Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Exam I Physics 11: Lecure 6, Pg 1
Brie Reiew Thus Far Newon s Laws o moion: SF=ma Kinemaics: x = x + + ½ a Dynamics Today we work in Dimensions! Physics 11: Lecure 6, Pg
y -Dimensions x X and Y are INDEPENDENT! Break -D problem ino wo 1-D problems Physics 11: Lecure 6, Pg 3
Physics 11: Lecure 6, Pg 4 Posiion, Velociy and Acceleraion Posiion, Velociy and Acceleraion are Vecors! x and y direcions are INDEPENDENT! r r a a a x x x y y y a x x x a y y y x y a x a y a x direcion y direcion
Velociy in Two Dimensions A ball is rolling on a horizonal surace a 5 m/s. I hen rolls up a ramp a a 5 degree angle. Aer.5 seconds, he ball has slowed o 3 m/s. Wha is he magniude o he change in elociy? A) m/s B) m/s C).6 m/s D) 3 m/s E) 5 m/s x-direcion ix = 5 m/s x = 3 m/s cos(5) y-direcion iy = m/s y = 3 m/s sin(5) y x D x = 3cos(5) 5 =-.8m/s D D x D y 5 m/s.6 m/s D y = 3sin(5)=+1.7 m/s 3 m/s Physics 11: Lecure 6, Pg 5
Acceleraion in Two Dimensions A ball is rolling on a horizonal surace a 5 m/s. I hen rolls up a ramp a a 5 degree angle. Aer.5 seconds, he ball has slowed o 3 m/s. Wha is he aerage acceleraion? y x-direcion y-direcion a x.8m/s.5 s 4.56 m/s 1.7m/s.5 s ay.54 m/s x a a x a y 5.1m/s 3 m/s 5 m/s Physics 11: Lecure 6, Pg 6
Kinemaics in Two Dimensions x = x + x + 1/ a x x = x + a x x = x + a x Dx y = y + y + 1/ a y y = y + a y y = y + a y Dy Mus be able o ideniy ariables in hese equaions! x and y moions are independen! They share a common ime Physics 11: Lecure 6, Pg 7
Train Ac/Demo A labed railroad car is moing along a rack a consan elociy. A passenger a he cener o he car hrows a ball sraigh up. Neglecing air resisance, where will he ball land? A. Forward o he cener o he car B. A he cener o he car C. Backward o he cener o he car correc x- direcion ball and car sar wih same posiion and elociy, a=, so always hae same posiion Demo - rain Physics 11: Lecure 6, Pg 8
ACT A labed railroad car is acceleraing down a rack due o graiy. The ball is sho perpendicular o he rack. Where will i land? A. Forward o he cener o he car B. A he cener o he car C. Backward o he cener o he car x direcion Ball m b g sin(q) = m b a b a b = g sin(q) correc x direcion Car m c g sin(q) = m c a c a c = g sin(q) Same acceleraion gies same posiion Physics 11: Lecure 6, Pg 9
Projecile Moion ACT One marble is gien an iniial horizonal elociy, he oher simply dropped. Which marble his he ground irs? A) dropped B) pushed C) They boh hi he ground a he same ime When ball his depends on y only! y() = y + yo + ½ a y Same or boh balls! Physics 11: Lecure 6, Pg 1
Monkey Pre-Fligh You are a e rying o shoo a ranquilizer dar ino a monkey hanging rom a branch in a disan ree. You know ha he monkey is ery nerous, and will le go o he branch and sar o all as soon as your gun goes o. In order o hi he monkey wih he dar, where should you poin he gun beore shooing? 74% 14% 1% 1 Righ a he monkey Below he monkey 3 Aboe he monkey correc Demo - monkey Poor monkey...i hope here's somehing so or he lile guy o land on. No animals were harmed in he making o his demo Physics 11: Lecure 6, Pg 11
Mos inriguing answer The jungle nigh is ho, bu I hae waied oo long o miss an opporuniy like his one. The rare Bare-eared Squirrel Monkey, indigenous only o Brazil, was in my sighs. This monkey could lead o mankind's surial and i was all up o me o capure i. This simple creaure, hanging rom a branch, was he key, he key o unlock he cure. Being he well-rained e I am, I quickly realized how skiish hese monkeys are...meaning I'd only hae one sho...one sho o sae he world. I lined up my dar gun and, hanks o my p.h.d in physics, did a quick calculaion o judge how quickly he dar would all and how quickly he monkey will all. Based on he weigh and reacion ime o he monkey and he power o my gun, I knew ha he dar and monkey will drop a he same rae. I hus aimed my weapon righ a he animal and ired! A he sound o he sho he lile guy dropped rom his branch. I wached as he dar me is arge dead on. I had done i. Wih his creaure in hand, I had he ools o sae he world. The only quesion ha remained was i I was already o lae... Physics 11: Lecure 6, Pg 1
See ex: 4-3 Shooing he Monkey... x = y = - 1 / g x = x y = - 1 / g Physics 11: Lecure 6, Pg 13
Shooing he Monkey... Sill works een i you shoo upwards! y = y - 1 / g y = y - 1 / g Dar his he monkey! Physics 11: Lecure 6, Pg 14
Projecile Moion a x = a y = -g x = x + x x = x y = y + y - ½ g y = y g y = y g Dy Choose direcion where you know inormaion Sole kinemaics in ha direcion. Use rom ha direcion as in oher direcion Physics 11: Lecure 6, Pg 15
Throw ball o Monkey You hrow a ball o a monkey who is on a plaorm 1 meers aboe and 5 meers o he righ o you. Deermine he speed and angle you should hrow i such ha i jus reaches he monkey. Y-direcion ( iy ) y iy = a Dy iy = sqr( 9.8 1) = 15.3 m/s y = iy + a = iy /g = 1.56 s. X-direcion ( ix ) ix = d/ = 5 m / 1.56 s = 3. m/s 1 m 5 m Physics 11: Lecure 6, Pg 16
Throw ball o Monkey You hrow a ball o a monkey who is on a plaorm 1 meers aboe and 5 meers o he righ o you. Deermine he speed and angle you should hrow i such ha i jus reaches he monkey. Y-direcion ( iy ) y iy = a Dy iy = sqr(*9.8*1) = 15.3 m/s y = iy + a = iy /g = 1.56 s. X-direcion ( ix ) ix = d/ = 5 m / 1.56 s = 3. m/s a=arcan( iy / ix ) 1 m = ( ix + iy ) 1/ 5 m Physics 11: Lecure 6, Pg 17
Summary o Conceps X and Y direcions are Independen! Posiion, elociy and acceleraion are ecors Share F = m a applies in boh x and y direcion Projecile Moion a x = in horizonal direcion a y = g in erical direcion Physics 11: Lecure 6, Pg 18