PHYS 1441 Section 002 Lecture #15

Transcription

1 PHYS 1441 Secton 00 Lecture #15 Monday, March 18, 013 Work wth rcton Potental Energy Gravtatonal Potental Energy Elastc Potental Energy Mechancal Energy Conservaton

2 Announcements Mdterm comprehensve exam Ths Wednesday, Mar. 0, n class n SH103 Covers CH1.1 through CH6.3 plus Appendces A1 A8 Mxture o multple choce and ree response problems No scantron s necessary Brng your calculator but do NOT nput ormulae A ormula sheet s gong to be provded Brng a blank scrap sheet or workng out problems Must transer your work and answers to the exam!! GOOD LUCK! Monday, Mar. 18, 013 PHYS , Sprng 013

3 Remnder: Specal Project #4 Usng the act that g9.80m/s on the Earth s surace, nd the average densty o the Earth. Use the ollowng normaton only but wthout computng the volume explctly The gravtatonal constant The radus o the Earth 0 pont extra credt Due: Monday, Mar. 5 G N m kg R E km You must show your OWN, detaled work to obtan any credt!! Monday, Mar. 18, 013 PHYS , Sprng 013 3

4 F r Work and Energy Involvng Knetc Frcton What do you thnk the work looks lke there s rcton? M v Statc rcton does not matter! Why? Then whch rcton matters? d v M Frcton orce F r works on the object to slow down The work on the object by the rcton F r s W r Knetc Frcton It sn t there when the object s movng. F r d cos( 180) F r d Δ KE F r d The negatve sgn means that the work s done on the rcton!! The nal knetc energy o an object, ncludng ts ntal knetc energy, work by the rcton orce and all other sources o work, s KE KE + W F d r t0, KE Monday, Mar. 18, 013 PHYS , Sprng 013 Frcton, Engne work tt, KE 4

5 Example o Work Under Frcton A 6.0kg block ntally at rest s pulled to East along a horzontal surace wth coecent o knetc rcton µ k 0.15 by a constant horzontal orce o 1N. Fnd the speed o the block ater t has moved 3.0m. F k M v 0 F Thus the total work s v M d3.0m Work done by rcton F k s Work done by the orce F s W F F d cosθ 1 3.0cos 0 36( J ) W k F k d F k d cosθ µ k mg d cosθ cos180 6( J ) W W W ( J ) F + k Usng work-knetc energy theorem and the act that ntal speed s 0, we obtan W W F + W k 1 mv Solvng the equaton or v, we obtan v W m m/ s 6.0 Monday, Mar. 18, 013 PHYS , Sprng 013 5

6 A 58kg sker s coastng down a 5 o slope. A knetc rctonal orce o magntude k 70N opposes her moton. At the top o the slope, the sker s speed s v 0 3.6m/s. Ignorng ar resstance, determne the speed v at the pont that s dsplaced 57m downhll. What are the orces n ths moton? F y Ex. Downhll Skng Gravtatonal orce: F g Normal orce: F N Knetc rctonal orce: k What are the X and Y component o the net orce n ths moton? Y component From ths we obtan Fgy FN o F N mg cos 5 What s the coecent o knetc rcton? + mg cos 5 o + k Monday, Mar. 18, 013 PHYS , Sprng 013 F N cos 5 o 515N µ k FN µ k k N F

7 Ex. Now wth the X component X component Total work by ths orce From work-knetc energy theorem Solvng or v F x W v W What s her acceleraton? Fgx ( F x ) k mg sn 5 k s mg sn 5 k KE W mv 0 m v KE Monday, Mar. 18, 013 PHYS , Sprng 013 o ( sn 5 o 70 ) 170N ma ( ) s ( o ) KE + F x ma a W + mv 0 m sn J mv W + KE W + ( ) F x m 58.93ms 1 mv ms

8 Potental Energy Energy assocated wth a system o objects è Stored energy whch has the potental or the possblty to work or to convert to knetc energy What does ths mean? The concept o potental energy can only be used under the specal class o orces called the conservatve orce whch results n the prncple o conservaton o mechancal energy. What are other orms o energes n the unverse? Mechancal Energy Electromagnetc Energy In order to descrbe potental energy, U, a system must be dened. Chemcal Energy Nuclear Energy EM Bologcal Energy These derent types o energes are stored n the unverse n many derent orms!!! KE + PE KE + PE Thermal Energy I one takes nto account ALL orms o energy, the total energy n the entre unverse s conserved. It just transorms rom one orm to another. Monday, Mar. 18, 013 PHYS , Sprng 013 8

9 Gravtatonal Potental Energy Ths potental energy s gven to an object by the gravtatonal eld n the system o Earth by vrtue o the object s heght rom an arbtrary zero level h h m m mg When an object s allng, the gravtatonal orce, Mg, perorms the work on the object, ncreasng the object s knetc energy. So the potental energy o an object at a heght y, the potental to do work, s expressed as PE F g y The work done on the object by the gravtatonal orce as the brck drops rom y to y s: What does ths mean? F g y cosθ Fg y Monday, Mar. 18, 013 PHYS , Sprng 013 mgh PE mgh W g PE PE mgh mgh ΔPE (snce ΔPE PE PE ) Work by the gravtatonal orce as the brck drops rom y to y s the negatve change o the system s potental energy è Potental energy was spent n order or the gravtatonal orce to ncrease the brck s knetc energy. 9

10 Ex. A Gymnast on a Trampolne A gymnast leaves the trampolne at an ntal heght o 1.0 m and reaches a maxmum heght o 4.80 m beore allng back down. What was the ntal speed o the gymnast? Monday, Mar. 18, 013 PHYS , Sprng

11 W W gravty mg h ( h ) ( )( ) o ( ) v g h h o o 9.80ms 1.0 m 4.80 m 8.40ms v o Ex. Contnued From the work-knetc energy theorem 1mv 1mv o Work done by the gravtatonal orce mg h ( h ) Snce at the maxmum heght, the nal speed s 0. Usng work-ke theorem, we obtan o mv 1 o Monday, Mar. 18, 013 PHYS , Sprng

12 Example or Potental Energy A bowler drops bowlng ball o mass 7kg on hs toe. Choosng the loor level as y0, estmate the total work done on the ball by the gravtatonal orce as the ball alls on the toe. Let s assume the top o the toe s 0.03m rom the loor and the hand was 0.5m above the loor. M U W g U mgy J Δ U ( U ) U mgy J 3.4J 30J b) Perorm the same calculaton usng the top o the bowler s head as the orgn. What has to change? Frst we must re-compute the postons o the ball n hs hand and on hs toe. Assumng the bowler s heght s 1.8m, the ball s orgnal poston s 1.3m, and the toe s at 1.77m. U J W g U mgy ( ) mgy ( ) Δ U ( U ) U 3.J 30J J Monday, Mar. 18, 013 PHYS , Sprng 013 1