Welcome'back'to'Physics'215
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1 Welcome'back'to'Physics'215 Today s' agenda: Work Power Physics'215 Spring'2018 Lecture'1071 1
2 Ask'a'physicist I've'seen'people'online,'including'some' famous'ones, saying'they'believe'the' earth'is'a'flat'disk'instead'of'a'globe' and'i'was'wondering'if'you'could' somehow'prove'the'earth'is'not'flat. For next class: pseudoscience'and' science'communication Physics'215 Spring'2018 Lecture'1071 2
3 Recall:'Gravitational'Potential'Energy For an object of mass m near the surface of the earth: U g = mgh h is height above arbitrary reference line Measured in Joules -- J (like kinetic energy) Physics'215 Spring'2018 Lecture'1071 3
4 Recall:'If'the'velocity'at'B'is'v,' then'what'is'the'velocity'at'c?' A. 2v B. v h A h/2 B C C. sqrt(2)'v D. v/sqrt(2) E. None'of'the'above Physics'215 Spring'2018 Lecture'1071 4
5 Recall:'Springs'77 Elastic'potential'energy Force'F'='7kx'(Hooke s'law) Area of triangle lying under straight line graph of F vs. x = (1/2)(+/-x)(-/+kx) frictionless table F U s = (1/2)kx 2 F = -kx x Physics'215 Spring'2018 Lecture'1071 5
6 Recall:'Work'7 Kinetic'Energy'Theorem W net =%!K =%K f # K i The'net$work done'on'an'object'is'equal'to' the'change$in$kinetic$energy of'the'object. Physics'215 Spring'2018 Lecture'1071 6
7 Work'and'Kinetic'Energy'in'2D Work'done'by'object'2'on'object'1: Kinetic'energy'of'an'object: K = 1 2 mv2 [or: 1 2 m( v v)] Physics'215 Spring'2018 Lecture'1071 7
8 Scalar'(or' dot )'product'of'vectors The'scalar'product'is'a'way'to'combine'two' vectors'to'obtain'a'number'(or'scalar).'it'is' indicated'by'a'dot'( )'between'the'two'vectors. (Note:'component'of'A'in'direction'n'is'just'A n) A B = ABcosθ = A x B x + A y B y + A z B z Physics'215 Spring'2018 Lecture'1071 8
9 SG'Is'the'scalar'( dot )' product'of'the'two'vectors A. positive B. negative C. equal'to'zero D. Can t'tell. Physics'215 Spring'2018 Lecture'1071 9
10 SG'Is'the'scalar'( dot )' product'of'the'two'vectors A. positive B. negative C. equal'to'zero D. Can t'tell. Physics'215 Spring'2018 Lecture'
11 SG'A'person'lifts'a'book'at'constant'speed.'' Since'the'force'exerted'on'the'book'by'the' person s'hand'is'in'the'same'direction'as'the' displacement'of'the'book,'the'work'(w 1 )'done'on' the'book'by'the'person s'hand'is'positive. The'work'done'on'the'book'by'the'earth'is: A. negative'and'equal'in'absolute'value'to'w 1 B. negative'and'less'in'absolute'value'than'w 1 C. positive'and'equal'in'absolute'value'to'w 1 D. positive'and'less'in'absolute'value'than'w 1 Physics'215 Spring'2018 Lecture'
12 A'person'lifts'a'book'at'constant'speed.''The' work'(w 1 )'done'on'the'book'by'the'person s' hand'is'positive. Work'done'on'the'book'by'the'earth: Net work'done'on'the'book: Change'in'kinetic'energy'of'the'book:' Physics'215 Spring'2018 Lecture'
13 SG'A'person'carries'a'book'horizontally'at' constant'speed.''the'work'done'on'the'book'by' the'person s'hand'is A. positive B. negative C. equal'to'zero D. Can t'tell. Physics'215 Spring'2018 Lecture'
14 Sample'problem:'The'two'ropes'seen'in' the'figure'are'used'to'lower'a'255'kg' piano'5.1'm'from'a'second7story' window'to'the'ground.'how'much'work' is'done'by'each'of'the'three'forces? Physics'215 Spring'2018 Lecture'
15 SG'Two'identical'blocks'slide'down'two'frictionless' ramps.''both'blocks'start'from'the'same'height,'but' block'a'is'on'a'steeper'incline'than'block'b.' Using'the'work7kinetic'energy'theorem,'the'speed'of' block'a'at'the'bottom'of'its'ramp'is' A. less'than'the'speed'of'block'b.' B. equal'to'the'speed'of'block'b. C. greater'than'the'speed'of'block'b. D. Can t'tell. Physics'215 Spring'2018 Lecture'
16 Solution' Which'forces'do'work'on'block? Which,'if'any,'are'constant? What'is'F!s for'motion? Physics'215 Spring'2018 Lecture'
17 Work'done'by'gravity N Work W = -mg j!s j mg!s Therefore, W'='7mg!h N'does'no'work! i Physics'215 Spring'2018 Lecture'
18 Work'done'on'an'object'by'gravity W (on object'by earth) =' m'g!h,' where'!h ='h final h initial is'the'change'in'height. Object moves Change in height Δh Work done on object by earth upward positive negative downward negative positive Physics'215 Spring'2018 Lecture'
19 Defining'gravitational'potential'energy W (on obj. by earth) = ΔK 0 = ΔK W (on obj. by earth) 0 = ΔK + ΔUg The'change in'gravitational'potential'energy'of'the'object7 earth'system'is'just'another'name'for'the'negative'value' of'the'work'done'on'an'object'by'the'earth. Physics'215 Spring'2018 Lecture'
20 Curved ramp!s = W = F!s = Work done by gravity between 2 fixed pts does not depend on path taken! Work done by gravitational force in moving some object along any path is independent of the path depending only on the change in vertical height Physics'215 Spring'2018 Lecture'
21 Demo:'4'tracks Physics'215 Spring'2018 Lecture'
22 Conservative'forces If'the'work'done'by'some'force'(e.g.' gravity)'does'not$depend$on$path the' force'is'called'conservative. Then'gravitational'potential'energy'U g only'depends'on'(vertical)'position'of' object'u g ='U g (h) Elastic'forces'also'conservative' elastic'potential'energy'u'='(1/2)kx 2... Physics'215 Spring'2018 Lecture'
23 Many'forces For'a'particle'which'is'subject'to'several' (conservative)'forces' F 1,'F 2!K='W 1 +W 2 + '''''or'equivalently:!k+!u 1 +!U 2 +.=0' i.e E"="(1/2)mv 2" +"U 1" +"U 2" + is'constant Principle'called' Conservation"of"total"mechanical"energy Physics'215 Spring'2018 Lecture'
24 Nonconservative'forces Can'do'work,'but'cannot'be'represented'by'a' potential'energy'function examples:'friction,'air'resistance Total'mechanical'energy'can'now'change'due'to' work'done'by'nonconservative force!k+!u 1 +!U 2 +.='W nonconservative For'example,'frictional'force'leads'to'decrease'of' total'mechanical'energy'77 energy'converted'to' heat,'or'internal'energy' Heat/internal'energy'is'really'just'energy'of' molecular'motion Physics'215 Spring'2018 Lecture'
25 Conservation'of'total energy The'total'energy'of'an'object'or'system'is'said' to'be'conserved'if'the'sum'of'all energies' (including'those'outside'of'mechanics'that'have' not'yet'been'discussed)'never'changes. This'is'believed'always'to'be'true. Physics'215 Spring'2018 Lecture'
26 Summary Work is'defined'as'dot'product'of'force' with'displacement'vector Each'individual'force'on'an'object'gives' rise'to'work'done The'kinetic*energy only'changes'if''net* work is'done'on'the'object,'which' requires'a'net*force Physics'215 Spring'2018 Lecture'
27 Average power = W Δt Power Power&=&Rate&at&which&work&is&done W Inst. power = lim Δt 0 Δt Units of power: Physics'215 Spring'2018 Lecture'
28 SG'A'ball'is'whirled'around'a'horizontal'circle'at' constant'speed.'' If'air'drag'forces'can'be'neglected,'the'power' expended'by'the'hand'is: A. positive B. negative C. zero D. Can t'tell. Physics'215 Spring'2018 Lecture'
29 SG'A'sports'car'accelerates'from'zero'to'30' mph'in'1.5's.''how'long'does'it'take'to' accelerate'from'zero'to'60'mph,'assuming'the' power'(=!w"/'!t)'of'the'engine'to'be'constant? (Neglect'losses'due'to'friction'and'air'drag.) A. 2.25's B. 3.0's C. 4.5's D. 6.0's Physics'215 Spring'2018 Lecture'
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