Work , energy and power

1. Work, energy and power Youshouldbeableto: statethedefinition of work done by a constantforce; understandthework done by a varyingforce; statethedefinition of kineticenergy, gravitationalpotentialenergy and elasticpotentialenergy; understandthat, whenfrictionalforces are absent, the total mechanicenergyisconserved; use thework-kineticenergyrelationthatstatesthatthework done bythe net forceisthechange in kineticenergy; understandthat, in thepresence of externalforces, thework done isthechange in themechanicalenergy; statethedefinition of power; calculatetheefficiency of simple machines; understandthatkineticenergyisonlyconserved in elasticcollisions.

2. Work done by a force Consider a constantforceFactingon a body of massm. Thebodymoves a distancedalong a straight line. We define a quantitycalledthework done bytheforceFby W = Fdcosθ whereθistheanglebetweentheforce and thedirectionalongwhichthemassmoves.

5. Work done by a varyingforce Theareaunderthegraphthat shows thevariation of themagnitude of theforcewithdistancetravelledisthework done.

6. Work done bygravity If a massis displaced horizontally, thework done bymgiszero. Ifthebodyfalls a vertical distance h, thenthework done byWismgh. Theforce of gravityisparalleltothedisplacement.

7. Work done bygravity Thework done bygravityisindependent of thepathfollowed and dependsonlyonthe vertical distanceseparatingtheinitial and final positions. Theindependence of thework done onthepathfollowedis a property of a class of forcescalledconservativeforces.

8. Gravitationalpotentialenergy Theabilityto do thisworkiscalledenergy. Whentheforce in questionistheweight, wecallthisenergygravitationalpotentialenergy: Ep = mgh Ifanexternalforceequalto mg isappliedtothemassvertically up and themassmoveswithoutaccelerationto a position h, thework done bytheexternalforceismgh. What has become of thiswork? Thiswork has goneintogravitationalpotentialenergy of themass. Thisenergyisstored as potentialenergy in the new position of themass.

9. Elasticpotentialenergy Similarly, if a springisinitiallyunstretched and anexternalforcestretchesitbyanamount x, thenthework done bythisexternalforceis½kx2. Thisworkisstored as elasticpotetialenergy in thespring. This a general result: whenanexternalforcechangesthestate of a systemwithoutacceleration and doesworkW in theprocess, thework so performedisstored as potentialenergy in the new state of thesystem.

11. Thework-kineticenergyrelation When a body of massmisacteduponby a net forceF, thenthisbodyexperiencesanaccelerationa=F/m in thedirection of F. Fromkinematics: Thework done bythe net forceon a bodyisequaltothechange in thekineticenergy of thebody Work done by net force = ∆EK

12. Examplequestions

13. Conservation of energy Considernowthe case wheretheonlyforcethatdoesworkon a bodyisgravity. Thework done bygravityis Which shows thatthe sum of thekinetic and potentialenergies of thebodystaysthesame. The total mechanicalenergyisconserved.

14. Examplequestions

17. Frictionalforces In thepresence of friction and otherresistanceforces, themechanicalenergy of a systemwillnotbeconserved. Theseforceswilldecreasethe total mechanicalenergy of thesystem. Similarly, externalforces, such as forcesduetoengines, mayincreasethemechanicalenergy of a system.

18. Examplequestion

19. Conservation of energy Thechange in themechanicalenergy has goneintootherforms of energynotincluded in themechanicalenergy, such as thermalenergy and sound. In thisway, total energyisconserved.

20. Power Poweristherate at whichworkisbeingperformed. P = ΔW/Δt

21. Kineticenergy and momentum Whereasmomentumisconserved in all cases, kineticenergyisnot. Whenkineticenergyisconserved, thecollisionissaidtobeelastic. Whenitisnot, thecollisionisinelastic. In aninelasticcollison, kineticenergyislost. Whenthebodiessticktogetherafter a collision, thecollisionissaidtobetotallyinelastic.

22. Examplequestion