PHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014

Transcription

1 PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 Work-Knetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o Energy Energy Dagram Thursday, Oct., 014 PHYS , Fall 014 1

2 Remnder or Specal Project #4 Two protons are separated by 1m. Compute the gravtatonal orce (F G ) between the two protons (10 ponts) Compute the electrc orce (F E ) between the two protons (10 ponts) Compute the rato o FG/FE (5 ponts) and eplan what ths tells you (5 pont) You must specy the ormulae or each o the orces and the values o necessary quanttes, such as mass, charge, constants, etc, n your report Due: Begnnng o the class, Tuesday, Oct. 7 Thursday, Oct., 014 PHYS , Fall 014

3 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 W r Knetc Frcton It sn t there when the object s movng. Frcton orce F r works on the object to slow down The work on the object by the rcton F r s F r d 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, takng nto account ts ntal knetc energy, rcton orce and all other sources o work, s KE KE + W F d r t0, KE Thursday, Oct., 014 PHYS , Fall 014 Frcton, Engne work tt, KE 3

4 Eample 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 Thursday, Oct., 014 PHYS , Fall 014 4

5 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 E. 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 Thursday, Oct., 014 PHYS , Fall 014 F N cos 5 o 515N µ k FN µ k k N F

6 E. Now wth the X component X component Total work by ths orce From work-knetc energy theorem Solvng or v F W v W What s her acceleraton? Fg ( F ) o mg sn 5 k v KE Thursday, Oct., 014 PHYS , Fall 014 k s mg sn 5 k KE W mv 0 m ( o ) sn N ma ( ) s ( o ) KE + F ma a W + mv 0 m sn J mv W + KE W + ( ) F m 58.93ms 1 mv ms

7 Potental Energy & Conservaton o Mechancal 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 EM Nuclear Energy Bologcal Energy These derent types o energes are stored n the unverse n many derent orms!!! KE + PE KE + PE 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. Thursday, Oct., 014 PHYS , Fall 014 7

8 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 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 m o an object at heght h, the potental to do work, s epressed as h mg PE F g y F g y cosθ Fg y mgh h m The work done on the object by the gravtatonal orce as the brck drops rom h to h s: What does ths mean? Thursday, Oct., 014 PHYS , Fall 014 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. 8

9 E. A Gymnast on a Trampolne The gymnast leaves the trampolne at an ntal heght o 1.0 m and reaches a mamum heght o 4.80 m beore allng back down. What was the ntal speed o the gymnast? Thursday, Oct., 014 PHYS , Fall 014 9

10 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 E. Contnued From the work-knetc energy theorem 1mv 1mv o Work done by the gravtatonal orce mg h ( h ) Snce at the mamum heght, the nal speed s 0. Usng work-ke theorem, we obtan o mv 1 o Thursday, Oct., 014 PHYS , Fall

11 Conservatve Forces and Potental Energy The work done on an object by a conservatve orce s equal to the decrease n the potental energy o the system W c Fd ΔU What does ths statement tell you? The work done by a conservatve orce s equal to the negatve change o the potental energy assocated wth that orce. Only the changes n potental energy o a system s physcally meanngul!! We can rewrte the above equaton n terms o the potental energy U So the potental energy assocated wth a conservatve orce at any gven poston becomes What can you tell rom the potental energy uncton above? Δ U U ( ) U U Fd + Potental energy uncton Snce U s a constant, t only shts the resultng U () by a constant amount. One can always change the ntal potental so that U can be 0. U Fd Thursday, Oct., 014 PHYS , Fall

12 h More Conservatve and Non-conservatve Forces m mg The work done on an object by the gravtatonal orce does not depend on the object s path n the absence o a retardaton orce. N l When drectly alls, the work done on the object by the gravtaton orce s θ When sldng down the hll o length l, the work s How about we lengthen the nclne by a actor o, keepng the heght the same?? W g Stll the same amount o workj W g mg snθ l mgh W g So the work done by the gravtatonal orce on an object s ndependent o the path o the object s movements. It only depends on the derence o the object s ntal and nal poston n the drecton o the orce. F g nclne l mg ( l snθ ) mgh mgh Forces lke gravtatonal and elastc orces are called the conservatve orce 1. I the work perormed by the orce does not depend on the path.. I the net work perormed on a closed path s 0. Total mechancal energy s conserved!! Thursday, Oct., 014 PHYS , Fall 014 EM KE + PE KE + PE 1

13 Eample 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 Thursday, Oct., 014 PHYS , Fall

14 Elastc Potental Energy Potental energy gven to an object by a sprng or an object wth elastcty n the system that conssts o an object and the sprng. The orce sprng eerts on an object when t s dstorted rom ts equlbrum by a dstance s F s k Hooke s Law The work perormed on the object by the sprng s The potental energy o ths system s What do you see rom the above equatons? Where else dd you see ths trend? W s ( k) d So what does ths tell you about the elastc orce? U s The work done on the object by the sprng depends only on the ntal and nal poston o the dstorted sprng. Thursday, Oct., 014 PHYS , Fall k 1 k The gravtatonal potental energy, U g k + A conservatve orce!!! k 1 1 k k 14