FUNDAMENTAL CONCEPTS

Transcription

1 UNDAMENTAL CONCEPTS ORCES AND MOTION Measuring an Describing Moion Spee (m/s) = isance (m) ime (s) Velociy is spee in a gien irecion (an example of a ecor i has size an irecion) Aerage spee = (m/s) oal isance (m) ime aken (s) Negaie elociy Posiie elociy Insananeous spee is spee a a gien ime 1 Aerage spee is spee oer a 2 perio of ime Acceleraion (m/s 2 ) = change in elociy (m/s) ime aken (s) Time oer a known isance Ticker ape 1 o eery 1/50 h secon 1/10 secon Measuring spee Ligh Gaes Inerrup car of known lengh Consan spee equally space os. Measure isance for 5 os, ime aken was 1/10 h secon. SCALAR size only Acceleraion os ge furher apar Lengh of a 5-ick is proporional o he spee. SPEED rae of change of posiion. VELOCITY spee in a gien irecion. ACCELERATION rae of change of elociy (usually aken as increasing, bu can be eiher). DECELERATION rae of ecrease of elociy. VECTOR size an irecion Aerage spee Spee in gae = 1 2 = Acceleraion = lengh of inerrup car ime beam blocke isance beween gaes ime beween gaes change in spee beween gaes ime beween gaes Quesions 1. A oy rain runs roun a circular rack of circumference 3 m. Afer 30 s, i has complee one lap. a. Wha was he rain s aerage spee? b. Why is he rain s aerage elociy zero? c. The rain is place on a sraigh rack. The rain accelerae uniformly from res o a spee of 0.12 m/s afer 10 s. Wha was is acceleraion?. Describe hree ifferen ways of measuring he rain s aerage spee an wo ifferen ways of measuring he rain s insananeous spee. e. How coul ligh gaes be use o measure he rain s acceleraion along a 1 m lengh of rack? 2. Explain he ifference beween a scalar an ecor. Gie an example of each. 3. A car leaks oil. One rip his he roa eery secon. Draw wha you woul see on he roa as he car acceleraes. 5

2 ORCES AND MOTION Moion Graphs change in isance (m) Graien = = = spee (m/s) change in ime (s) Disance Graphs o no hae o sar a (0,0) Cure geing seeper = increasing graien = increasing spee = acceleraion Time change in elociy (m/s) acceleraion Graien = = = change in ime (s) (m/s 2 ) Aerage elociy ( + u) = 2 Velociy Iniial elociy, u, oes no hae o be zero Area uner graph = oal isance raelle inal elociy, Negaie elociies ell us ha he objec is raelling backwars Zero elociy saionary objec Horizonal line = consan elociy (zero acceleraion) Time Quesions 1. Copy an complee he following senences: a. The slope of a isance ime graph represens b. The slope of a elociy ime graph represens c. The area uner a elociy ime graph represens 2. Reraw he las four graphs from p7 for an objec ha is eceleraing (slowing own). 3. Skech a isance ime graph for he moion of a ennis ball roppe from a secon floor winow. 4. Skech a elociy ime graph for he moion of a ennis ball roppe from a secon floor winow. Take falling o be a negaie elociy an bouncing up o be a posiie elociy. 6

3 Disance ime Saionary Velociy ime Disance always says a same alue Velociy says a zero Disance is increasing objec moing away Consan elociy Posiie elociy = going away Going away Disance is ecreasing objec geing closer Geing closer Negaie elociy = geing closer Acceleraing Acceleraing as isance increases eer more rapily Going away Posiie elociy = going away Increasing spee Acceleraing as objec ges closer (smaller isance) eer more quickly Geing closer Increasing spee Negaie elociy = coming closer 7

4 ORCES AND MOTION Equaions of Moion Time aken, Consan acceleraion or eceleraion, a inal spee, Iniial spee, u Disance, x N.B. This moion coul also be a falling objec, or a rising one, like a rocke. N.B. aerage spee ( + u) = 2 = Velociy ime graph for his moion oal isance oal ime x = So ( + u) = x 2 x = 1 / 2 ( + u) u an herefore Velociy change in elociy ( u) Graien = acceleraion = = ime aken Rearranging a = Area of riangle = 1 / 2 base heigh = 1 / 2 ( u) Area of recangle = u u gies = u + a. 1 Time Toal isance raelle = x = area uner graph = u + 1 / 2 ( u) rom 1 : ( u) = a so x = u + 1 / 2 (a) x = u + 1 / 2 a 2 2 Area of rapezium Alernaiely, isance raelle = x = area uner graph q same resul = area of rapezium = 1 / 2 (u + ) p A = 1 / 2 (p + q)r Bu from 1 = ( u) a so x = 1 / 2 (u + ) ( u) a r Rearranging 2 = u 2 +2ax 3 Quesions Show ALL your working. 1. Wha quaniies o he ariables x, u,, a, an each represen? 2. Wrie a lis of hree equaions which connec he ariables x, u,, a, an. 3. A car acceleraes from 10 m/s o 22 m/s in 5 s. Show ha he acceleraion is abou 2.5 m/s Now show he car in (3) raelle 80 m uring his acceleraion: a. Using he formula 2 = u 2 + 2ax. b. Using he formula x = u + 1 / 2 a A ball falls from res. Afer 4 s, i has fallen 78.4 m. Show ha he acceleraion ue o graiy is 9.8 m/s Show ha x = 1 / 2 (u + )( u)/a rearranges o 2 = u 2 + 2ax. 7. A ball hrown sraigh up a 15 m/s, feels a ownwar acceleraion of 9.8 m/s 2 ue o he pull of he Earh on i. How high oes he ball go before i sars o fall back? 8

5 ORCES AND MOTION Describing orces Roaion Change shape Push Descripion E.g. Type of force Graiaional pull Cause by of he Earh Acing on on he moon EECTS O ORCES ORCES Are ecors Pull Spee up T w i s Direcion Slow own Shown by size/lengh of arrow ree boy iagrams E.g. Sliing box Push of floor on box E.g. penulum E.g. rocke Acceleraion (ouble-heae arrow no aache o objec) Size Shown by irecion of arrow Elecrosaic Normal conac ricion TYPES O ORCE Magneic Graiaional Drag Tension Thrus Simple iagrams o show all he forces acing on an objec. properly calle Push of floor = weigh (arrows same lengh bu ac in opposie irecions) ricion of floor on box Weigh (graiaional pull of Earh on box) Tension (pull of sring on bob) Weigh (graiaional pull of Earh on bob) Thrus (push of gas on rocke) Velociy (arrow no aache o objec) Weigh (graiaional pull of Earh on rocke) Normal conac force N.B. no he forces cause by he objec acing on anoher objec Push of one surface on anoher a righ angles o he surface. Due o aoms in each surface being slighly squashe ogeher an pushing back Weigh shorhan for he graiaional pull of a plane or moon (usually he Earh) on an objec Resulan force a single force ha can replace all he forces acing on a boy an hae he same oerall effec as all he iniiual forces acing ogeher. I is he sum of all he iniiual forces aking heir irecions ino accoun. Drag of waer on boa Quesions 1. Lis hree effecs forces can hae. 2. Explain wha he erm resulan force means. 3. To escribe a force fully, wha hree pieces of informaion shoul be recore? 4. Copy an a arrows o hese iagrams o show all he forces (an heir irecions) acing on: a. A neball flying hrough he air. b. A je ski. Parallel forces a Perpenicular forces Pyhagoras Theorem Push of win on boa Resulan = push of win on boa rag of waer on boa Tension 1 Tension 2 E.g. Bow an arrow Resulan force on arrow, R R 2 = (ension 1) 2 + (ension 2) 2 Shows opposie irecion c. A cyclis freewheeling own a hill.. A chil on a swing pushe by an aul. 5. Calculae he resulan force in he following cases: 4 N 3 N a. b. c. 3 N 5 N 7 N 10 N 4 N 4 N 8 N. e. 5 N 10 N 1 N 3 N 2 N 7 N 4 N 4 N 9

6 ORCES AND MOTION Balance orces Newon s irs Law Alreay saionary Remains saionary Push of groun Weigh Push of groun weigh = 0 Thrus Weigh Acceleraes in he irecion of he resulan force Push of groun Resulan = 0 Acceleraion Iniially saionary Thrus orce Lif of wings Lif weigh = 0 Thrus rag = 0 Resulan no zero Change in elociy Resulan = 0 Weigh Thrus Thrus > rag Resulan force in irecion of moion Alreay moing Drag Acceleraion Thrus Thrus < rag Velociy Resulan force in opposie irecion o moion Velociy Weigh Acceleraion Coninues o moe wih same spee an irecion. (No change in elociy.) Lif of wings Lif of wings Weigh Lif weigh = 0 (leel fligh) Acceleraion Drag Lif weigh = 0 (leel fligh) Drag Deceleraion Why o moing objecs seem o slow own? On Earh objecs moe: Oer soli surfaces In or oer waer In he amosphere More Moion Moion ricion Moion examples ricion Moion Drag Air resisance In all cases, resisie forces ac o oppose moion. Therefore, unless a force is applie o balance he resisie force he objec will slow own. In space, here are no resisie forces an objecs will moe a consan spee in a sraigh line unless anoher force acs. Newon s irs Law of Moion: If he resulan force acing on a boy is zero, i will remain a res or coninue o moe a he same spee in he same irecion. If he resulan force acing on a boy is no zero, i will accelerae in he irecion of he resulan force. 10 Quesions 1. In which of he following siuaions is he resulan force zero? Explain how you ecie. a. A snooker ball resing on a snooker able. b. A car acceleraing away from raffic lighs. c. A ball rolling along leel groun an slowing own.. A skier raelling own a pise a consan spee. e. A oy rain raelling roun a circular rack a consan spee. 2. A lif an is passengers hae a weigh of 5000 N. Is he ension in he cable supporing he lif: i. Greaer han 5000 N, ii. Less han 5000 N, iii. Exacly 5000 N when: a. The lif is saionary? b. Acceleraing upwars? c. Traelling upwars a a consan spee?. Deceleraing whils sill raelling upwars? e. Acceleraing ownwars? f. Traelling ownwars a consan elociy? g. Deceleraing while sill raelling ownwar? 3. Explain why all objecs moing on Earh will eenually come o res unless anoher force is applie?

7 ORCES AND MOTION Unbalance orces Newon s Secon Law Velociy Velociy Spee up orce Acceleraion Direcly proporional o Non-zero resulan force Experimens show acceleraion is Slow own orce Inersely proporional o Deceleraion (negaie acceleraion) orce Mass Velociy 3 acceleraion m m Velociy 1 acceleraion 2 acceleraion m 2m 1 / 2 acceleraion 1 acceleraion m 1 / 3 acceleraion Time We efine he Newon as he force neee o accelerae a 1 kg mass a 1 m/s 2. Therefore, we can wrie: orce (N) = mass (kg) acceleraion (m/s 2 ). Newon s Secon Law E.g. 800 N Mainly air resisance 1000 kg (Driing 3600 N force) Resulan force = 2800 N Acceleraion = force/mass = 2800 N/1000 kg = 2.8 m/s 2. Wha is mass? A measure of he amoun of maerial in an objec. Neer aries from place o place. (ricion/air resisance) 3m 20 N The relucance of he objec o accelerae when a force is applie (is ineria). Large mass Large force for small acceleraion Ouch! Concree ball Time 0.3 m/s 2 Driing force 100 kg Resulan force = mass acceleraion = 100 kg 0.3 m/s 2 = 30 N Resulan force = riing force 20 N Driing force = 50 N Small mass ooball Means resisance o change (in his case is elociy). Small force gies large acceleraion. Quesions 1. Calculae: a. The force neee o accelerae a 70 kg spriner a 6 m/s 2. b. The acceleraion of a 10 g bulle wih 2060 N explosie force in a gun barrel. c. The mass of a ship acceleraing a 0.09 m/s 2 wih a resulan hrus of N from he propellers. 2. An unergroun ube rain has mass of kg an can prouce a maximum riing force of N. a. When acceleraing in he unnel using he maximum riing force show he acceleraion shoul be 5.7 m/s 2. b. In realiy, he acceleraion is only 4.2 m/s 2. Hence show he resisie forces on he rain are N. 3. Explain why owing a caraan reuces he maximum acceleraion of a car (wo reasons). 4. A fooball mae of concree woul be weighless in eep space. Howeer, i woul no be a goo iea for an asronau o hea i. Why no? 11

8 ORCES AND MOTION Graiaional orces A graiaional fiel is a region of space where objecs wih mass feel forces. Since we lie in he Earh s graiaional fiel, graiaional forces are ery common o us. We gie he graiaional force beween a mass an he Earh a special name, weigh. 1 kg up o 20 km W = 9.8 N EARTH 1 kg W = 2.5 N 6400 km Inisible graiaional fiel lines show irecion he force on a mass acs owars he cenre of he Earh. Away from he Earh, he graiaional fiel ges weaker, bu his is no significan unil you hae gone abou 20 km aboe he surface. Weigh always acs owars he cenre of he Earh. The force per kilogram of mass is a goo way of measuring he srengh of he Earh s graiaional fiel. Near he surface of he Earh, he Earh s graiaional fiel exers abou 9.8 N (ofen roune o 10 N) per kilogram of mass. Graiaional fiel srengh g, efine as he force per kilogram of mass place a he poin of ineres. Weigh (N) = mass (kg) graiaional fiel srengh (N/kg). 12 m W = mg 10 m/s 2 g = 10 N/kg Earh If an objec is in free fall, he only force on i is weigh (ifficul in pracice because of air resisance). The mass of an objec is he same eerywhere. The weigh epens on he graiaional fiel srengh. Hence, acceleraion ue o free fall is equialen o graiaional fiel srengh. Applying Newon s secon law All masses fall wih an (proiing here 5 kg 8 N Howeer, his Moon g = 1.6 N/kg Resulan force = mass acceleraion Then acceleraion (m/s 2 ) = weigh (N) / mass (kg). acceleraion of abou are no resisie forces). 1 kg 10 m/s m/s 2 10 m/s N 1.6 m/s 2 5 kg 50 N You can hink of his as he weigh increasing o compensae for he increase mass so all objecs fall a he same rae, inepenen of heir mass. 10 N Earh g = 10 N/kg Quesions 1. Near he surface of he Earh, wha are he alues of: a. The acceleraion ue o free fall? b. The graiaional fiel srengh? 2. Wha are he weighs on he Earh of: a. A book of mass 2 kg? b. An apple of mass 100 g? c. A girl of mass 60 kg?. A blae of grass of mass 0.1 g? 3. Wha woul he masses an weighs of he aboe objecs be on he moon? (Graiaional fiel srengh on he moon = 1.6 N/kg) km aboe he surface of he Earh a 1 kg mass has a weigh of 2.5 N. Wha is he graiaional fiel srengh here? If he mass was roppe, an sare falling owars he cenre of he Earh, wha woul is iniial acceleraion be? 5. Wrie a few senences o explain he ifference beween mass an weigh. is also he efiniion of graiaional fiel srengh. 1 kg 10 m/s 2

9 ORCES AND MOTION Terminal Velociy Velociy Terminal elociy occurs when he acceleraing an resisie force on an objec are balance. Key ieas: Drag/resisie forces on objecs increase wih increasing spee for objecs moing hrough a flui, e.g. air or waer. When acceleraing an resisie forces are balance, Newon s irs Law says ha he objec will coninue o rael a consan elociy. Terminal elociy Driing force remains consan bu air resisance increases as ehicle spees up Time Acceleraion Air resisance Air resisance increases as spee increases Weigh Air resisance Air resisance Driing force Air resisance Driing force Terminal elociy Weigh Driing force > air resisance Vehicle acceleraes Velociy Driing force = air resisance No acceleraion Deceleraion Terminal elociy Spee ecreases Air resisance Large surface area grealy increases air resisance Terminal elociy (parachue close) Acceleraing Deceleraing Terminal elociy (parachue open) New, lower erminal elociy Reacion of groun Weigh Weigh Air resisance Slowing own reuces air resisance Lubricaion ricion Time Wear on moing pars Weigh Grip of yres/shoes on groun Parachue Use wheels raher han sliing Nuisance Resisie forces Useful Shulecock Brakes Reuce fuel economy Drag on ehicles Quesions 1. Wha happens o he size of he rag force experience by an objec moing hrough a flui (e.g. air or waer) as i spees up? 2. Wha force aracs all objecs owars he cenre of he Earh? 3. Why oes a car nee o keep is engine running o rael a consan elociy? 4. A ho air balloon of weigh 6000 N is release from is mooring ropes. a. The upwar force from he ho air rising is 6330 N. Show he iniial acceleraion is abou 0.5 m/s 2. Sreamline shapes b. This acceleraion graually ecreases as he balloon rises unil i is raelling a a consan elociy. Explain why. c. A mass of 100 kg is hrown oerboar. Wha will happen o he balloon now?. Skech a elociy ime graph for he whole journey of he balloon as escribe in pars a c. 5. Explain why he following are likely o increase he perol consumpion of a car: a. Towing a caraan. b. Aing a roof rack c. Driing ery fas. 13

10 ORCES AND MOTION Projeciles A rue projecile only has one force, weigh, acing on i when i is in fligh. The secre is o consier he elociy of he projecile o be mae up of horizonal an erical elociies, which can be consiere separaely. W a = 0 m/s 2 g = 9.81 m/s 2 We ignore air resisance; herefore, here is no horizonal acceleraion (or eceleraion). A any ime moion is mae up of 1. Horizonal elociy: No horizonal forces (ignoring air resisance). Therefore by Newon s irs Law, no change in elociy horizonally. 2. Verical elociy: Projecile acceleraes ownwars uner graiy, slowing as i rises, sopping a he op an falling back. Examples: Kicke fooball Dars Cannon ball Golf ball Use V = u V + g an x V = u V + 1 / 2 g 2 where g = 9.81 m/s 2 Long jumper Thrus Iniial elociy. u V V H H a = 0 m/s 2 NOT rockes H Two forces Weigh Pah is calle he rajecory. x V resulan g = 9.81 m/s 2 Shape is parabolic, same as he graph of Range = V H ime of fligh y = c x 2 H Time of fligh = H 2 ime o y maximum Iniial elociy is mae up c heigh. from wo ecors a righ angles, calle V componens. The oerall effec (he resulan) is he iniial Impac elociy elociy of he projecile an is foun by by Pyhagoras Theorem. x Pyhagoras Theorem. H resulan = uv R 2 V + 2 H R = u V + H H V V resulan 14 Quesions 1. In an ieal worl how many forces ac on a projecile, an wha are hey? 2. Sae he alue of he erical acceleraion of a projecile. 3. Explain why he horizonal acceleraion of a projecile is zero. Wha assumpion has o be mae? 4. Explain why a firework rocke canno be analyse as a projecile wih he mehos shown here. 5. A ball is kicke so i has a elociy of m/s horizonally an 9.0 m/s erically. a. Show ha he resulan elociy of he ball has a magniue of 18.0 m/s. b. Show ha he ball akes 0.92 s o reach is maximum heigh aboe he groun. c. or how long in oal is he ball in he air an how far along he groun will i rael?. Show he maximum heigh he ball reaches is 4.1 m. e. Wha will he magniue of is resulan elociy be when i his he groun? Hin: no calculaion neee.

11 ORCES AND MOTION Newon s Thir Law Wheneer an objec experiences a force i always exers an equal..... an..... opposie force on he objec causing he force. 0 N 10 N 10 N 0 N Always hae he same size. These pairs of forces are calle Thir Law pairs. Always he same ype of force. Always ac on ifferen boies (compare wih Newon s irs Law where we are only inerese in he force acing on he boy in quesion). Always ac in opposie irecions. Push of he book ownwars on he able. Equal Graiaional pull ownwars of Earh on he book. Weigh of he book. Push upwar of he able on he book. The reacion of he able on he book. Thir law pairs follow his forma: Equal orce of A on B in one irecion = orce of B on A in he oher irecion Graiaional pull upwars of book on Earh. Normal conac forces. Push of he han on he block. Push of he block on he han. Molecules in he surface are pushe slighly closer ogeher an push back. This is ofen calle he reacion of a surface. ricional push of he surface on he block. ricional push of he block on he surface. Examples Push of he rocke on gas ownwars (ou of he rocke). Push of gas on he rocke upwars (propelling he rocke upwars). ricional push of he foo on he groun (pushes Earh back slighly). ricional push of he groun on he foo (pushes foo forwar his is he force ha propels us forwar). ricional push of he yre on he groun. ricional push of he groun on he yre (pushes car forwars). If he groun is icy, boh hese forces are ery small an we canno walk or rie forwars. Quesions 1. Explain wha is mean by he erm normal conac force. 2. A je engine in an aircraf exers N on he exhaus gases. Wha force o he gases exer on he aircraf? 3. Describe he force ha forms a Thir Law pair wih he following. In each case, raw a iagram o illusrae he wo forces: a. The push eas of he win on a sail. b. The push lef of a bowsring on an arrow. c. The fricional push souh of a rain wheel on a rail.. The normal conac force ownwars of a plae on a able. e. The aracion righ of he norh magneic pole of a bar magne on a souh magneic pole of a ifferen magne. 4. Why are he following no Thir Law pairs? (There may be more han one reason for each.) a. The weigh of a mug siing on a able; he normal conac force of he ableop on he mug. b. The weigh of he passengers in a lif car; he upwar ension in he lif cable. c. The weigh of a pool ball on a able; he horizonal push of he cue on he ball.. The aracion beween he norh an souh magneic poles of he same bar magne. 5. Explain why i is ery ifficul (an angerous) o rie a bicycle across a shee of ice. 15

12 ORCES AND MOTION Momenum an orce (Newon s Laws reisie) Momenum helps o escribe how moing objecs will behae. Momenum (kgm/s) = mass (kg) elociy (m/s) Momenum is a ecor. I has size an irecion (he irecion of he elociy). Newon s Secon Law Resulan force = mass acceleraion = m a = m mu acceleraion = change in a = ( Rearranging elociy/ime aken u)/ Resulan force = mass change in elociy / ime aken = m ( u) / Impulse (Ns) Change in momenum (kgm/s) Hence, an alernaie ersion of Newon s Secon Law If a resulan force acs on a boy free o moe a change in momenum occurs equal o he prouc of he force an he ime for which i acs. orce, Iniial elociy, u Mass, m Time, inal elociy, = m mu Also consier A Zero resulan force A on B No change in momenum Coninues o moe a a seay spee in a sraigh line. B on A Newon s Thir Law As A on B = B on A an objecs mus be in conac for he same ime,, B = m mu = change in momenum. No change in elociy Alreay moing? hen ( A on B ) = ( B on A ) Gain of momenum by B Equal Loss of momenum by A Saionary? Momenum ransferre from A o B Newon s irs Law Says saionary Momenum is consere Consisen wih he iea ha when wo objecs collie hey exer equal an opposie forces on each oher. 16 Quesions 1. Wha unis o we use o measure momenum an impulse (2 answers)? 2. Calculae he momenum of: a. A 55 kg girl running a 7 m/s norh. b. A kg aircraf flying a 150 m/s souh. c. A 20 g snail moing a 0.01 m/s eas. 3. Wha is he connecion beween force an change in momenum? 4. Wha is he change in momenum in he following cases: a. A 5 N force acing for 10 s? b. A 500 N force acing for 0.01 s? 5. Wha force is require o: a. Accelerae a 70 kg ahlee from 0 o 9 m/s in 2 s? b. Accelerae a 1000 kg car from res o 26.7 m/s in 5 s? c. Sop a 10 g bulle raelling a 400 m/s in s? 6. Wha woul be he effec on he force neee o change momenum if he ime he force acs for is increase? 7. A 2564 kg space probe is o be accelerae from 7.7 km/s o 11.0 km/s. If i has a rocke moor ha can prouce 400 N of hrus, for how long woul i nee o burn assuming ha no resisie forces ac? Why migh his no be pracical? How else migh he space probe gain sufficien momenum (see p113 for ieas)?

13 ORCES AND MOTION Momenum Conseraion an Collisions Law of Conseraion of Momenum: Momenum canno be creae or esroye bu can be ransferre from one objec o anoher when hey inerac. There are no excepions o his. I is applie o analyse ineracions beween objecs, which can be classifie as: Velociies Up an righ are aken as posiie. Or Objecs iniially moing owars each oher Objecs originally saionary an moe apar Down an lef are aken as negaie. Collisions or Explosions 1. Momenum before collision 30 m/s 20 m/s 3 kg rifle A up all he iniiual momena aking care oer heir irecions kg 2.0 kg Acs lef so negaie Iniial momenum is always zero for an explosion kg bulle Momenum = 0 kgm/s m 1 u 1 + m 2 u 2 = 0.16 kg 30 m/s + 2 kg ( 20 m/s) = 35.2 kgm/s Oerall momenum acs o he lef. 2. By momenum conseraion: momenum before = momenum afer 0.01 kg m/s m/s 3kg Again ake care oer he irecion of he elociies, are hey posiie or negaie? 0.16 kg 2.0 kg Momenum afer collision = 35.2 kgm/s (i.e. o he lef) 400 m/s Acs lef so negaie Momenum afer explosion = 0 kgm/s (rifle an bulle moe off in opposie irecions) 3. Equae momenum before an afer o fin unknown masses or elociies. Do no worry abou he irecion of an unknown elociy. The mahs will ell you wheher i is posiie or negaie, an herefore is irecion. Momenum afer = m 1 1 +m gm/s = 0.16 kg + 2 kg ( m/s) = 48 m/s Negaie sign ells us he ball raels o he lef (as expece). 4. The force inole epens on he size of he change of momenum an he ime i is exere for. If ime of collision = 0.02 s he force on he ball Momenum afer = m m kgm/s = 0.01 kg ( 400 m/s) + 3 kg = m/s Posiie ells us he rifle recoils o he righ (as expece). If ime of explosion = s hen he force on he bulle Use = m mu 0.02 s = 0.16 kg ( 48 m/s) (0.16 kg 30 m/s) = 624 N (i.e. o he lef) s = 0.01 kg 400 m/s (0.01 kg 0) = 2000 N (i.e. o he lef) 17

14 ORCES AND MOTION Momenum Conseraion an Collisions (coninue) The calculaion of he force exere on he bulle an he ball woul work equally well if he force on he ba or he rifle were calculae. The size of he force woul be he same, bu in he opposie irecion accoring o Newon s Thir Law. Again using = m mu. orce of ball on ba 0.02 s = 2 kg ( m/s) 2 kg ( 20m/s) = 624 N (posiie, o he righ). orce of bulle on gun s = (3 kg 1.33 m/s) (3 kg 0 m/s) = 2000 N (posiie, o he righ). These calculaions show ha he force inole epens on. Boh 1 kg Meal hea s. Wooen hea Time of impac Change of momenum Shor impac ime larger force. Someimes i appears ha momenum is no consere kg Rainrop 5 m/s 0.01 kg 0 m/s Where i he rop s momenum go? Long impac ime less force. Larger change of momenum exers a larger force. Slege hammer = 10 kg This is where he incorrec iea of a force being neee o keep somehing moing comes from. 2 m/s 0 m/s 1.0 kg 1.0 kg Rough surface Where i he ball s momenum go? Boh rop an ball hae an exernal force applie (conac force of he groun on he rop an fricion wih he groun on he ball). Exerna l force applie by Earh means Boh meal heas hae he same conac ime. Their momenum was ransferre o he Earh. Momenum is consere proie no exernal forces ac. Ligh hammer = 1 kg Therefore, a beer form of he Principle of Conseraion of Momenum is... If exernal forces ac, momenum is ransferre o or from he boy exering he force. 18 Quesions 1. When a rainrop his he groun where oes is momenum go? 2. Why o boxers wear pae gloes? 3. A squash ball is hi agains a wall an bounces off. An equal mass of plasicine is hrown a he same wall wih he same spee as he ball, bu i sicks on impac. Which exers he larger force on he wall an why? 4. A golfer swings a 0.2 kg club a 45 m/s. I his a saionary golf ball of mass 45 g, which leaes he ee a 65 m/s. a. Wha was he momenum of he club before he collision? b. Wha was he momenum of he ball afer he collision? c. Hence, show ha he club s elociy is abou 30 m/s afer he collision.. If he club is in conac wih he ball for s, wha is he aerage force he club exers on he ball? 5. A 1.5 kg air rifle fires a 1 g pelle a 150 m/s. Wha is he recoil elociy of he rifle? Show ha he force exere by he rifle on he pelle is abou 70 N if he ime for he pelle o be fire is s. 6. Assume ha he aerage mass of a human being is 50 kg. If all humans on Earh soo shouler o shouler in one place, an jumpe upwar a 1 m/s wih wha elociy woul he Earh, mass kg recoil? 7. Two friens are ice-skaing. One frien wih mass 70 kg is raelling a 4 m/s. The oher of mass 60 kg raelling a 6 m/s skaes up behin he firs an grabs hol of hem. Wih wha spee will he wo friens coninue o moe while holing ono each oher?

15 ORCES AND MOTION Moion in Circles an Cenripeal orces Objec moing in circular pah. Inwar force neee o preen he objec coninuing in a sraigh line as Newon s irs Law preics i shoul. Means cenre seeking. Cenripeal force = resulan force owars cenre of he circle. Cenripeal force changes objec s irecion, no is spee. orce increases as mass increases spee increases raius ecreases. 1 Direcion is coninually changing. Cenripeal acceleraion (changes irecion, no spee). 2 Since elociy is a ecor (spee in a gien irecion), he elociy is coninually changing een hough he spee is consan. 3 Changing elociy implies acceleraion. This cenripeal acceleraion acs owars he cenre of he circle. 4 Therefore, force owars cenre of circle. Cenripeal acceleraion (m/s 2 ) = [elociy (m/s)] 2 Cenripeal force = mass (kg) acceleraion (m/s 2 ) a = 2 /r raius (m) = mass (kg) [elociy (m/s)] 2 = m 2 /r raius (m) Cenripeal force is no a force in is own righ i mus be proie by anoher ype of force. Tension proies cenripeal force Penulum ricional push sieways of roa on yres. e nucleus + Elecrosaic aracion of elecron in aoms o he nucleus proies cenripeal force. Normal conac force on clohes in washing machine rum proies cenripeal force. M Graiaional aracion of Moon o Earh proies cenripeal force. E Quesions 1. Wha force proies he cenripeal force in each of hese cases? a. The Earh moing in orbi aroun he Sun. b. Running aroun a sharp ben. c. A chil on a swing. 2. Explain how a passenger on a rounabou a a funfair can be moing a consan spee aroun he circle an ye acceleraing. In wha irecion is he acceleraion? 3. Wha is he cenripeal acceleraion of, an force on, he following: a. A we sweaer of mass 1 kg, spinning in a washing machine rum of raius 35 cm, moing a 30 m/s. b. A snowboarer of mass 70 kg raelling roun a half pipe of raius 6 m a 5 m/s. 4. The Earh has a mass of kg. Is orbi raius is m an he graiaional aracion o he Sun is N. a. Show ha he circumference of he Earh s orbi is abou m. b. Show ha he Earh s spee aroun he Sun is abou m/s. c. Therefore, show ha he ime o orbi he Sun is abou s.. Show ha his is abou 365 ays. 5. On a ery fas roaing rie a a funfair, your frien says ha hey feel a force rying o hrow hem sieways ou of he rie. How woul you conince your frien ha acually hey are experiencing a force pushing inwars? You shoul refer o Newon s irs an Thir Laws in your explanaion. 19

16 ORCES AND MOTION Momens an Sabiliy A momen (or orque) is he urning effec of a force. Line of acion of force Axis of roaion A boy will no roae if here is no resulan momen. f Aniclockwise = Clockwise momen momen f D Cenre of mass: D Momen (Nm) = orce (N) perpenicular isance from line of acion of he force o he axis of roaion (m). Sum of aniclockwise momens = sum of clockwise momens when in equilibrium. You coul hink of he mass behaing as if i were all concenrae here. 4 N 2.4 m 3.6 m 1.2 m 1 m 3 N 6 N 2 N (4 N 2.4 m) = (3 N 1.2 m) = (6 N 1 m) + (2 N 3.6 m) 13.2 Nm = 13.2 Nm The cenre of mass of a hin shee of maerial can be foun: Eery paricle in a boy is arace o he Earh. To be sable a boy mus keep is cenre of graiy as low as possible. Therefore facors ha affec sabiliy are: Mass isribuion. Shape. Neural equilibrium Equilibrium Cenre of mass is he poin a which he weigh appears o ac. Tipping raises cenre of mass Tipping will lower he cenre of mass. Sable equilibrium Cenre of mass alreay as low as possible Unsable equilibrium Boy will roae unil cenre of mass is irecly below poin of suspension. Mark line wih plumb line. Repea wih new suspension poin. Where lines cross is he cenre of mass as i is he only poin ha is on all he lines. Cenre of mass can be lowere Roaion 20 Roaion neiher raises, nor lowers, he cenre of mass. Objec opples if he line of acion of he weigh is ousie he base of he boy. Quesions 1. Wha is he momen in each of he iagrams below? 0.2 m 5 N 7 N a. b. c. 75 cm. 40 cm 2. If he forces in quesion 1 ace a 60º o he spanner raher han 90º woul he momen be greaer, he same as, or less han ha calculae in quesion 1? Explain. 3. Wha are he missing forces or isances in he iagrams below? a. b. 5 N c. 50 N. e. 100 m 3 m 1 m 2 m? 2.4 N 4 N 100 N 10,000 N 50 N 6000 N 4000 N 4. A leer P is cu from hin carboar. Explain how o locae is cenre of mass. 5. The following leers are cu from a hick plank of woo. W, P, O, I, H, L, U. If soo uprigh in heir normal posiions, which are in sable equilibrium, which unsable, an which neural? Which leer woul you expec o be easies o opple an why? 1 m 5 m 12 cm 4 cm 75 cm 20 N 0.4 m 6 N