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Unformatted text preview: Energy 10:1 A“Natural Money" Called Energy 1. One month, John has income of $3000, expenses of $2500, and he sells $300 of stocks. a. Can you determine John’s liquid assets L at the end of the month? If so, what is L? If not,
Why “or? I40 , VJL 60"“0idt'l'ef‘m'ewt. L— bzca‘u‘vz. we. ((onhlknow wdA «144+ lt‘alnlal mssc'l's 14¢ S+ﬁr+€ﬂ( +Lx2 WHM'HM b. Can you determine the amount by which John’s liquid assets changed during the month?
Ifso, what is AL? YE s_ I zInwmc E :. ghoul“, 5:. g +ocit'5ales AL: '13 “E *5 : $Booow$2roo+$soo :l+$300l 2. John begins the month with $2000 of liquid assets and $5000 of savings. His ﬁnancial activity for the month is as follows: (“Arid L : Liam :91 «Sgtrs
Day of Month Activity S : Savm’ls
l + L Receives a $3000 paycheck; deposits it in Checking
3 L Spends $500 3 —L {+5 Buys a $1000 savings bond 10 «— L. Pays bills totaling $1000 15 + L Receives a $ 100 birthday present from Grandma
23 +1.. ,'5 Sells $1500 of stock 28 — L. Buys a $1200 bicycle a. What are John’s liquid assets and saved assets at the end of the month? L1: $2ooo 3'“ 0°”! 5.: $5000 55 "MY
+3000 l ﬂow 3
5
 gag
 two 8 n [5‘00 l3
#1000 “'0 $
H: a 15‘ : L} 'HSL : 26100
:rsoo 23 Li H“
.. [300 at? ge L s; 435M“ _ 3‘15'00
b. Show that John’s monetary relationship AW 2 I — E is satisﬁed.
TramsPm: i I E 9"?” AN ; 1‘ .— 5
J, @000 I J
wiz $5000 +£30.30 5'00 3 : #3190  2700
: g 7000 {000 to u
w _ $q§ao+ 37.4100 r00 1 5‘ 3“} I“; 500
F— ' {ZIJD 2,3 .1 $7400 W 14); :57004000 4339, 102 CHAPTER 10  Energy “3&2 Kinetic: Emmy and vaitaﬁﬁmi Wmmi’aﬁ Enemy 3. Upon What basic quamity deas kinetic {3:36ng dweﬁé‘? . Q3 2 e 0‘
Upon What basic quantity (1063 pgtemial energy depand‘? ___(‘22iih_°“—_ 4. Can kinetiiz easrgy £3213: be aegative? M_
(31% a plausibis $651583? {13: yam" angwer wiﬂmm making use 0f any femuias. ~
WAan were” is Enemy 0‘; Maﬁa". MOh‘on may sfopl‘bw“ ‘1' OOwd" be neaa'hWQ . 3941A has he dtirtc‘ﬁoﬁ 9““ CNM°+ be ne5achv£ 5‘ Caz: gravimtionai peieniiaé mag}; ever be negaﬁvs? L
Give a giausibis mama fa: yew? 3113:3961 Wiihsuii making use. of any f0mulas. ‘ _l_ 1, e
(Eakan'h'J an "37 Wmis upon ?0 {Thva which cam 52— ?05 m“ ° r “‘3“ ‘ ' 6. a, If a §mici€s sgeed margasas by a factm’ 9f ﬂares, iay whai fame: {3065 its kiraeiic saggy
changa‘? ( 1 I A 7. “
mam when) {1% Kk'axucascs ‘DY 0‘ Q‘d—z’r oi? 01' b. Particle A, has hzﬁf the 31355 33d ﬂight; ﬁrms the. Eigeéie €335ng 0f gazﬁck: B. What is the spgad ram} 'Rgil’93? MA ; 3 We 2
\ a J. g M
‘ ’L ‘ 2 V 2 " ‘1
1%VA*37‘{%V3 7/9314 “‘3 7. 81; the axes baiaw, draw graphs {3? 1:133 kinetic saggy 0f 2;. A 15331} kg car that unifﬁﬁniy acceiaraies from {3 £9 28 11133 in 2G b. A 1000 kg car mmng a: 20 mﬁs that: biakas t0 3 ha}: Wiih 31:}:me ﬁscaéezaiien in 4 s.
' C. A 100% kg car {hai dikes OECﬂ 3:033:33 & 48—m—cﬁamcie: circie 31' a spesd of 20 mls. Calculate K a: S€¥€fﬁi $313353, pm: the paima 333;} draw a smaoth cums between them. a. K :3) h. if (3} c. g {3) i
25am; § 77  200,000 I 300,000 isoxxm ~ 153mg Immoii . E £89,000 ~» 563mg} . m 2 [(1 3 £1 mocha (10’, t  ( 4L (9))"
moot; (20% J Kg”): 000 a :ﬁ 1
K11 L ,_ (000%,) C0 ’5) Energy 1 CHAPTER [0 10—3 10.3 A Closer Look at Gravitational Potential Energy 8. Below we see a 1 kg object that is initially 'l m above the ground and rises to a height of 2 m.
Anjay, Brittany, and Carlos each measure its position, but each of them uses a different
coordinate. system. Fill in the table to show the initial and ﬁnal gravitational potential energies
and AU as measured by our three aspiring scientists. r'\ nja) Brittany Carlos         Ends hurt: l Ll.) t = . E ! i ; i .7 m ‘ {1 l
i l i _. _ _ u I 9. A roller coaster car rolls down a frictionless track. reaching speed W at the bottom.  ﬁla rlx herr: _._._T.___ a. If you want the car to go twice as fast at the bottom, by what factor must you increase the .heightoi’thetraek? K; : Ji “Cam‘ : 4K SO Yo“ "HMf
i/itt I: {acreage H“ inc—‘51.“ ;Y A {kct.” oi1 ‘f.
m3h' m; been”, when U910 m ed 1.. —=; M Q El '0.
b. Does your answer to part a depend on whether the track is straight or not?J Explain. NC)Ir ‘i‘La gmm‘l‘a'honai Poles—ital amp?” Agpendx only
on line misgu 10. Three halls of equal mass are [1er simultaneously with equal speeds
from the same. height above the ground. Ball 1 is tired straight up,
ball 2 is ﬁred straight down. and ball 3 is tired horizontally. Rank in
order, from largest to smallest, their speeds v1. v2, and 1'3 as they hit
the ground. Order: vi 1 V1 ’ V3
Explanation: .T—kéY edict“ Shef ul‘i’h "HA; Samc LCIne'hc energy Bull .3 Nd m7 eML‘ kt“ HAL saw“ UWM'De [bx ?0‘iCh'h;ki
emerald? , So Hour {.th uii'lq Ht; same. himit‘ll}. Engryr mot, +kus , irks. Same speed 104 CHAPTER 10 A Energy 11. Below are shown three frictionless tracks. A ball is released from rest at the position shown on
the left. To which point does the ball make it on the right before reversing direction and rolling
back“!I Point B is the same height as the starting position. Makes it to L Makes it to B Makes it to B Exercises 1214: Draw an energy bar chart to show the energy transformations for the situation
described. 12. A car runs out of gas and coasts up a hill until ﬁnally K] + Usi = XI + Ugl
stopping. +
/
f /
r‘ /
x /
0 + — = ——r +
13. A pendulum is held out at 45° and released from rest. it. + up = Kr + Uzi
A short time later it swings through the lowest point on +
its are. . ..... ..
é .
0 + = + m
14. A ball starts from rest on the top of one hill, rolls Ki + Up. = Kr + mgr without friction through a valley, and just barely makes
it to the top of an adjacent hill. II
+ Energy  CHAPTER 10 105 10.4 Restoring Forces and Hooke’s Law 15. A spring is attached to the ﬂoor and pulled straight up by 21 mpg. The spring’s tension is
measured. The graph shows the tension in the rope as a function of the r0 paj’s length L. a. Does this spring obey Hooke’s Law? Explain why or why not.
Y95/ 'HAL Plot It 5 (imam AT: k bl” b. If it does, what is the spring constant? k t 91‘: ‘ 10M / ﬂ“ : [00¢
A ’ to mm C 16. Draw a ﬁgure analogous to Figure 10.17 in the textbook for a spring that is attached to a wall
on the right end. Use the ﬁgure to show that F and As always have opposite signs. (‘1’ )5 Um s+r¢+cN bl S+r£11MA
A54 0 com pressed
As>o 106 CHAPTER 10  Energy 17. A spring has an unstretched length of 10 cm. It exerts a restoring force F when stretched to a
length of 11 cm. a. For what length of the spring is its restoring force 3F? E? 5'k AX $0 “$0!” F931;, bx—aBberCM {05” +36)! : l3¢m b. At what compressed length 18 the restoring force 2F? F F) '2 F by a ’ZAX : #2:,“ 10CMFQCM : S’Cm ____—a—.. l8. The left end of a spring is attached to a wall. When Bob polls on the right end with a 200 N
force, he stretches the spring by 20 cm. The same spring is then used for a tug—of~war between
Bob and Carlos. Each pulls on his end of the spring with a 200 N force. a. How far does Bob’s end of the spring move? Explain. H.9ch Tlﬂouwolq 'HA; 3p£fn5 gfrgﬁhcﬁ 10 CM
ollﬂl“ll1, Fl": Cen'f‘Cr wow; ‘07! 10cm, ImHﬂls Catt. Carlos TrawllclQJ "Hal 01999925
‘EBFCL pane«sly PromJig; ’9? flue. wallleaccepf 'l'lvm'i‘ IA! moves Odie. b. How far does Carlos’s end of the spring move? Explain. “F” loch“ S'l'N‘icln Lhaﬂlr DVLUO ﬁasian
th‘f sill] loe 30cm. linergy  (“I{AFTER 10 107 10.5 Elastic Potential Energy 19. 20. 2]. A heavy object is released from rest at position 1 above a spring.
It falls and contacts the spring at position 2. The spring achieves
maxiurnum compression at position 3. Fill in the table below to
indicate whether each of the quantities are +. —, or 0 during the
intervals l—>2, 2—93, and l—>3. _.  .J Rank in order, from most to least, the amount of elastic potential energy (Ugh to ((15).; stored in
each of these springs. i t 2t t
1W 2W 3W4W Stretc h cd (I Order: \mSJqp Us}; “> @SX: (Us), Explanation: 1
Us :_ 1?: RCA 5) Compressed d Stretched a’ Stretched 2d Tﬁcdﬁsens Ox ﬁg‘i‘ur oil 2.
TﬂCROxItj 4'th gl—optaﬁ initiate, b? 0‘ p.141”. 0? ‘i. A spring gun shoots out a plastic ball at speed v0. The spring is then compressed twice the
distance it was on the ﬁrst shot. a. By what factor is the spring’s potential energy increased? gar. QM?" 2 «Ems»? ‘lX ._—‘ b. By what factor is the ball‘s velocity increased? Explain. 7. 7. 1 X
Ji it. (15.5.) : a; MGM) (BoH't HAIL. spitch outix ‘31 0”— Spuderrc in the cur:17; JLF passions . 108 CHAPTER 10 . Energy Exercises 22—23: Draw an energy bar chart to show the energy transformations for the situation
described. 22. A bobsled sliding across frictionless, K. + ’ U, + Ui = K + U + U
horizontal ice runs into a giant spring.
A short time later the spring reaches
 its maximum compression. 23. A brick is held above a spring that is K 3+ U. + U. = K + U + U
standing on the ground. The brick is
released from rest, and a short time later the spring reaches its maximum 1
+ / + compression. ll Iowa it) 24. Ball 1 with an initial speed of 14 m/s has a perfectly elastic collision with ball 2 that is initially
at rest. Afterward, the speed of ball 2 is 21 m/s. 10.6 Elastic Collisions ‘ <ﬂ¥>z : wag—91A“ Glaxx‘ wtl‘e'lQI‘Q, (JEX)‘ (Vi3&2 : 1 x 2'I_V,"‘s_ : b. What will be the speed of ball 2 if the mass of ball 1 is doubled?
\
t W ‘_ 2 M \ /
PM at poem s par'l' a» CU a; , .2s 6% g) Mama, by in
V"! Mﬁm
, Q.
Sgt—(12 a; 2"; : (HZ?) solutes??? = A3
‘I {Damblm’s Mi Yteiois {1a a i’ We“ (QR/>1; (it; (a; Z I Energy  CHAPTER 10 109 10.7 Energy Diagrams 25. The ﬁgure shows a potentialenergy curve. Suppose a
particle with total energy E I is at position A and
moving to the right. 26. a. Energy For each of the following regions of the x—axis,
does the particle speed up, slow down, maintain a
steady speed, or change direction? A to B 2" low: Jami Btoc SECG’QS i«E E2
CIOD S‘lews deem DICE 98684? MB Etol: Sluu’S‘c‘nJﬂ F Where is the particle's turning point? . For a particle that has total energy £2. what are the possible motions and where do they occur along thexaxis? ,ﬂu. FMﬁcu “Whig k“ “‘0qu Ib£+w£m x: 0 “Mg
«Hue. peu‘ai' incittskai 51 HM. CLnSlAteQ it‘M H'fu’aLnARJB; (TLL Paritem Conic; [9* 05;: “63633 “Lahi— ram—+ C
Mi‘Wn iii/u, ktar‘ts‘i‘ aims Lani lines. . What position or positions are points of stable equilibrium? For each, would a particle in equilibrium at that point have total energy S E2, between E2 and E1, or 2 El?
C tau00» E. are, Poiﬂ'b vi“ S‘i‘kiyk editMil lawnm,
MKJ be A E: (Jer WEIIIJEL
A'i' CK HAL LinerJr (,9 z [m PM E, HA: Mal «are? “Mil” b€+mn :EI M452. . What position or positions are points of unstable equilibrium? For each, would a particle in equilibrium at that point have total energy S 52, between E; and E1, or 2 E1? Bans: '0 a” “ﬁg—{151... egkk'liibm'um fat«1‘3. The pap542,; would
have 0qu energy loafth ElanJ. EL A particle with the potential energy shown in the Energy
graph is moving to the right at x = 0 m with total E
energy E. a. At what value or values ofx is the particle’s speed a maximum? 54i Rﬂ GLAL. Ni" 9"“ PE 1010 CHAPTER 10 v Energy b. At what value or values ofx is the particle’s speed a minimum? (Dr—{' 5m c. At what value or values ofx is the potential energy a maximum? A’r gm d. Does this particle have a turning point in the range ofx covered by the graph? If so, where? ’Tltc. A065 no'l" MQJ‘E (a ‘l‘m‘nraa P';a+ pa'ﬂml to car). 2?. Below are a set of axes on which you are going to draw a potentialenergy Curve. By doing
experiments. you find the following information: ' A particle with energy El oscillates between positions D and E.
' A particle with energy E2 oscillates between positions C and F.
 A particle with energy E3 oscillates between positions B and G.
' A particle with energy E4 enters from the right, bounces at A, then never returns. Draw a potentialenergy curve that is consistent with this information. Energy ABC D L 1" G ...
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