PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1
Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx = change of posiion Today Velociy average insananeous Acceleraion average Insananeous Newon s Laws of Moion Lecure 2 Purdue Universiy, Physics 220 2
Posiion and Displacemen An objec s change in posiion is is displacemen Displacemen: Δx = x final - x iniial Average velociy is he displacemen per uni ime: v ave = x final x iniial final iniial = x 2 x 1 2 1 = Δx Δ If an objec moves wih a consan speed, he average velociy is consan hroughou he moion Lecure 2 Purdue Universiy, Physics 220 3
The average velociy is he change in posiion (vecor) divided by he change in ime. v av = Δx Δ = x f x i f i Velociy (m/s) Insananeous velociy is he limi of average velociy as Δ ges small. I is he slope of he x() plo. v = lim Δ 0 Δx Δ along he direcion of displacemen Lecure 2 Purdue Universiy, Physics 220 4
Velociy The following plos are x vs x x x x Which plo represens an objec a res? Which plo represens an objec wih a uniform velociy in he -x direcion? Lecure 2 Purdue Universiy, Physics 220 5
Exercise Find he average velociy for he objec during he period =5 s and =6 s v= x f x i f i = 1m 6m 6sec 5sec = 5m 1sec = 5m/s Lecure 2 Purdue Universiy, Physics 220 6
If he average velociy of a car during a rip along a sraigh road is posiive, is i possible for he insananeous velociy a some ime during he rip o be negaive? A - Yes Exercise correc B - No The car migh have reversed for a lile while along he rip creaing a negaive insananeous velociy a he poin. If he overall displacemen of he car is posiive for ha paricular ime inerval, han he average velociy is posiive as well. If he car is raveling in a sraigh pah he velociy will always be posiive. The car needs o ravel in he opposie direcion o ge a negaive velociy. Lecure 2 Purdue Universiy, Physics 220 7
Velociy vs Speed Velociy is a vecor Only depends on he displacemen beween he iniial and final posiions Independen of acual pahs beween he iniial and final posiions The direcion of he velociy gives he direcion of he moion Speed is a scalar The magniude of he velociy is called he speed This is he disance raveled per uni of ime Depends on he lengh of he acual pah beween he iniial and final posiions Remember ha speed and velociy are no he same Lecure 2 Purdue Universiy, Physics 220 8
Velociy vs Speed One-dimensional moion Direcion of velociy will be parallel o he x-axis Will have only one componen One-, wo- or hree-dimensional moion Velociy may be posiive, negaive, or zero Speed is equal o he magniude of he velociy Speed canno be negaiv Lecure 2 Purdue Universiy, Physics 220 9
Acceleraion (m/s 2 ) The average acceleraion is he change in velociy divided by he change in ime. a av = Δv v() Insananeous acceleraion is limi of average acceleraion as Δ ges small. I is he slope of he v() plo. a = lim Δ 0 Δv Δ Δ = v f v i f i v() Lecure 2 Purdue Universiy, Physics 220 10 Δ Δv
Acceleraion Is i possible for an objec o have a posiive velociy a he same ime as i has a negaive acceleraion? A - Yes B - No Yes, he objec could be moving forward bu deceleraing or slowing down. If he velociy of some objec is no zero, can is acceleraion ever be zero? A - Yes An objec can have a consan B - No velociy, which means ha he acceleraion is zero. Lecure 2 Purdue Universiy, Physics 220 11
Graphical Analysis To find he velociy graphically Find he slope of he line angen o he graph a he appropriae imes For a ime inerval, find he slope of he line connecing he wo imes To find he acceleraion graphically The acceleraion is he slope of he velociy-ime graph Find he angen lines a various locaions on he graph Skech an acceleraion graph Lecure 2 Purdue Universiy, Physics 220 12
Posiion vs Time Plos Gives locaion a any ime Displacemen is change in posiion Slope gives velociy x (m) 3 Posiion a =3, x(3) = Displacemen beween =5 and =1. Δx = 1-1.0 m 4 (s) 1.0 m - 2.0 m = -1.0 m Average velociy beween =5 and =1. v = -1 m / 4 s = -0.25 m/s -3-0.25 m/s Lecure 2 Purdue Universiy, Physics 220 13
Velociy vs Time Plo Gives velociy a any ime Area gives displacemen Slope gives acceleraion Velociy a =2, v(2) = 3 m/s Displacemen beween =0 and =3: Δx = 7.5 m =0 o =1: ½ (3m/s) (1 s) = 1.5 m =1 o =3: (3m/s) (2 s) = 6 m Average velociy beween =0 and =3? v= v (m/s) Change in v beween =5 and =3. Δv = -2 m/s 3 m/s = -5 m/s Average acceleraion beween =5 and =3: a = -5 m/s / (2 s) = -2.5 m/s 2 Lecure 2 Purdue Universiy, Physics 220 14 3 1.5-3 6 4 (s) 7.5 m / 3s = 2.5 m/s
Acceleraion vs Time Plos Gives acceleraion a any ime Area gives change in velociy a (m/s 2 ) 3 Acceleraion a =4, a(4) = -2 m/s 2 Change in v beween =4 and =1. Δv = +4 m/s 6 2 4 (s) =1-3: Δv = (3m/s 2 )(2s) = 6 m/s -3 =3-4: Δv = (-2m/s 2 )(1s) = -2 m/s Lecure 2 Purdue Universiy, Physics 220 15
Dropped Ball A ball is dropped from a heigh of wo meers above he ground. Draw v y vs 3 v v v A 3 B 3 C y x -2 4 3 v D -2 4 3 v E -2 4 4 4-2 -2 Lecure 2 Purdue Universiy, Physics 220 16
Tossed Ball A ball is ossed from he ground up a heigh of wo meers above he ground and falls back down. y Draw v vs 3 v v v A 3 B 3 C x -2 4 3 v D -2 4 3 v E -2 4 4 4-2 -2 Lecure 2 Purdue Universiy, Physics 220 17
Problem A ball is hrown sraigh up in he air and reurns o is iniial posiion. During he ime he ball is in he air, which of he following saemens is rue? A) Boh average acceleraion and average velociy are zero. B) Average acceleraion is zero bu average velociy is no zero. C) Average velociy is zero bu average acceleraion is no zero. D) Neiher average acceleraion nor average velociy are zero. V ave = Δy/Δ = (y f y i ) / ( f i ) = 0 a ave = Δv/Δ = (v f v i ) / ( f i ) No 0 since V f and V i are no he same! Lecure 2 Purdue Universiy, Physics 220 18
Galileo s Moion Experimens Experimened wih balls on an incline When he ball was released from res, is velociy varied wih ime As shown in he graph in b The acceleraion was consan and posiive As shown in he graph in c The slope of he line in b is he value of he acceleraion shown in c Lecure 2 Purdue Universiy, Physics 220 19
Galileo s Moion Experimens Repeaed he experimen by rolling he ball up he incline Give he ball an iniial velociy The slope of he velociy-ime graph is negaive The slope of he v- graph was always consan and depended upon he angle of he incline Lecure 2 Purdue Universiy, Physics 220 20
Galileo s Moion Experimens The acceleraion when a ball rolled up a paricular incline was always equal in magniude, bu opposie in sign, when compared wih he acceleraion when he ball rolled down he same incline Reasoned ha if he il of he incline was exacly zero, he ball would move wih a consan velociy Proposed ha on a perfecly horizonal ramp, he ball would roll forever Lecure 2 Purdue Universiy, Physics 220 21
Ineria The Principle of Ineria An objec will mainain is sae of moion unless i is aced upon by a force The velociy is is sae of moion Demonsraed by Galileo s experimens Showed ha one can have moion wihou a force Broke Arisole s link beween force and velociy Sill did no explain how he force is linked o he moion Newon s Laws provide his link Lecure 2 Purdue Universiy, Physics 220 22
Newon s Firs Law Objecs a res remain a res and objecs in moion remain in moion in a sraigh line unless aced upon by an exernal agen INERTIA! - exernal agens are called Forces - Forces change he sae of moion of an objec Lecure 2 Purdue Universiy, Physics 220 23
Force Quanifies he ineracion beween wo objecs Four Fundamenal Forces Graviaional force Elecromagneic force Srong force Weak force Force is a vecor Has magniude and direcion Be careful when you add wo forces! Lecure 2 Purdue Universiy, Physics 220 24
Newon s Second Law The ne force on a body is equal o he produc of he mass of he body and he acceleraion of he body F = ma - This is a vecor equaion 1 N = 1 kg x m/s 2 - The direcion of he ne force is he same as he direcion of he acceleraion - In 3 dimensions F x = ma x F y = ma y F z = ma z 2 N Lecure 2 Purdue Universiy, Physics 220 25
Direcions The direcion of he acceleraion is always parallel o he direcion of he oal force The velociy and he oal force do no need o be in he same direcion Example Iniial velociy is upward The oal force is downward The acceleraion is downward Lecure 2 Purdue Universiy, Physics 220 26
Ineria and Mass Ineria is also a measure of an objec s resisance o changes in is moion This resisance depends on he objec s mass The mass of an objec is a measure of he amoun of maer i conains SI uni of mass is kg Mass is an inrinsic propery of an objec I is independen of he objec s locaion I is independen of he objec s velociy or acceleraion Lecure 2 Purdue Universiy, Physics 220 27
Newon s Third Law For every acion here is an equal an opposie reacion N Forces in naure come in pairs mg T F F f F F The objec acceleraes IF F > F f F f Lecure 2 Purdue Universiy, Physics 220 28
Newon s Third Law When one objec exers a force on a second objec, he second objec exers a force of he same magniude and opposie direcion on he firs objec Ofen called he acionreacion principle Example Force on ball Force on ba Lecure 2 Purdue Universiy, Physics 220 29
Summary of Conceps Velociy: rae of change of posiion average : Δx/Δ insananeous: slope of x vs. Acceleraion: rae of change of velociy average: Δv/Δ insananeous: slope of v vs. Acceleraion and velociy do no necessarily reach a maximum value a he same ime The acceleraion can be in he opposie direcion o he velociy Newon s Laws of Moion Ineria F = ma Pairs Lecure 2 Purdue Universiy, Physics 220 30