Wiley Plus. Assignment 1 is online:

Transcription

1 Wile Plus Assignmen 1 is online: 6 problems from chapers and 3 1D and D Kinemaics Due Monda Ocober 5 Before 11 pm!

2 Chaper II: Kinemaics In One Dimension Displacemen Speed and Veloci Acceleraion Equaions of Kinemaics for Consan Acceleraion Applicaions of he Equaions of Kinemaics Freel Falling Bodies Graphical Analsis of Veloci and Acceleraion

3 Graphical Analsis of Veloci and Acceleraion Aerage speed / 8/ 4 m/s The slope of he cure is consan, so he speed is consan. Sepember 9 3

4 4 1 m/s 4 m/s m/s Sepember 9 4

5 Speed is no consan Insananeous speed a = s is (6 m)/(5 s) = 5. m/s Sepember 9 5

6 Consan Acceleraion Acceleraion = (1 m/s)/( s) = 6 m/s The slope of he cure is consan, so he acceleraion is consan Sepember 9 6

7 Eample: A person who walks for eercise produces he posiion-ime graph gien below. a) Wihou an calculaions, decide which segmen of he graph (A, B, C, or D) indicaes a negaie aerage eloci. B) decide which segmen indicaes a zero aerage eloci. Sepember 9 7

8 Eample: A bus makes a rip according o he posiion-ime graph shown below. Wha is he aerage acceleraion (in km/h ) of he bus for he enire 3.5 hour period? Sepember 9 8

9 Chaper 3 Kinemaics in Two Dimensions Equaions of Kinemaics in Two Dimensions Projecile Moion Displacemen, eloci, acceleraion eended o wo dimensions Moion in can be separaed compleel from moion in, proided air resisance is negligible reamen of projecile moion Sepember 9 9

10 Speed, Veloci and Acceleraion in One Dimension Disance o Aerage speed elapsed ime o Displacemen Aerage eloci elapsed ime o Insanane ous Veloci lim change ineloci Aerage acceleraion elapsed ime Insanane ous Accelerai on lim Sepember 9 1 o o

11 Speed, Veloci and Acceleraion In Two Dimensions Posiion ecors r, r a, Displacemen r r r r Aerage eloci o r Insanane ous Veloci lim o Aerage acceleraion o Insanane ous Accelerai on lim There is an acceleraion wheneer here is a change of speed or direcion! Sepember 9 11

12 Vecors can be resoled ino componens Insananeous eloci cos ˆ sin ˆ The componens separael follow he same equaions of moion as in he one dimensional case, since he moion for each componen happens in one dimension! Sepember 9 1

13 Sepember 9 13 a 1 a 1 o a Equaions of Kinemaics in Two Dimensions 1) ) 3) 4) a 1 a 1 o a Same as before, onl wih subscrips for each direcion of moion

14 Problem 3.8: A skaeboarder rolls down a 1 m ramp, reaching a speed of 7.7 m/s a he boom. Wha is her aerage acceleraion? If he ramp has an angle of 5 degrees wih respec o he horizonal, wha is he componen of acceleraion in he horizonal direcion? 1 m a ŷ ˆ 7. 7 m/s Sepember 9 14

15 a 1 m ŷ ˆ 7. 7 m/s Sepember 9 15

16 Eample: A spacecraf is raeling wih a eloci of = 548 m/s along he posiie direcion. Two engines are fired for 84 seconds. Engine 1 : Wha is he final speed in he and direcions? Wha is he oal final eloci? a Engine : a 1. m/s 8. 4 m/s Sepember 9 16

17 Sepember 9 17

18 Projecile Moion Consider moion in and separael Ignore air resisance eloci in -direcion is consan Wrie down posiions in and as a funcion of ime Remember ha he projecile raels ericall (up and down ) in he same ime ha i is raeling aboe he horizonal () The onl acceleraion is ha due o grai, acing downward (a rocke or an objec which is self propelled is no considered a projecile and does no undergo projecile moion, because i can be acceleraed arbiraril in an direcion.) Sepember 9 18

19 ŷ g is consan ˆ a a g ˆ m g 9. 8 ˆ s In he absence of air resisance: no forces ac in -direcion, so, he speed in -direcion is consan hroughou he pah. Speed changes in -direcion because of grai. Sepember 9 19

20 Sepember 9 Projecile moion herefore follows ha of a parabola: 1 a 1 a 1 g 1 g 1 g Equaion of an upside down parabola in and

21 Sepember 9 1