2, 6Sep. 22, 2004 Phy 107, Lecture 8From Last Time… Chaos• Although Newton’s laws are deterministic, somedynamical systems depend so sensitively on the initialconditions that the final outcome is almost impossibleto predict.• e.g. models for forecasting weather, a single planetorbiting two suns, etc.• ‘Chaotic’ systems have this property.• The motion can be quite complicated, but can beunderstood to some degree.• In a driven system, chaos is often approached in aprocess where the period of motion doubles,quadruples, etc, before becoming chaotic.Sep. 22, 2004 Phy 107, Lecture 8Today’s lecture• Work• Energy• Relation between work and energy• Different forms of energy• Transferring energy from one object to another.• Conservation of energy.Sep. 22, 2004 Phy 107, Lecture 8Work• Work is done whenever a body iscontinually pushed or pulled through a distance.• Twice as much work is done when the body is movedtwice as far.• Pushing twice as hard over the same distance doestwice as much work.• Work = Force x DistanceSep. 22, 2004 Phy 107, Lecture 8Work, cont.• Force has units of Newtons (N)Distance has units of meters (m) So work has units of N-m, defined as Joules (J).• Example:The Earth does work on an apple when the apple falls.The force applied is the force of gravity• Example:I do work on a box when I push it along the floor.The force applied is from my musclesSep. 22, 2004 Phy 107, Lecture 8QuestionA man holds up a bowling ball in a fixed position. Thework he does on the ball A. Depends on the weight of the ball. B. Cannot be calculated without more information. C. Is equal to zero.Although the man is exerting force against gravity to hold thebowling ball up, he has not shifted its position.So the work done by him on the ball is zero.Work = Force x DistanceSep. 22, 2004 Phy 107, Lecture 8Multi-part questionI lift a body weighing 1 N upward at a constant verticalvelocity of 0.1 m/s. The net force on the body isA. 1 N upwardB. 1 N downC. 0 NSince the acceleration is zero,the net force must be zero.Sep. 22, 2004 Phy 107, Lecture 8Question, cont.The force I exert on the body isA. 1 N upB. 1 N downC. 0Since net force is zero, and thegravitational force is 1 N down,I must be exerting 1 N up.Sep. 22, 2004 Phy 107, Lecture 8Question, cont.After lifting the 1 N body a total distance of 1 m, thework I have done on the body isA. 1 JB. 0.1 JC. 0 JWork = Force x Distance = 1 N x 1 m = 1 N-m = 1 JouleSep. 22, 2004 Phy 107, Lecture 8EnergyA object’s energy is the amount of work it can do.Energy comes in many formsIt is convertible into other forms without loss(i.e it is conserved)Kinetic EnergyGravitational Energy Electrical EnergyThermal EnergySolar EnergyChemical EnergyNuclear EnergySep. 22, 2004 Phy 107, Lecture 8Energy of motionIn outer space, I apply a force of 1 N to a 1 kg rock for adistance of 1 m.I have done Force x Distance = (1 N)x(1 m) = 1 J of work. After applying the force for 1 m,the rock is moving at some final velocity vfinalas a result of the acceleration Force/mass.So the energy I expended in doing work has caused thebody to change its velocity from zero to vfinal.Sep. 22, 2004 Phy 107, Lecture 8Kinetic energy (energy of motion)• Work = Force x Distance• A constant applied force leads to an acceleration.• After the distance is moved, the body is traveling atsome final velocity vfinal.• So the result of the work done is to change thebody’s velocity from zero to vfinalSep. 22, 2004 Phy 107, Lecture 8Work-energy relation• The acceleration of the bodyis related to the net force by F=ma€ Work = Fnet× d = (ma) × d = m × (ad)€ Work = Fnet× d =12mvfinal2 is called Kinetic Energy, or energy of motion€ 12mv2€ vfinal= at = a2da= 2ad€ ad =12vfinal2For a bodyinitially at rest,constant accel.says€ d =12at2, so t =2daSep. 22, 2004 Phy 107, Lecture 8Work-energy relation• The kinetic energy of a body is€ 12mv2• The kinetic energy will change by an amount equalto the net work done on the body.Sep. 22, 2004 Phy 107, Lecture 8A more general form• If the object initially moving at some velocity vinitialit has kinetic energy• As the result of a net work Wnet, the velocityincreases to vfinal,and the Kinetic Energy increases to€ 12mvinitial2€ 12mvfinal2€ Wnet=12mvfinal2−12mvinitial2The change in kinetic energy is equal to thenet work done.Sep. 22, 2004 Phy 107, Lecture 8QuestionWhen you do positive work on an object, its kineticenergy A. increases. B. decreases. C. remains the same.Sep. 22, 2004 Phy 107, Lecture 8Gravitational energy• An object in a gravitational field can do work whenit falls.• We might say that energy is stored in the system.Sep. 22, 2004 Phy 107, Lecture 8Ball falls down in gravity• Ball initially held at rest.– vinitial==0– Kinetic energy = 0• Ball released.• Gravitational force = mg, falls with acceleration g• Work done by gravitational force in falling distanceh is Force x Distance = mgh.• Ball final kinetic energy = mgh =€ 12mvfinal2Sep. 22, 2004 Phy 107, Lecture 8Ball moved up in gravity• Work done by me on ball– Ball initially held at rest by me.– I move the ball slowly upward a distance h.– Force applied by me is mg upward.– Work done by me on ball is Force x Distance = mgh• Work done by gravity on ball– Force x Distance = -mgh• Net (total) work done on ball = mgh-mgh = 0• Consistent with zero change in kinetic energy of ballduring this time (I.e. ending velocity is same asstarting velocity).Sep. 22, 2004 Phy 107, Lecture 8Work 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 istakenSep. 22, 2004 Phy 107, Lecture 8QuestionTwo marbles, one twice as heavy as the other, are dropped to theground from
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