Topic 1: Linear motion and forces

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1 TOPIC 1 Topic 1: Linear moion and forces 1.1 Moion under consan acceleraion Science undersanding 1. Linear moion wih consan elociy is described in erms of relaionships beween measureable scalar and ecor quaniies, including displacemen, disance,, and elociy 1 Sole problems using = s Inerpre soluions o problems in a ariey of conexs. Explain and sole problems inoling he insananeous elociy of an objec. 2. Acceleraion is a change in moion. Uniformly acceleraed moion is described in erms of relaionships beween measurable scalar and ecor quaniies, including displacemen,, elociy, and acceleraion. Sole problems using equaions for consan acceleraion and a =. Inerpre soluions o problems in a ariey of conexs. Make reasonable and appropriae esimaions of physical quaniies in a ariey of conexs. 3. Graphical represenaions can be used qualiaiely and quaniaiely o describe and predic aspecs of linear moion. Use graphical mehods o represen linear moion, including he consrucion of graphs showing: posiion ersus ime elociy ersus ime acceleraion ersus ime. Use graphical represenaions o deermine quaniies such as posiion, displacemen, disance, elociy, and acceleraion. Use graphical echniques o calculae he insananeous elociy and insananeous acceleraion of an objec. 4. Equaions of moion quaniaiely describe and predic aspecs of linear moion. Sole and inerpre problems using he equaions of moion: = 0 a s= a2 2 = 0 2 2as 5. Verical moion is analysed by assuming ha he acceleraion due o graiy is consan near Earh s surface. 6. The consan acceleraion due o graiy near he surface of he Earh is approximaely g = 9.80 ms -2. Sole problems for objecs undergoing erical moion because of he acceleraion due o graiy in he absence of air resisance. Explain he concep of free-falling objecs and he condiions under which free-falling moion may be approximaed. Describe qualiaiely he effecs ha air resisance has on erical moion. 7. Use equaions of moion and graphical represenaions o deermine he acceleraion due o graiy. Speed The of an objec is defined as he disance he objec raels per uni ime. The disance raelled by an objec is simply how far i moes. The uni of is kilomere per hour (kmh -1 ) or mere per second (ms -1 ). Noe: We wrie kmh -1 no km/h and ms -1 no m/s. The sandard inernaional (SI) uni is ms -1. SACE 2016 Essenials Educaion 3

2 STAGE 1 PHYSICS TOPIC 1: LINEAR MOTION AND FORCES The equaion for calculaing is = disance ime Using symbols we wrie = s Where =, s = disance and = ime. If he disance is in kilomeres and he ime is in hours, he uni of is kmh -1. If he disance is in meres and he ime is in seconds, he uni of is ms -1. Differen ypes of Aerage Calculaing he of an objec ofen inoles calculaing an aerage. Aerage does no ake ino accoun any changes in moion. I inoles he oal disance raelled and he oal ime. I doesn indicae wheher he objec s up, slows down or sops during he journey. For insance, a car may rael beween wo owns. I s up as i akes off from a se of lighs, i slows down as i approaches he nex se of lighs and i emporarily sops when i reaches a red ligh. Consan a = s oal oal Consan means ha an objec raels exacly he same disance eery uni of ime. Ligh raels wih a consan of meres eery second. Sound waes rael wih a consan of 330 meres eery second in air (his can change depending on he densiy of he air). If a car is raelling wih a consan of 60 kmh -1, his means ha i raels exacly 60 kilomeres eery hour. The diagram aboe illusraes consan moion or. The dos are equally spaced, which means he objec raels he same disance per uni of ime, i.e. i raels wih consan. Insananeous Insananeous is he of an objec a a paricular insan in ime. I is wha he omeer in a car measures. As he car s up or slows down he needle on he omeer poins o he of he car a a paricular insan of ime. Science as a human endeaour Laser guns Laser guns work by sending ou pulses of infra-red laser ligh owards a moing objec, such as a car. The ime aken for a pulse o reurn o he gun is recorded. The disance o he car is calculaed using: s = = The objec coninues moing, and he ime aken for a second pulse o reurn o he laser gun is recorded. The new disance o he car is calculaed using: s = = The disance raelled by he car beween he wo pulses is he difference beween hese wo alues. The of he car is calculaed using: = s raelled beween pulses beween pulses Inesigae oher ways of calculaing he of an objec, e.g. radar gun, poin-o-poin cameras. Wha are he benefis and limiaions? Running wih dinosaurs How did Rober Alexander (1976) deelop a mehod for deermining he gai and of dinosaurs? 4 Essenials Educaion

3 TOPIC 1 Common Conersions useful o problem soling km o m 1000 or 10 3 cm o m 100 or 10 2 minues o seconds (s) 60 hours o s days o s kmh -1 o ms ms -1 o kmh Worked examples 1. A dog runs 30 m in 4.0 s. Calculae he aerage of he dog. = s = 30 4 = 7.5 ms-1 2. A marble circles he inside rim of a bowl of radius 15.0 cm fie imes in 20.0 s. Deermine he aerage of he marble. radius = 15.0 cm = 0.15 m (The disance coered is he circumference of he bowl. We calculae he circumference using 2 r) = 20.0 s = s = 2 r 5 20 = A boa raels 10.0 km in 30.0 minues. = ms -1 (a) Calculae he aerage of he boa in kmh -1 and ms -1. s = 10.0 km = 30.0 minues = = 0.5 h = s = 10 = 20.0 kmh kmh -1 = = 5.56 ms -1 (b) Calculae he disance raelled by he boa in 6.50 hours. s = = = 130 km 4. Ligh raels wih a of ms -1. Calculae he ime aken for ligh o rael from he Sun o Earh, a disance of m. = s = = 500 s Essenials Educaion 5

4 STAGE 1 PHYSICS TOPIC 1: LINEAR MOTION AND FORCES Vecor and scalar quaniies Quaniies ha hae size or magniude only are called scalar quaniies. Examples include mass, ime, energy and emperaure. Quaniies ha hae boh magniude and direcion are called ecor quaniies. One example is force (a push or a pull). This is because an objec can be pulled or pushed in a gien direcion e.g. 5 N eas. We will come across many ecor quaniies hroughou his course. We will deal wih each as i arises. Some examples of scalar and ecor quaniies are summarised in he able below. Scalar quaniies disance ime mass olume emperaure charge hea energy power Represening ecor quaniies Vecor quaniies displacemen elociy acceleraion force momenum elecric field magneic field From your Year 10 sudies, you will be familiar wih a force being a push or pull. Force has magniude and direcion, and is herefore a ecor quaniy. Head A ecor quaniy is denoed in bold ype or wih an arrow aboe he symbol. F = 5 N or F = 5N An arrow is used o represen he ecor quaniy. The lengh of he arrow represens he magniude of he ecor and he arrow head poins in he direcion of he ecor. Tail This may represen 5 N norh. 6 Essenials Educaion

5 TOPIC 1 Adding ecor quaniies Worked examples 5 N norh + 4 N norh 5 N 4 N 1 9 N norh 4 N norh + 3 N eas 4.0 N 3.0 N The oal or resulan force is A ecor riangle is drawn in order o add he wo ecors. The ecors are added head o ail. The order doesn maer. Pyhagoras Theorem is used o find he magniude of he resulan force and rigonomeric raios are used o find he direcion. 3 N 2 2 F = = 5N R opposie 3 anθ = = adjacen 4 θ an ( 3 1 = 4 ) θ = 37 o 4 N θ F R The final answer is expressed wih magniude and direcion. F R = 5.0 N N37 Noe: A scale diagram could hae been used o sole he aboe problem. Essenials Educaion 7

6 STAGE 1 PHYSICS TOPIC 1: LINEAR MOTION AND FORCES Displacemen and elociy Disance is how far an objec has raelled (or lengh coered). I is a scalar quaniy because no direcion is inoled. Posiion is he locaion of a body. Displacemen is he change in posiion and includes direcion. I is a ecor quaniy since i inoles boh magniude (size) and direcion. Velociy is defined as displacemen per uni ime. Velociy is a ecor quaniy. Worked examples 1. A man walks 5.0 km in a norherly direcion and hen 2.0 km in a souherly direcion. (a) Sae he disance raelled by he man. 7.0 km (b) Sae he displacemen of he man. 3.0 km Norh 2. A ferre races 20.0 m S and hen 10.0 m eas. (a) Calculae he disance raelled by he ferre m (b) Calculae he displacemen of he ferre. 2 2 s = = 22.4m 20.0 m s = 22.4 m S26.6 E 3. A boa is rowed wih a of 3.00 ms -1 in a norherly direcion. I encouners a waer curren flowing a 1.00 ms -1 in an easerly direcion. (a) Calculae he resulan elociy of he boa ms -1 = 3.16 ms -1 N18.4 E (b) Calculae he boa s displacemen afer 10.0 minues. s θ 10.0 m = = 3.16 (10 60) = 1896m = m N18.4 E (c) Assume ha he rower s inenion was o row o a desinaion direcly norh of his saring poin. How far off course is he boa afer 10.0 minues? s = = 1 (10 60) = 600m s 1.00 ms -1 θ opposie 10 anθ = = adjacen 29 θ an ( 10 1 = 20 ) θ = 26.6 o (d) How could he effec of he curren be compensaed for? = = 3.16ms θ an ( 1 1 = 3 ) θ = 18.4 o opposie 1 anθ = = adjacen 3 Row ino he curren wih a elociy of 3.16 ms -1 N18.4 W 8 Essenials Educaion

7 TOPIC 1 4. A man for his morning finess rouine walks 5.50 km W and hen urns and walks 10.0 km S in 3.00 hours and 15.0 minues. Calculae he (a) disance raelled by he man km = 16.0 km (b) man s final displacemen km 5.50 km s θ s 2 2 = = 11.4km opposie 10 anθ = = adjacen 5.5 θ an ( 10 1 = 5.5 ) θ = (c) man s aerage for he journey. s 15.5 = = = 4.80 kmh (d) man s aerage elociy for he journey. s 11.4 = = = 3.50 kmh Subracing ecors s = 11.4 km W61.2 S If 5 N norh is represened as 5N, hen -5N mus mean 5N or 5 N souh. When subracing a ecor, i is added in reerse. Therefore 5N norh 5 N souh = 5N 5N = 5N + 5N = 10N Examples 1. 50N 100N = 50N + 100N = 150N 2. 2N 3N = 2N + 3N = 1N Acceleraion If an objec is no raelling wih consan (i.e. i is ing up or slowing down) is said o be acceleraing. Acceleraion is he change in elociy per uni ime or he rae of change in elociy. a = Δ Δ = f i Δ where = change in elociy f = final elociy in ms -1 i = iniial elociy in ms -1 = ime aken for he change in elociy in s Unis: ms -2 Since elociy is a ecor quaniy, hen he acceleraion will also hae a magniude and direcion and is herefore considered a ecor quaniy. Essenials Educaion 9

8 STAGE 1 PHYSICS TOPIC 1: LINEAR MOTION AND FORCES Noes: 1. If direcion is no inoled i.e. only he changes, hen he acceleraion of an objec is he change in per uni ime. 2. Alhough he of an objec may be consan, a change in direcion consiues a change in elociy. The objec is said o accelerae. 3. A consan acceleraion of 3 ms -2 means ha he objec s up by 3 ms -1 eery second i.e. he increases as follows afer eery second: 0 ms -1, 3 ms -1, 6 ms -1,9 ms -1, 12 ms -1, 15 ms If an objec s up, he acceleraion is posiie. 5. If an objec slows down, he acceleraion is negaie. This is someimes called a deceleraion. 6. The acceleraion due o graiy is consan near he surface of he Earh and is g = 9.80 ms -2 owards he cenre of he Earh. Worked examples 1. A car acceleraes from res o a of 60.0 kmh -1 in 5.00 seconds. Calculae he acceleraion of he car. 60 a = f i = = 3.33ms 2 Δ 5 2. A ruck can accelerae from res a a rae of 4.00 ms -2. Calculae is afer 8.00 seconds. Answer in ms -1 and kmh -1. a = f i Δ f = i +a = = 32.0ms 1 =115kmh 1 3. A ball is hrown erically ino he air wih a of 10.0 ms -1. Calculae he ime aken o reach is maximum heigh. a = f i Δ Δ = f i a 4. A ball collides wih a wall as shown. = =1.02s 7.0 ms ms -1 (a) Calculae he ball s change in elociy. = f i = 7 7 = 7 +7 =14ms 1 (90 away from he wall) (b) If he collision akes s, calculae he acceleraion experienced by he ball. a = Δ Δ = =120ms 2 Helpful online resources Explore he relaionship beween elociy and acceleraion using he compuer ineracie The Maze Game. hps://phe.colorado.edu/en/simulaion/legacy/maze-game 10 Essenials Educaion

9 TOPIC 1 Graphing Moion Saionary Moion disance acceleraion S a 1 Consan Speed disance S acceleraion a The gradien of a disance-ime graph represens. gradien = rise run = Δs Δ Consan acceleraion disance S acceleraion a The disance ime graph aboe indicaes ha he disance raelled per uni ime increases. This represens acceleraed moion. disance S acceleraion a The disance ime graph aboe represens a negaie acceleraion or deceleraed moion as he disance raelled per uni ime is decreasing. Essenials Educaion 11

10 STAGE 1 PHYSICS TOPIC 1: LINEAR MOTION AND FORCES The gradien of he angen of a disance ime graph a any paricular ime represens he insananeous elociy a ha ime. We wrie = Δs Δ as Δ 0 The area under of a ime graph represens disance. Non consan acceleraion A cured ime graph indicaes ha he is consanly changing. The gradien of he angen a a gien poin represens he insananeous acceleraion. i.e. he change in elociy ha akes place oer a ery shor period of ime 0. We wrie Worked examples a = Δ Δ 1. Consider he graph below for he moion of a oy car. 30 as Δ 0 S (m) 20 (a) Describe he moion of he oy car (s) Noe: This diagram is no o scale The oy car raels wih consan, raelling 20 m in 5 s. The car hen remains saionary for 5 s and hen raels wih a higher consan for he remaining 3 seconds. (b) Sae he oal disance raelled by he oy car. 30 m (c) Calculae he aerage of he oy car. = s = = 2.3ms 1 12 Essenials Educaion

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