Physics. Lesson Plan #9 Energy, Work and Simple Machines David V. Fansler Beddingfield High School

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1 Physics Lsson Plan #9 Engy, Wok an Simpl Machins Davi V. Fansl Bingfil High School Engy an Wok Objctivs: Dscib th lationship btwn wok an ngy; Display an ability to calculat wok on by a foc; Intify th foc that os th wok; Diffntiat btwn wok an pow an coctly calculat pow us. - Engy an Wok o If you hav v mov, you know what wok it is to pick up a box an mov it to anoth location. Sliing it acoss th floo is not much btt u to fiction. Woking poblms in physics also pobably sms lik ha wok but th manings of wok fo moving boxs is not th sam as th maning fo woking poblms o Whn you scib an objct, you might giv it s siz, colo, wight, an if it can pouc a chang. Th ability of an objct to pouc a chang in itslf o it s nvionmnt is call ngy. Engy can b in sval foms thmal, chmical, lctical, nucla, o motion. Lt s look at th ngy of motion. If w go back to Nwton s 2 n law, w know that F = ma Using ou last favoit vlocity quation v 2 1 = v a an aanging w gt v 2 1 v 2 0 =2a. An substituting a = F/m, w gt v 2 1 v 2 0 =2F/m, an finally iviing both sis by 2 w gt 2 2 1/2mv 1/2mv = F o Calculating Wok Th tm 1/2mv scibs th ngy of th systm, is call kintic ngy an givn th symbol K Th ight han si of th quation F fs to th nvionmnt, a foc though a isplacmnt. This mans that som agnt in th nvionmnt chang a popty of th systm. As w not ali, changing th ngy of a systm is call wok an is givn th symbol W, wh W = F. If w substitu W an K into th oiginal quation, w n up with K 1 K 0 = W, o wok is th chang in kintic ngy so W = K. W = K is call th wok-ngy thom. Th finition of th unit of masu fo W is 1kg mov at on m/s has a kintic ngy of 1kg m 2 /s 2, known as 1 Joul o 1J An appl wighs about 1 N, so whn you lift it a istanc of on mt, thn you o 1J of wok on it Davi V. Fansl Bingfil High School - Pag 1

2 Whil th quation fo wok is W = F, this only woks fo constant focs xt in th iction of th motion. Sampl Poblm A 105g hocky puck is sliing acoss th ic. A play xts a constant 4.5N foc ov a istanc of 0.15m. How much wok os th play o on th puck? What is th chang in th puck s ngy? Sinc th foc an th iction of motion a th sam, al th units woul b positiv W = F W = 4.5Ni0.15 m=.68 Nim=.68J An sinc K = W, thn chang in ngy woul b 0.68J o Constant Foc at an Angl In talking about calculating wok, w inicat that th constant foc ha to b in th iction of motion. So how about th situation wh you a pushing a lawnmow? Th foc you a applying is not in th iction of motion ath at an angl of about 25º to th motion, so a you oing any wok? Of cous you a! Back to tigonomty! As you can s w n to fin th componnt of foc in th x-axis, sinc that is th iction of motion of th mow. Fx = FcosΘ Insting this into ou W = F quation w gt W = F cosθ What about oth focs on th lawnmow? Gavity is xting a foc, but it is balanc by th nomal foc an bsis, th is no componnt of it in th hoizontal iction Th is fiction an it is always opposit th iction of motion, an thfo woul hav ngativ sign. Ngativ wok on by a foc in an nvionmnt ucs th ngy of th systm in this cas, just maks th pson hav to push th mow with mo foc, oing mo wok! o Fining Wok whn Focs Chang W hav bn caful to stat that whn a constant foc is appli..., an w can s why whn w look at a gaph of a constant foc ov a istanc. Th wok woul simply b th foc tims th istanc but Davi V. Fansl Bingfil High School - Pag 2

3 what about whn th foc is not constant? Suppos that w apply a foc of 20N to an objct ov a istanc 1.5m, th wok on woul b simpl to calculat th foc tims th istanc. But what if w stat out with a foc of 0N an incas it vnly to 20N whil w push th objct 1.5m? Fo th constant foc cas w s that th foc tims th istanc is th aa un th cuv. W can us th sam concpt fo a foc that is changing. Whn th foc is plott against th istanc, if w calculat th aa un th gaph w can gt th wok. In this cas, w a looking at a tiangl, which th aa is ½ lh, o W = ½ F. So W = ½ (20N)(1.5m) = 15N m = 15J o Pow Up until now, w hav not iscuss how long it has takn th wok to tak plac. Dos it matt? If you walk up a flight of stais, you a oing wok, but what if you un up th sam stais? Do you o th sam amount of wok? Ys you o, but th pow is iffnt. Pow is a masu of how much wok is on in a pio of tim th at of wok. Th long it taks to o wok, th lss pow. Pow is signat by th ltt P. W Th quation fo pow is P =. Th unit of masu fo pow is th t watt (W). On watt is 1J of ngy tansf in on scon. A glass of wat wighs about 2N, an if you mov it.5 m to you mouth, thn you hav on 1J of wok. If it taks 1 scon to mov th glass thn you a woking at th at of 1W. Sinc th watt is such a small unit, pow is mo oftn xpss in kilowatts (1000W) Sampl Poblm An lctic moto lifts an lvato 9.00 m in 15.0s by xting an upwa foc of 1.20 x 10 4 N. What pow os th moto pouc in watts an kilowatts? Using th finitions of wok (W = F) an pow (P = W/t) w can solv spaatly o combin th quations to solv at on tim (P = F/t) P = F/t = (1.20 x 10 4 N)(9.00m)/15.0s = 7200W o 7.2kW Davi V. Fansl Bingfil High School - Pag 3

4 Machins Objctivs: Dmonstat knowlg of why simpl machins a usful; Communicat an unstaning of mchanical avantag in ial an al machins; Analyz compoun machins an scib thm in tms of simpl machins; Calculat fficincis fo simpl an compoun machins. - Simpl an Compoun Machins o Onc upon a tim, soft inks ha caps on thm that qui a spcial vic to opn thm, call a bottl opn. Th bottl opn woul gab un th cap an lift th cap off th bottl. Th cap coul not b takn off th bottl by ba hans alon! o This is an xampl of a simpl machin. Th foc you xt on th n of th opn is th ffot foc F. Th foc that is xt by th machin is th sistanc foc F. Th atio of th sistanc foc to F th ffot foc is call th mchanical avantag. MA = F Many machins hav a mchanical avantag gat than on whn MA is gat than on, thn th machin incass th amount of foc you apply. Som machins (such as a simpl pully) hav a MA of 1 whil th is no incas in foc, th is a iction of th foc which can b hlpful. You can wit th mchanical avantag of a machin using th finition of wok. Sinc you xt a foc though a istanc, th wok in (Wi) woul b F. Th output of a machin is going to b a foc though a istanc, so wok out (Wo) woul b F. In an ial wol Wi = Wo, o F F = F. W can -wit this quation to b =. W know that F F mchanical avantag is MA =, an fo an ial machin thn F MA =, but bcaus this is fo an ial machin thn th mchanical avantag is call th ial mchanical avantag an is wittn IMA =. Fom this quation, w s that you masu th istancs to calculat th IMA, but you hav to masu th focs xt to fin th actual MA. Davi V. Fansl Bingfil High School - Pag 4

5 o Efficincy Sinc in th al wol th a no ial machins, th will always b som focs lost (typically to fiction). Any focs lost mans that not all th ngy put into a systm will b mo than th focs takn out of th systm. Th fficincy of a machin is fin as a atio of th output wok to th Wo input wok - fficincy = x 100%, o w can -wit this to b Wi F / F fficincy = x 100% / an onc mo as MA fficincy = x 100% IMA An fficint machin will b clos to 100% ffctiv. o Simpl Machins All machins, no matt how complx, a a combination of on o mo of th six simpl machins Lv Pully Whl an axl Davi V. Fansl Bingfil High School - Pag 5

6 Inclin plan Wg Scw Davi V. Fansl Bingfil High School - Pag 6

7 o You can s ths simpl machins in many itms, such as a bicycl what machins o you s in a bicycl? Whl an Axl, fo th pal an a whl Lv fo th hanl bas o Th IMA of all machins is th atio of th istancs mov. Whn talking about whl an axl, you us th istanc btwn wh th foc is appli an th otational point - Compoun Machins o A compoun machin consists of 2 o mo simpl machins, link so th sistiv foc of th fist machin bcoms th ffot foc of th scon. An xampl woul b a bicycl th pal an ga act as whl an axl. Th foc you plac on th pal bcoms th sistanc foc on th ga, but though th chain this sistanc foc bcoms th ffot foc fo th ga on th a whl an th sistanc foc sis th whl on th goun. o Th mchanical avantag of a compoun machin is th pouct of th mchanical avantags of th simpl machins that mak it up, such that MA = MAmachin 1 x MAmachin2 If w tak th xampl of a bicycl, thn w Fon chain Fon oa Fon oa hav MA = x = F F F on pal by chain on pal Fo calculating th IMA of ach whl an axl, it is th atio of th istancs mov, So th pal an ga you woul hav pal aius IMA = font spockt aius Davi V. Fansl Bingfil High School - Pag 7

8 An fo th a whl you woul hav a spockt aius IMA = whl aius Thn fining th pouct w woul pal aius a spockt aius hav IMA = x font spockt aius whl aius which w can aang to b pal aius a spockt aius IMA = x whl aius font spockt aius Sinc both spockts us th sam chain, thn w can count th tth an us that as a masumnt an wit onc again to pal aius tth on a spockt IMA = x whl aius tth on font spockt Shifting gas on you bicycl is a way of ajusting th atio of spockt aii to obtain th si IMA You shoul mmb that focs a always takn to b in th iction of motion, so th most foc you can plac on a pal of a bicycl is whn th pal am is hoizontal to th goun. Whn v foc on a bicycl is spcifi, it shoul b takn that th pal is hoizontal to th goun. Exampl Poblm Whil xamining a a whl of a bicycl, you fin that it has a aius of 35.6cm an an attach ga which has a aius of 4.00cm. Whn th chain is pull with a foc of 155N, th whl im movs 14.0cm, Th fficincy of this pat of th bicycl is 95.0%. a. What is th IMA of th whl an ga? b. What is th MA of th whl an ga? c. What foc os th scal gist?. How fa was th chain pull to mov th im that amount? Using th quation IMA = 4.00cm = = cm Davi V. Fansl Bingfil High School - Pag 8

9 MA Sinc w know that fficincy = x 100%, th w can aang to fin MA, IMA fficincy i IMA 95.0% i0.112 MA = = = % 100% To fin what foc th scal gists w us th b -wittn F = MAiF = i 155N = 16.4N MA F F = quation, wh it can - An lastly to fin th lngth of chain pull, w woul go back to -wit it to = IMAi =.112 i 14.0cm= 1.57cm IMA = an Davi V. Fansl Bingfil High School - Pag 9