CHAPTER 1. Motion. CHAPTER s Objectives

Transcription

1 1 CHAPTER 1 Moion CHAPTER s Objecives Moion was he firs naural even ha riggered human ineres o sudy naural phenomena long before recording ime. To he ancien people, everyhing in he universe seems o move from one posiion o anoher and in a manner, which became par of heir everyday life experience. To inroduce he properies of moion (posiion, speed and velociy, and acceleraion) To use he meric (or SI) sysem of measuremen and o learn how o conver unis To differeniae beween speed and velociy To differeniae beween velociy and acceleraion To learn how o analyze problem saemens and o ranslae he informaion ino a recipe, and To develop a problem solving skill. The ancien Greeks, beween 600B.C. and 300B.C. learn a grea deal of moion based on philosophical views of cause and effec. Arisole is one of heir own who wroe many heories abou moion ha capured people aenion unil he 16 h cenury. In he mid of 16 h cenury a modern and correc view of moion was esablished. Many conribued o his new undersanding, bu he ousanding conribuion of Galileo and hen Newon in he 17 h cenury was significan. Mechanics is he science of moion. I is divided ino kinemaics, which deals wih moion wih no reference o forces and dynamics ha sudies he effec of forces on moion. This chaper deals wih kinemaics only.

2 2 1.1 Moion Moion is a change in he objec s posiion wih respec o ime. Figure (1.1) describes an objec changing posiion wih ime. A complee descripion of moion requires A reference from which he posiion is measured or deeced. The ree in Figure (1.1) is a reference o measure how far or close is he car from he ree A coordinae sysem (x, y) of measuring posiion According o his descripion, he moion of any objec is considered as Relaive. For example, he moion of he car in Figure (1.1 )is relaive o he ree Usually, he moion is eiher a long sraigh line as in Figure (1.1 a&b) or a long a curve (a circle for example) as shown in Figure (1.2) (a) (b) Figure (1.1) sraigh line moion. (a) a horizonal moion relaive o a ree, and (b) verical moion relaive o earh. In boh cases, he objec posion is changing wih ime. Credi: Physics for scieniss and engineers sraegic approach by Randall D. Knigh, Pearson- Addison Wesley 2004.

3 3 Figure 1.2 moion of an objec along a curve. Credi: Physics for scieniss and engineers sraegic approach by Randall D. Knigh, Pearson-Addison Wesley Arisole and Galileo Views of Moion The Greek philosopher Arisole (4 h Cenury BC) sudied moion and divided i ino o wo kinds 1. Naural moion Moion ha is caused by no exernal forces. For example, he downward moion of a falling sone and he rise of smoke Heavy objecs fall faser han ligh objecs The sae of res is he only equilibrium sae. All moving objecs will end up a res 2. Violen moion Moion ha is caused by an exernal force. For Arisole, he force is any push or pull on an objec. He hough, objecs do no move unless a force ac on hem. For example, he moion of a car pulled by a horse and he moion of an arrow by a sreched bow Arisole used raional hinking and no experimenaion as a key o describe and undersand moion. His view capured people aenion for over 2000 years (unil 16 h cenury). For Galileo (16 h Cenury), on he oher hand, boh raional hinking and experimenaion were he keys o describe and undersand moion. He developed his own views of moion, which can be oulined by he following Forces ac hrough a physical conac (push or pull) or non-conac (a a disance, graviaional force for example) o move objecs. Noice ha a non conac force is Galileo s erm Forces change objec s velociy or direcion over ime. A force cause an objec iniial a res move (hrowing a ball, for example) or o sop i if i was moving (caching a ball, for example). Forces can also cause a moving objec o change is direcion (hiing a moving ball wih a ba, for example)

4 4 Fricion is a conac force ha ac beween wo objecs ha move pas each oher. Fricion force is parallel o he surfaces in conac and ac in a direcion ha opposes he moion. Fricion was inroduced firs by Galileo Wihou air fricion, all objecs heavy and ligh would reach he ground a he same ime dropped from he same heigh and a he same ime In he absence of fricion force, an objec does no need a force o keep i moving Galileo s experimens on moion: Forces and fricion A ball rolling down an inclined plane (a) speeds up because of graviy. A ball rolling up an incline plane (b) slows down because of graviy (a) (b) If fricion could be eliminaed hen he iniial and final heighs of he ball are equal ((c), and (d)), or he ball will never sops (e). _ (c) (d) (e) 1.3 Scalars and Vecors A Scalar is a physical quaniy ha has magniude only. Mass, lengh, ime, and emperaure are examples of scalar quaniies. A scalar can be described by a number wih a uni. For example, he lengh of an objec is 3 meers and is mass is 10 kilograms. A vecor is a physical quaniy ha has boh magniude and direcion. Vecors are usually represened by an arrow; he lengh of he arrow gives he magniude and he arrow s ip or head indicaes is direcion.

5 5 Force, weigh, acceleraion, velociy, and displacemen are jus few examples of vecors. Usually, a vecor is represened by an upper or lower case leer and an arrow on op. For insance, A, B or a b,. Figure (1.3) shows a picorial represenaion of a vecor. Figure 1.3: A vecor v is represened by is lengh (magniude) and direcion. Credi: Physics for scieniss and engineers sraegic approach by Randall D. Knigh, Pearson-Addison Wesley The Role of Measuremens in Physics Measuremens in physical sciences are so imporan. I consiss of comparing of a physical quaniy like lengh or mass wih a sandard or uni using a ool. The process of measuremen consiss of he following four seps 1. Selec a sandard uni of measuremen. 2. Follow a procedure or operaion of how he comparison is made. Choose a ool of measuremen 3. Coun how many sandard unis ha mach he physical quaniy. 4. Record he resul. The resul consiss of numerical number and a uni. The following example explains his procedure. Example 1.1 Measure he lengh of your humb Soluion This example is concerned wih he physical quaniy lengh. Lengh can be measured by sandard unis of cenimeer, meer, kilomeer, inch, foo, and mile. The choice mus mach he demand 1. Selec he cenimeer as he sandard uni of measuremen. This is a reasonable choice. 2. Follow a procedure or operaion o measure (compare). (a) Use a ruler or a measuremen ape as a ool. Place he ruler parallel o and along your humb so ha i lined up wih he boom edge of he humb. (b) Make a small pencil mark a he ruler a he poin ha maches he end of your humb. You can use your eye sigh insead of he pencil mark. 3. Coun how many cenimeers are in he finger lengh. You come up wih he number Record your final resul: 3.2 cm Cauion: A number wihou uni carries no informaion and does no serve he purpose.

6 Measuremen sysems: The Meric Sysem and Is Modificaion he SI sysem There are many measuremen sysems. The op hree are he cgs (cenimeer, gram, second) sysem, mks (meer, kilogram, and second) sysem, and he English (foo, slug, and second) sysem. The meric sysem of measuremen (esablished in 1791) or i s SI (Sysem Inernaional) modernized version (esablished in 1960) is he mos common and widely used sysem by scieniss worldwide. Table (1.1) shows measuremens of some basic physical quaniies and heir sandard unis in boh meric and SI unis. Table (1.1) Measuremens in Meric and SI Sysems measuremen Meric (symbol) SI (symbol) Lengh Meer (m) Meer (m) Mass Gram (g) Kilogram (kg) Volume Lier (L) Cubic meer (m 3 ) Time Seconds (sec) Seconds (sec) Temperaure Celsius ( 0 C) Kelvin (K) In his course we will use he meric sysem. This sysem employs prefixes or powers of 10 o describe large or small quaniies. This will make i easy in wriing large and/or small numbers. Table (1.2) liss some prefixes wih heir abbreviaion and heir meaning. Table (1.2) Some Common Prefixes

7 7 Each prefix up or down in Table (1.2) represens an increase or decrease by power of 10. Example 1.1 Use Table (1.1) and indicae wheher he uni of each of he following measuremens describes (1) lengh, (2) mass, or (3) volume A. A baske of apples is 5.7 kg. B. A bridge is 10.4 m all. C. A medicaion pill conains 0.35 g aspirin. D. A bole conains 1.5 L of waer. Example 1.2 Idenify he measuremen ha has an SI uni. 1. Salem s heigh is (A) 1.75 yd (B) 5.8 f (C) 1.75 m (D) 0.5 km 2. The emperaure is (A) 75 0 C (B) 345 K (C) F (D) The mass of an orange is (A) 59 lb (B) 65 L (C) 34 oz (D) kg 4. The 100m dash race was won in (A) 10.1 s (B) 12.7 min (C) 1.3 hr (D) 0.25 yr Scienific Noaion In science, scieniss use scienific noaion o wrie very large or very small numbers. The scienific 7 noaion for a large number such as , 000 is and for a small number such as is A number in a scienific noaion conains wo pars, a coefficien and a power of 10. In he wo examples above, he 5.6 and 5 are he coefficiens followed by he powers of en respecively. The procedure of wriing a number in scienific noaion consiss of he following seps: A. If he number is greaer han 1 (1) Move he decimal poin o he lef afer he firs digi o give a number beween 1 and 9. (2) The spaces moved are shown as a power of en. (3) The power is posiive

8 8 For example: = (5 spaces moved o he lef, and 3 is he firs digi) B. If he number is less han 1 (1) Move he decimal poin o he righ afer he firs digial poin o give a number beween 1 and 9. (2) The spaces moved are shown as a power of en. (3) The power is negaive. For example: = ( 3 spaces moved o he righ, and 3 is he firs digi) Example 1.3 Wrie he following numbers in scienific noaion (1) Diameer of earh is m = m (2) Mass of a human is 78 kg = kg (3) Lengh of a virus is cm = cm 1.4 Properies of Moion: speed, velociy, and acceleraion Speed Speed v is a measure of how fas or how slowly an objec moves. I is defined as he disance raveled per uni of ime, and can be wrien as disance speed, or ime d v (1.1) Speed is a scalar quaniy and does no include a direcion. In he meric (SI) sysem, he uni for speed is kilomeer per hour (km/hr) or meer per second (m/s). Pracically, he speed is no consan. Therefore, an average speed is used, which can be represened by a dash over he leer v and shown as d v For example, if you drive 240 km disance from Yanbu o Jeddah in 2.5 hr, hen your average speed is 240 km v 96 km/ hr 2.5 hr

9 9 The Change in a physical quaniy For any physical quaniy such as he disance x, he change in x is wrien as Δ x x x (always he final value iniial value). The symbol Δ (or dela), a Greek leer, represening a change, and x, x are he final and he iniial (saring) values of he quaniy x respecively. Figure (1.4) shows an objec changing is posiion during a ime of ravel. f i f i f i x0 1 1 x i x f Figure 1.4: During ime inerval, he objec (person and a car) changes is posiion by x. The average speed can, herefore, be wrien as x x v f x i (1.2) Velociy Velociy v is how fas or slowly an objec changes is displacemen (posiion). The displacemen D is a vecor quaniy, which ells us boh he disance raveled by he objec as well as he direcion of moion. From his we conclude ha velociy is a raio of displacemen (no disance) over ime and, herefore, i is a vecor quaniy. The average velociy is wrien as displacemen velociy, or ime o cover ha displacemen D v (1.3) Example 1.4 A man sars moving from home (origin (0)) and walks 6m eas (o he righ), sopped and found ha he forgo his walle a home. Therefore, he rushed backward (wes) heading home. If he oal ime of his walk boh ways is 2min hen find (a) his average speed and (b) his average velociy. Soluion (a) oal disance raveled 12m v v 0.1m / sec oal ime 260sec

10 10 (b) Displacemen (6 6) 0 v v 0m/ sec oal ime 260sec 120 Cauion: if an objec doesn change is direcion, hen speed and velociy are he same. For convenience, we will drop boh he arrow on op of he velociy vecor and speed, bu will keep he disincion beween speed and velociy. 1.5 Problems Solving Mehod One of he objecives of his chaper is o help sudens learn a procedure for solving problems in science. The procedure can be oulined in he following: Read he problem carefully. Read i a leas wice, slowly and compleely from he beginning o he end Make a skech of he problem if i is necessary. You can subsiue or represen any objec by a do or a box In your noebook, wrie down all given informaion (daa) wih unis. Look a some erms ha carry some informaion. For example, moion from res means iniial velociy equals zero. Also, he erm smooh surface indicaes no fricion Wrie down he unknown quaniy or quaniies he quesion asked for Wrie down he basic equaion or formula ha relaes all he known and he unknown quaniies Find he working equaion or formula for he unknown quaniy Subsiue he daa in he working equaion, including he unis. Verify your work The following example illusraes his procedure Example 1.5 Find he disance raveled by a car ravels wih an average speed of 80km/hr in 2.0 hr. Soluion: Skech: Daa (given informaion): Basic equaion: Working equaion: Subsiue and solve: 0 d=? v 80 km/ hr, 2. 0hr, waned: d? d v d v d ( 80km/ hr) (2hr) 160km x

11 Types of Moion: Uniform (consan) and Non Uniform Moion Uniform moion Uniform moion is defined as: Moion on a sraigh line, and Occur when successive displacemen/disances are equal a equal ime inervals If you drive a car a a consan velociy of 80 km/h, you will cover 80km during he firs hour, anoher 80km during he second hour, anoher 80km during he hird hour, and so on. The 80km covered during each hour is no he posiion bu he change of posiion or displacemen. Also, he ime of 1 hour is he ime inerval beween successive equidisance displacemens. On ( x, ) diagram, he uniform moion is shown as sraigh line wih a slope giving he velociy. Figure (1.5(a)) illusraes a picorial and graphical represenaion of uniform moion in ( x, ) plane Non Uniform Moion Non Uniform moion is defined as: Moion on a curve, and Occur when successive displacemens/disances are no equal a equal ime inervals A picorial and graphical represenaion of non uniform moion is shown in Figure (1.5 (b)) (a) Figure 1.5: picorial and graphical represenaion of a uniform (a) and (b) non uniform moions. The erm frame referes o an even. Credi: Physics for scieniss and engineers sraegic approach by Randall D. Knigh, Pearson-Addison Wesley (b)

12 12 Insananeous Velociy The insananeous velociy vins is he average velociy when he ime inerval beween displacemens approach zero (no zero). The insananeous velociy is herefore he velociy a he momen and no he average over he enire hour. Usually, car s speedomeer gives he insananeous velociy. 1.7 Acceleraion a Acceleraion a is a measure of how fas or how slowly is he change in velociy. I is defined as he change in velociy over ime. I is a vecor and always poins in he same direcion as velociy change vecor and has a uni of m/s 2. a a avg avg Change in velociy Time of change v v f vi final velociy iniial ime velociy, or (1.4) The change in velociy is eiher Up (speeding up) and he acceleraion and velociy are a he same direcion (posiive acceleraion), or Down (slowing down) and he acceleraion and velociy are opposiely direced (negaive acceleraion.). Figure (1.6) demonsraes his fac for a moving car Fig (1.6): Moion diagram of a speeding car (lef diagram) and a slowing down car (righ diagram). Credi: Physics for scieniss and engineers a sraegic approach by Randall D. Knigh Pearson-Addison Wesley Example 1.6 A car sars from res (velociy = 0 m/s) and speeds up o 20 m/s in 10 s. Find is acceleraion. Soluion:

13 13 Skech: No needed Daa: Δ v =20 m/s 0 m/s = 20 m/sec, = 10 s, waned: a? Working equaion: v a Subsiue: v a f v i 20m/ s 0m/sec 2m/ s 10s Uni Conversion To a scienis or a suden sudying science, uni conversion is exremely imporan. Therefore, he sudens mus be able o conver back and forh beween meric (SI) unis. Uni conversion is based on he availabiliy of conversion facors. Table (1.3) shows a few common conversion facors. Table (1.3) some useful conversion facors 1 km = 10 3 m 1m = 10-3 km 1 m = 10 2 cm 1 cm = 10-2 m 1 cm = 10 mm 1 mm = 10-1 cm 1 kg = 10 3 g 1g = 10-3 kg 1 day = 24 hr 1 cm 3 = 10-6 m 3 1 min = 60 sec 1 y = 365 d The process of uni conversion is based on replacing an unwaned uni by a waned uni; i can be summarized as follows Wrie down he given number wih is unwaned uni Muliply his by a raio of 1. The raio is wrien from a given conversion facor and i consiss of wo unis, he unwaned uni and he waned uni. Remember ha you need o cancel he unwaned uni

14 14 Cauion: I should be kep in mind ha muliplying any expression by one does no change is value bu change is uni. Wriing a conversion facor as a raio equal o 1 Using informaion from able1.3 and pick up a conversion facor such as 1 m = 10-3 km From his conversion facor, we can consruc wo raios each equal o 1, namely, 3 1m 10 km 1 and km 1m In solving a problem, one should pick up he righ raio; he one ha eliminae he unwaned uni and keep he waned. Example 1.7 Conver 54 m o km. Soluion The meer (m) is unwaned uni and he kilomeer (km) is he waned uni. Following he above seps of conversion of unis, one ges 3 10 km (54 m) ( ) m km Noice ha we chose he second raio wih he meer (m) a he boom because i cancels he meer (m) uni from boh quaniies in he wo parenheses. In some problems you are asked o coninue his process of muliplying by 1 as many imes as necessary o complee he conversion (look a exercise 7 of Chaper s 1 workshee.)

15 15 SUMMARY OF CHPTER 1 Moion is a change in posiion/displacemen over ime. Moion can be measured by is hree properies; speed, velociy, and acceleraion. Speed is a measure of how fas or how slowly an objec is moving. I is a raio of he disance raveled divided by ime. Disance and ime are wo examples of scalar quaniies. A scalar quaniy can be compleely described by a number (magniude) and uni. Because speed is no consan over he enire disance raveled, a mos common average speed is used. Measuremen in physical sciences is so imporan. I consiss of comparing a quaniy o a sandard or uni and associaing a numerical number and uni o he measured quaniy. Usually, numerical values are eiher exremely large or small. Scieniss used scienific noaion o make hese numbers more readable. Conrary o speed, velociy is a vecor quaniy, which requires a direcion for a complee descripion. Acceleraion is a measure of how fas or slowly is he change in velociy (no speed). I is a vecor quaniy and is direced in he direcion of he change in velociy. Average values of velociy and acceleraion are again more common. Insananeous speed is he speed a he momen, namely i is he speed a very shor inervals of imes ha reach, bu no equal zero. Moion is eiher uniform or non uniform. Uniform moion is moion on a sraigh line and occurs when is successive disances or displacemens are equal a equal imes. Conrary o his is he non uniform moion. The meric sysem of measuremen or is exended version SI is he mosly used sysem around he world because i is based on prefixes or power of en. Acceleraion is a measure of how fas or how slowly is he change in velociy over ime. I is a vecor and poins in he direcion of he change in velociy. Changing unis require conversion facors. A conversion facor is a saemen ha relaes wo unis. Forming a raio of value 1 from his saemen allows us o eliminae he unwaned unis and come up wih he waned uni. Basic Equaions d speed v d average speed v, D velociy v v v f accelerai on a x or v i x f x i

16 16 Chaper 1 Workshee Par 1: Senence Compleion 1. Moion is a in he objec s wih respec o A is needed o measure he posiion of an objecs in moion. 3. A physical quaniy ha has a magniude (number and a uni) only is called a A physical quaniy ha has boh magniude and direcion is called a meer is equivalen o cenimeer and 1 millimeer is equivalen o cenimeer. 6. The is he meric (SI) uni of lengh in he meric sysem and he is he uni for ime. 7. The prefix has a power of en as and he 10-9 has he prefix The measure of how fas or how slowly an objec is called The measure of how fas or how slowly he velociy is changing is called Change of velociy over ime is called The is any sraigh line moion in which equal displacemens occurs during any successive equal ime inervals. 12. The velociy is he velociy (speed and direcion) a he momen and no he average over he enire hour. 13. Millisecond = second. Par 2: General Review Quesions 1. Wha is he basic meric uni of mass? Wha is he basic SI uni of mass? 2. Give he meric prefix for 1000, Give he power of en of Wrie he abbreviaion of 5.6 kilomeers, 2.3 millimeers 5. Which is larger? 1cm or 1mm, 100m or 1km 6. Does he car speedomeer measures average speed or he insananeous speed?

17 17 7. You hrow a ball agains a wall and he ball bounces back oward you wih he same speed as i had before i his he wall. Does he velociy of he ball remain he same as he speed? 8. Suppose in an unidenified sysem of measuremen he disance/velociy is measured by he uni J and ime by K A. Wha would he uni of speed be in his sysem? B. Wha would he uni of velociy be in his sysem? C. Wha would he uni of acceleraion be in his sysem? 9. Two cars A and B are moving wih consan velociies v and 2v respecively a a cerain amoun of ime. During his ime inerval, which car A or B is moving wih greaer acceleraion? Par3: Muliple Choices 1. Which is a vecor quaniy? A. Speed. B. Displacemen. C. Disance. D. Mass. 2. When a quaniy is muliplied or divided by one, he value is A. Increased. B. Decreased. C. Unchanged. D. None of he above. 3. The uni m/s 2 is for A. Velociy B. Speed C. Insananeous speed D. Acceleraion 4. Displacemen A. Is a measuremen of mass B. Is a measuremen of ime C. Can be described only wih a number D. Showing direcion and disance 5. Temperaure is A. A vecor quaniy. B. A scalar quaniy. C. Neiher a vecor nor a scalar.

18 18 D. None of he above. Par4: True/False (If your answer is F, hen ry o correc he saemen) 1. Velociy is he same as speed. A. True B. False 2. Velociy is always consan. A. True B. False 3. Velociy is a scalar and speed is a vecor quaniy. A. True B. False 4. Uniform moion is moion along a sraigh line of consan slope. A. True B. False 5. The average speed and insananeous speed are he same. A. True B. False Par6: Exercises 1. A driver covers a disance of 300 km in a ime of 2.5 hours. Wha is he average speed for his rip? 2. A driver drives for 4.5 hours a an average speed of 65 km/h. Wha disance does he ravel in his ime? 3. A suden walks a disance of 320 m wih an average speed of 1.5 m/s. Wha ime was required o walk his disance? 4. Saring from res and moving in a sraigh line, a runner runs wih velociy of 6 m/s in a ime of 2 s. Wha is average acceleraion of he runner? 5. The velociy of a rain decreases from 40 m/s o 20 m/s in 4 s. Wha is he average acceleraion of he rain? 6. A car is moving a 25 m/s when he driver applies he brakes. If i sops in 3 s, wha is is average acceleraion? 7. Conver 0.05 km o cenimeers

19 19 Par 7: Challenge Problems 1. A car is ravelling in a sraigh line wih an iniial velociy of 10 m/s acceleraes a 2 m/s 2 o a velociy of 20 m/s. A. How much ime does i ake for he car o reach velociy of 20 m/s? B. Wha is he disance raveled by he car during his ime? 2. A car raveling around a circle rack wih consan speed. Is his car moving wih consan velociy? Explain 3. Wha is your age in milliseconds?

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