This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: final 01 KELLERMANN, MARC Due: Dec 19 2006, 11:00 pm 1 Gravity 9 F 21 = G m 1 m 2 r 2 12 r 12 , for r R , g ( r ) = G M r 2 G = 6 . 67259 10 11 N m 2 /kg 2 R earth = 6370 km, M earth = 5 . 98 10 24 kg Circular orbit: a c = v 2 r = 2 r = 2 T 2 r = g ( r ) U = G mM r , E = U + K = GmM 2 r F = dU dr = mG M r 2 = m v 2 r Keplers Laws of planetary motion: i ) elliptical orbit, r = r 1 cos r 1 = r 1+ , r 2 = r 1 ii ) L = r m r t A t = 1 2 r r t = L 2 m = const. iii ) G M a 2 = 2 a T 2 1 a , a = r 1 + r 2 2 , T 2 = 4 2 GM r 3 Escape kinetic energy: E = K + U ( R ) = 0 Fluid mechanics Pascal: P = F 1 A 1 = F 2 A 2 , 1 atm = 1 . 013 10 5 N/m 2 Archimedes: B = M g , Pascal=N/m 2 P = P atm + g h , with P = F A and = m V F = P dA g 8 h ( h y ) dy Continuity equation: Av = constant Bernoulli: P + 1 2 v 2 + g y = const, P Oscillation motion f = 1 T , = 2 T SHM: a = d 2 x dt 2 = 2 x , = d 2 dt 2 = 2 x = x max cos( t + ), x max = A v = v max sin( t + ), v max = A a = a max cos( t + ) = 2 x , a max = 2 A E = K + U = K max = 1 2 m ( A ) 2 = U max = 1 2 k A 2 Spring: ma = k x Simple pendulum: ma = m8 = mg sin Physical pendulum: = I = mg d sin Torsion pendulum: = I = Wave motion Traveling waves: y = f ( x v t ), y = f ( x + v t ) In the positive x direction: y = A sin( k x t ) T = 1 f , = 2 T , k = 2 , v = k = T Along a string: v = F Reflection of wave: fixed end: phase inversion open end: same phase General: E = K + U = K max P = E t = 1 2 m t ( A ) 2 Waves: m t = m x x t = m x v P = 1 2 v ( A ) 2 , with = m x Circular: m t = m A A r r dt = m A 2 r v Spherical: m t = m V 4 r 2 v Sound v = B , s = s max cos( k x t ) P = B V V = B s x P max = B s max = v s max Piston: m t = m V A x t = A v Intensity: I = P A = 1 2 v ( s max ) 2 Intensity level: = 10 log 10 I I , I = 10 12 W/m 2 Plane waves: ( x,t ) = c sin( k x t ) Circular waves: ( r,t ) = c r sin( k r t ) Spherical: ( r,t ) = c r sin( k r t ) Doppler effect: = v T , f = 1 T , f = v Here v = v sound v observer , is wave speed relative to moving observer and = ( v sound v source ) /f , detected wave length established by moving source of frequency f . f received = f reflected Shock waves: Mach Number= v source v sound = 1 sin Superposition of waves Phase difference: sin( k x t ) + sin( k x t ) Standing waves: sin( k x t ) + sin( k x + t ) Beats: sin( kx 1 t ) + sin( k x 2 t ) Fundamental modes: Sketch wave patterns String: 2 = 8 , Rod clamped middle: 2 = 8 , Openopen pipe: 2 = 8 , Openclosed pipe: 4 = 8 Temperature and heat...
View
Full
Document
This note was uploaded on 11/03/2010 for the course PHYSICS 303 taught by Professor Shih during the Spring '10 term at University of Texas at Austin.
 Spring '10
 SHIH
 Gravity

Click to edit the document details