Fowles02

Fowles02 - CHAPTER 2 NEWTONIAN MECHANICS: RECTILINEAR...

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CHAPTER 2 NEWTONIAN MECHANICS: RECTILINEAR MOTION OF A PARTICLE 2.1 (a) () 1 x Fc t m =+ D ±± 2 0 1 2 t x t d t t t mm = + D D ± m 22 0 26 t FF cc 3 x tt d m m  = +   DD t (b) sin F x ct m D = 0 0 sin cos 1 cos t t F x ct dt ct ct mc m c m == = D ± 0 1 1c o s 1 s i n t x ct dt ct cm cm c =− = (c) ct F x e = m D 0 1 t ct ct xe e cm cm ± 2 11 1 ct ct x et e cm c c c m =− c t 2.2 (a) dx dx dx dx x x dt dx dt dx ⋅= ± ± 1 dx x x dx m D ± ± 1 xdx F cx dx m D 2 2 cx xF x m D ± 1 2 2 x x x m    D ± (b) 1 cx dx x dx m D ± ± e 1
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1 cx xdx F e dx m = D ±± () 2 1 11 2 cx cx FF xe cm cm −− =− = DD ± e 1 2 2 1 cx F cm    D ± (c) 1 cos dx x xF dx m D ± ± c x == cos F xdx cx dx m = D 2 1 sin 2 F x cx cm = D ± 1 2 2 sin F x cx cm  =   D ± 2.3 (a) () ( ) 2 2 x x cx F c xd x F x C + + D Vx (b) x cx cx x F F e d x e C c = + D D D (c) cos sin x x F F c x d x c x C c + D D D 2.4 (a) dV x k x dx Fx 2 0 1 2 x k x d x k x (b) TT () () xV x =+ D 2 1 2 T Vx kA x = D Tx (c) 2 1 2 ET k A D (d) turning points @ 1 0 1 x A 2.5 (a) 3 2 kx Fx k x A −+ so 34 2 22 0 24 x kx kx k x d x k x AA =− =− (b) 4 2 2 kx T k x A + (c) = D 2
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(d) V has maximum at () x ( ) 0 m Fx 3 2 0 m m kx A −= kx m x A = ± 4 22 2 11 1 24 4 m kA x kA kA A =− = V If turning points exist. ( m EVx < ) Turning points @ Tx let u 1 0 2 1 x = 2 2 11 0 24 ku Ek u A −+ = solving for u , we obtain 1 2 2 2 4 E kA       uA or 1 2 1 2 4 E xA kA 2.6 xvx x α == ± 2 23 xx x x =− ±± ± 2 3 m m x x 2 . 7 sin FM g θ 2.8 dx Fm xm x dx ± ± 3 x bx = ± 4 3 dx bx dx ± ( 34 3 F m bx bx −− ) 27 3 b x 2.9 (a) 2 .145 9.8 1250 .3048 541 mm g x k g f t J sf t = Vm 3
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(b) 2 2 2 2 2 11 1 1 22 2 2 . 2 2 t mg m g v m cD  == = =   Tm () ( )() ( ) 2 2 2 .145 9.8 87 2 .22 2 .0366 m kg s kg m ==   TJ 3 23 tanh t t Fdx cv dx c v dt c v dt τ = − =− ∫∫ 3 2 1 tanh tanh 2 t tt
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This note was uploaded on 03/09/2008 for the course PHYS 301 taught by Professor Mokhtari during the Fall '04 term at UCLA.

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Fowles02 - CHAPTER 2 NEWTONIAN MECHANICS: RECTILINEAR...

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