# Chapter 8 Potential Energy And Conservation Of Energy

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pring force (conservative forces) do work,(No friction, no resistance (in air, on ice, not water ),no external forces or energy source does work, (no human,animal, motor, lift, push ) K U will stay unchanged.Kinetic EnergyU mgyPotential EnergyK ½mv2U ½k( x) 2Got Conservation of Mechanical Energy, when Wnc 0Copyright Dr. Weining Man and Pearson

8-3 Conservation of Mechanical EnergyEnergy conservation can make kinematicsproblems much easier to solve:When there is no work done bynon-conservative forces,Ki Ui Kf Uf; (happily)You don’t need to calculate workhere, because work done bygravity and spring forces areincluded in the change of potentialenergy. K - U Work of gravity or springCopyright Dr. Weining Man and Pearson

8-3 Conservation of Mechanical EnergyYou can solve v easily if h is known.Q1: If initial height was lower, thefinal speed to hit the ground wouldbe more or less?Q2: Had the initial height wasdoubled, the final speed to hit theground would becomeHalf, Twice,, or 4 times ?Similarly, if an object was thrownUPWARD with v0, maximum heightcan be easily found.Copyright Dr. Weining Man and Pearson

Figure 8-9When no work is done bynon-conservative forces,Ki Ui Kf Uf;When we look for changeof KE or PE, only initialand final height matters.½ mv02 mgh0 ½ mvf2 mghfNo matter which direction velocities are.If no friction, K U does not change. It’s true forall middle positions, not only the start and the end.You have ½ mv02 mgh0 ½ mvf2 mghf ½mv12 mgh1 ½ mv22 mgh2,or any middle position at 1,2,3, . regardlessvelocity directions.

For A object launched at angle θ and V0, throughthe entire motion, for all points in between.½ mv02 mgh0 ½ mvf2 mghf ½mv12 mgh1 ½ mv22 mgh2At maximum height,½ mv02 mgh0 ½mvtop2 mghmaxIs vtop 0 ?Sure, vtop y 0,But vtop vtop x v0cosθ; ax 0.But for a pendulum, or an object sliding up alone aincline, track etc, total v IS zero at maximum height.Copyright 2010 Pearson Education, Inc.Copyright Dr. Weining Man

Example, A truck slide down for distance Lfrom rest, on an incline. (θ)LIf there is no friction,After distance L what willhθbe its final speed?Don’t memorize conclusionslike v2 2gh0 mgh0 ½ mvf2 0 It only works without frictionand when initial or final v 0h0 L sinθLearn the physics,mg L sinθ ½ mvf2 UNDERSTAND it,UNDERSTAND when to useg L sinθ ½ vf2vf2 2g L sinθ the sweetKi Ui Kf Uf;Copyright 2010 Pearson Education, Inc.

Total Energy conservation:Energy cannot be created or destroyed. It onlychange forms.When Energy seems to be created/ destroyed, itactually is being converted from/to other forms.When friction does work, it reduces kineticenergy and convert that into Heat.Copyright Dr. Weining Man

When nonconservative forces do work, the total mechanicalenergy is not conserved: we need to calculate work done byNon-Conservative forces. (Wnc sum of all work except formg and spring’s work)Wexternal, Wpush, pull, wind, man, wave, elevator, Kinetic EnergyU mgyPotential EnergyK ½mv2U ½k( x) 2Wkinetic-friction – fkdCopyright Dr. Weining Man and Pearson

8-4 Work Done by Nonconservative ForcesIn this example, thenonconservative forceis water resistance:By comparing Ef and EiYou can find Wnc,which is otherwise hardto calculate since waterresistance may not beconstant force.Copyright Dr. Weining Man and Pearson

m 1000kg, v0 0, µk 0.2φ 30ο, d 0.5m,Find vfN mgcosφfk µkN µkmgcosφfk 0.2 9800 cos30 1697(Ν)New Problem solving strategy :1.Ananlyze all forces and decide whether NonConservative force does work or not.2. Only compute total work down by NC forces3. Set equationYeah! No need to calculate ALL work anymore, when I understand conservative andnon-conservative forces.WNC Wfk – fk d – 1697*0.5 – 849 J ;Kf Uf Ki Ui WNC½mvf2 0 0 mgh – fk d ;h d sin φ½mvf2 mg d sin30 – fk d 1601Jvf 1.79m/s

Summary of Chapter 8 Conservative forces conserve mechanicalenergy. They do work to convert energy betweenKinetic Energy and Potential Energy. Conservative force does zero work on anyclosed path Work done by a conservative force isindependent of path Conservative forces: gravity, spring force. Nonconservative forces convert mechanicalenergy into other forms.Copyright Dr. Weining Man and Pearson

Summary of Chapter 8 Work done by nonconservative force on closedpath is not zero, and depends on the path Nonconservative forces: friction, air resistance,pull, push, most other forces Energy in the form of potential energy can beconverted to kinetic or other forms Work done by a conservative force is thenegative of the change in the potential energy Gravity: U mgy Spring: U ½ k( x)2Copyright Dr. Weining Man and Pearson

Summary of Chapter 8 Mechanical energy is the sum of the kinetic andpotential energies; it is conserved only insystems with purely conservative forces to dowork. Nonconservative forces change a system’smechanical energy Work done by nonconservative forces equalschange in a system’s mechanical energy (K U) Gravitational Potential energy at distance r fromearth center:U GMearth m/rCopyright Dr. Weining Man and Pearson

reduces Kinetic Energy and increase Potential Energy A: The energy is stored as potential energy. PE is like your saving account. Potential energy gain (mg h) during the rising part. We can get that energy back as kinetic E if the ball falls back off. During falling, Kinetic Energy will increase mg h. Potential energy will reduce mg h.

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