Reiew: Physics 13 Lecure 1 Dimensinal Min Displacemen: Dx = x - x 1 (If Dx < 0, he displacemen ecr pins he lef.) Aerage elciy: (N he same as aerage speed) a slpe = a x x 1 1 Dx D x 1 x Crrecin: Calculus is a c-requisie fr his curse, n a prerequisie. If yu hae n aken calculus befre, yu will learn abu deriaies his semeser in Analyical Physics and in Calculus. Quiz in reciain nex week: Based n las week s hmewrk. x- diagram: x = x() ( ) ( ) > ( 1 ) Undersand hw sle HW prblems. Be able sle prblems fairly quickly (here are nly 10 minues fr he quiz). () Insananeus elciy: lim Dx D D0 dx d () is slpe f angen x- pl a ime. i-clicker Quesin Hw many beans are in he 900 ml beaker? A. Fewer han 1000 is n cnsan in ime = () accelerain accelerain: ime rae f change f elciy B. 1000-1500 C.1500-000 D.000-500 E. Mre han 500 aerage accelerain: insananeus accelerain: (slpe f line angen () a ime ) d d x a d d aa 1 1 a lim D0 D D D D a is slpe f () graph. a is curaure f x() graph. d d In - pl abe, () is a sraigh line cnsan accelerain Shw esimain game! i.e.: () = [cns] d/d = [cns] N always rue! Suppse: () = C 3 Then: a = a() = d/d = 3C cnsan in ime!
Finding accelerain n a - graph Accelerain frm x- pl: The () graph may be used find he insananeus accelerain and he aerage accelerain. (> A ) (> B ) (< C ) Slpef -pl gies insananeus accelerain Cpyrigh 01 Pearsn Educain Inc. i-clicker Quesin Cnsan accelerain is an impran special case! Deseres special aenin!! differeniae a * (- a ) () = ( a ) + a * (- a ) x ( a ) Le a = 0 () = + a ½a differeniae Shw min sensr! x x() = x + + ½a
KINEMATIC EQUATIONS in 1D 1 () = + a x() = x + + ½ a Oher helpful relainships: x x 3 a ; 4 a ALGEBRA: ax subs. frm 4 3 x x = a rewrie 1 plug 6 in 5 = ( - ) / a x ) x ) x ) cnsan accelerain a 6 a cns. acc. nly 5 Les pu hese equains wrk! Drag race: Cnsan accelerain alng Knwn: (x x ) = 400 m; = 150 m/s; = 0 Need: a =? 0 x ) a a x ) (150 m/s) a 8 m/s (400 m) Hw lng des he race ake? Knwn: (x x ),,, and a Need: =? x() = x + + ½a 400 m rack. = 150 m/s a end. Wha is he accelerain? 400 m = ½ (8 m/s ) = 5.3 s 0 x - x = + ½a Yellw Ligh iclicker Driing a 30 m/s Ligh urns yellw when yu are 30 m frm in. Decelerae a 10 m/s. Will yu sp befre inersecin? N! Knwn: = 30 m/s; a = -10 m/s ; f = 0 m/s; Need: (x f - x ) =? f 0 (30 m/s) f x ) 45 m a ( 10 m/s ) Wha shuld a be? Knwn: (x f - x ) = 30 m; = 30 m/s; f = 0 m/s Need: a =? a f f 0 (30 m/s) x ) (30 m) 15 m/s A mrcycle raeling alng he xaxis is acceleraingaaraef a=4m/s. a. The mrcycle is speeding up. b. The mrcycle is slwing dwn. c. The mrcycle is neiher speeding up nr slwing dwn. d. Themrcycleisbhspeedingupand slwing dwn. e. Themrcyclemaybeslwingdwnr speeding up. a Slwing dwn If a = -30 m/s, where will I sp? (x f - x ) ~ 1/a s (x f - x ) = 15 m a Speeding up
Freely falling bdies Free fall is he min f an bjec under he influence f nly graiy. In he figure, a srbe ligh flashes wih equal ime inerals beween flashes. The elciy change is he same in each ime ineral, s he accelerain is cnsan. a = -g where g = 9.80 m/s () = - g y() = y + - ½g ( y y ) FREE FALL Min in 1-D under he influence f graiy. accelerain due graiy is cnsan (a Earh s surface) graiy acs erically dwnward (chse y-axis as erical) Same equains f min BUT: a is replaced wih g! g Cpyrigh 01 Pearsn Educain Inc. EXAMPLE: REACTION TIME (red rulers) EXAMPLE: Drp a penny frm p f he Empire Sae Building! (DO NOT TRY THIS!) Obsere: The penny akes 8.1 s hi grund Hw all is building? Knwn: y = 0 m; = 0 m/s ; a = -g ; y f = - 0.10 m Need: =?? y = y + - ½g y f = - ½g Knwn: = 0 m/s; a = -g; = 8.1 s; y = 0 Need: y - y y = y + - ½g y = - ½g = -(½)(9.8 m/s )(8.1 s) y g ( 0.10 m) 9.8 m/s y = - 30 m Wha s he elciy f he penny jus befre i his he grund? 0.0 s 0.14 s Knwn: = 0 m/s; a = -g; = 8.1 s; and (y - y )= -30 m = -g = - (9.8 m/s )(8.1 s) = -79 m/s
Wha if I firs hrw cin upward wih speed f 67 mi/hr (=30 m/s)? When will cin reach max heigh? Knwn: = +30 m/s; a = -g Need: when = 0 = - g 0 m = 30 m/s (9.8 m/s ) g (abe saring pin) 30 m/s 9.8 m/s 3s Things yu always waned knw bu were afraid ask 1. Can a penny drpped frm he Empire Sae Building kill a persn r embed iself in he sidewalk?. Is i OK neglec air resisance? Ask he Myhbusers! When will i pass me n he way dwn? y = y + - ½g bu y = y = 0 0 = - ½g = ( - ½g) = 0 r = 6 s Wha is elciy jus befre hiing grund? ( y y ) g = - 85 m/s 18 EXAMPLE: Drp a penny frm p f he Empire Sae Building! (DO NOT TRY THIS!) Obsere: The penny akes 8.1 s hi grund Hw all is building? Knwn: y = 0 m/s; a = -g; = 8.1 s; y = 0 Need: y - y y = y + y - ½g y = - ½g = -(½)(9.8 m/s )(8.1 s) y = - 30 m Wha s he elciy f he penny jus befre i his he grund? Knwn: y = 0 m/s; a = -g; = 8.1 s; and (y - y )= -30 m = -g = - (9.8 m/s )(8.1 s) = -79 m/s BUT: Terminal elciy = -9 m/s!!!