Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume, disance, speed, color, ec. I makes no sense o say i B. Vecor describes boh magniude and direcion; e. displacemen, elociy, orce, ec. 1. Speed is he magniude (amoun) o elociy; elociy mus include boh magniude (speed) and direcion. On diagrams, arrows are used o represen ecor quaniies; he direcion o he arrow or he angle a which i poins gies he direcion o he ecor and he magniude o he ecor is proporional o he lengh o he arrow. Vecors displacemen elociy acceleraion orce weigh momenum Scalars disance speed mass ime olume emperaure work and energy Frames o reerence sandard or comparison; any moemen o posiion, disance, or speed is made agains a rame o reerence; wih respec o Earh is mos common We can say i is norheas because i is eacly 45 degrees rom each ais BUT i i were 35 degrees aboe he ais insead?? We would need o say 35 degrees Norh o Eas! II. Disance s. Displacemen Disance oal lengh moed or oal ground coered; a scalar quaniy No direcion necessary! I you ran around he rack, you would go a disance o 400 meers. Displacemen Deined as he change in posiion ( or dela means - i ) wih respec o a reerence poin. I is a ecor quaniy. I you ran around he rack, your displacemen would be ZERO meers. We can use displacemen and disance inerchangeably in his course, bu hey are no necessarily he same hing. Noe displacemen is no always equal o he disance raeled
Here are some graphs o posiion ersus ime: 1 Quesions: Which graph(s) show a saring posiion away rom and moing arher away rom he origin in he posiie direcion? Which graph(s) show an objec reurning oward he saring posiion? III. Velociy s. Speed Aerage speed oal disance coered diided by he oal ime aken; scalar quaniy Aerage elociy displacemen or /ime; ecor quaniy. Since elociy is a ecor, we mus deine i in erms o anoher ecor, displacemen. Oenimes aerage speed and aerage elociy are inerchangeable or he purposes o he AP Physics B eam. Speed = d or is he magniude o elociy, ha is, speed is a scalar and elociy is a ecor. For eample, i you are driing wes a 50 miles per hour, we say ha your speed is 50 mph, and your elociy is 50 mph wes. We will use he leer or boh speed and elociy in our calculaions, and will ake he direcion o elociy ino accoun when necessary. Insananeous elociy is he elociy a a speciic ime which may be dieren rom he aerage elociy which will be seen in he graphs below. Eample #1 : Le s say you raelled 5 meers Norh in minues, sopped or 10 minues, hen coninued in he same direcion going 400 meers in 8 minues calculae your aerage elociy or he rip.
IV. Acceleraion: In his course we will only calculae wih consan acceleraions. (In order o work well wih changing acceleraions, you would need o use calculus.) Aerage acceleraion is he rae o change o elociy; change in elociy wih ime (a = / ) i an objec s elociy is changing, i s acceleraing een i i s slowing down and een i he only hing changing is is direcion o rael. An objec raeling in a circle a a consan speed is sill changing is elociy because is direcion is changing consanly SO i is acceleraing!! Eample # : I a car goes rom res o 48 mph (miles per hour) in 4 seconds, calculae is acceleraion. Noe A irs you migh hink ha + acceleraion is speeding up and negaie acceleraion is slowing down NOT necessarily. You only hae negaie acceleraion when he direcion o he acceleraion is opposie o he direcion ha is deined as posiie. I s all abou he direcion o he acceleraion no speed up or slow down. V. Free Fall We say an objec is in ree all when is moion is conrolled by graiy. i a= = In he picure o he righ, a ball is hrown upward wih some iniial elociy. As i goes up, is speed decreases unil i insananeously becomes zero a he op. Then i speeds up as i alls back down. I up has been deined as posiie, hen he balls elociy is: posiie as i moes upward slowing down; becomes zero a he op negaie as i moes downward gaining speed BUT, he ball s acceleraion has he same negaie alue a all posiions! Try i using he ormula!! a= E: iniial speed going up is 40 m/s and i raels upward or 4 seconds and sops momenarily hen alls or 4 seconds and reaches a inal speed o 40 m/s. Using he signs or up and down moion (gien aboe), calculae he aerage acceleraion or each par o he rip, hen he aerage acceleraion or he oal rip. i This acceleraion is also presen a he op EVEN WHEN he insananeous speed is ZERO! This acceleraion is due o graiy and (when a is his special case, due o graiy we label i g and call i ree all acceleraion). Graiy does no ake a holiday jus because he objec reached he op o is rajecory! On Earh, g = 3 /s = 3 Fee per second each second. This is he same as 9.81 meers per second each second (ha is or 9.81 m/s (we regularly round i o 10 m/s o make calculaions easier). Eample #3: A ball is dropped rom he op o a cli. How as will i be raeling aer 1,, and 3 seconds? How high is he cli i he ball his he boom in 5 seconds?
In he absence o air resisance, all objecs, regardless o heir mass or olume, dropped near he surace o a plane all wih he same consan acceleraion. Look a he picure aboe. The eaher and he apple in a acuum chamber all a he same rae! In he presence o air resisance, objecs dropped will iniially accelerae a g and hen he acceleraion will decrease o zero once erminal elociy is reached. See he kinemaic ormulas (las page o hese noes) or use in hese eamples. Eample # 4 : A rocke raeling a 88 m/s is acceleraed uniormly o 13 m/s oer a 15 s ineral. Wha is he displacemen during his ime? Eample # 5 : A lowerpo alls rom res on a windowsill 5.0 m aboe he sidewalk. a. How as is he lowerpo moing when i srikes he ground? b. How much ime does a bug on he sidewalk below hae o moe ou o he way beore he lowerpo his he ground or he bug?
VI. Graphs o Moion Relaionship beween displacemen s. ime graph, elociy s. ime graph, and acceleraion s. ime graph Eample #6: The graph shows posiion as a uncion o ime or wo rains running on parallel racks. Which is rue? 1. A ime B, boh rains hae he same speed.. Boh rains speed up all he ime. 3. Boh rains hae he same speed a some ime beore B. 4. Boh rains hae he same acceleraion a some ime beore B.
Simple Kinemaic Formulas (For cases where he objec sars rom res; in oher words, he iniial elociy is 0.) = 00mi = 50mi/hr X 4hrs. 50mi/hr mus be he aerage elociy or he whole rip. Do no use his ormula or insananeous elociy or o ry o ind a elociy a a paricular momen. ******************************************************************************************* Use his ormula o ind he elociy a a paricular momen (insananeous = a elociy), he acceleraion, or he ime i he oher erms are known. aerage a = = 1 a Use his o ind acceleraion, he change in elociy, or he elapsed ime i he oher erms are known. Use his o ind he displacemen (change in posiion,) he acceleraion, or he ime when he oher erms are known. General Kinemaic Formulas: The Big Three Formulas or uniormly acceleraed moion {The ormulas below are general. I he objec sars rom res hen he iniial elociy is 0 and he ormulas may be simpliied o he orms aboe.} = i + a Use his o ind he inal elociy, he original elociy, he acceleraion, or he elapsed ime when he oher erms are known. = + a i Use his o ind he inal elociy, he original elociy, he acceleraion, or he displacemen when he oher erms are known. = i + 1 a Use his o ind he displacemen, he original elociy, he elapsed ime, or he acceleraion when he oher erms are known. Physics HW probs: P 69-73 # s 3, 8, 10, 13, 16-19, 1, 3, 7, 30, 3, 34, 38, 4, 43, and 46. Reised 009 kjl