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### Lectures_03

Course: PHYSICS P531, Spring 2009
School: Tennessee
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Word Count: 603

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21,22 HW2 9/18/2008 LL #5 Weihao Ge Irakli YK u u u L = T ( y, , ) F t = 6my (CM) u t F s = F =T 2 u = y a cos 1 v= u 10 L* = T * ( y, , ) L* p = p ( , y ) = 0 ? L* = T * ( y, , ) py = L* y m u 2 2 T = ? mu py = v= 9y 10l = v= 1 u 10 9y 10l 1 u 10 1 9/18/2008 HW2 #7 Is it possible to express Qu and Qw in terms of Fr and F only ? F r = F q i i i i i, j ri j q j = Q j q j...

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21,22 HW2 9/18/2008 LL #5 Weihao Ge Irakli YK u u u L = T ( y, , ) F t = 6my (CM) u t F s = F =T 2 u = y a cos 1 v= u 10 L* = T * ( y, , ) L* p = p ( , y ) = 0 ? L* = T * ( y, , ) py = L* y m u 2 2 T = ? mu py = v= 9y 10l = v= 1 u 10 9y 10l 1 u 10 1 9/18/2008 HW2 #7 Is it possible to express Qu and Qw in terms of Fr and F only ? F r = F q i i i i i, j ri j q j = Q j q j j Q j = Fi i ri q j Qu = Fr r + r F u u HW2 HW2 #7 t= d 2 E U eff ( ) ml 2 U eff = = Mz d sin 2 E U ( ) l 2m eff M z2 mgl cos = E 2ml 2 (1 cos 2 ) Motion of planets: p = 1 + e cos r p latus rectum (not momentum) = e eccentricity = 1 + where U = 2 EM 2 m 2 and < 0; > 0 M2 m r = r How the equation of orbit will change if we change sign of (or )? If > 0 (repulsive force) how we can find the region of the finite motion? When the trajectory of motion in attractive Coulomb field is a hyperbola and when a parabola? 2 9/18/2008 What is called perihelion and aphelion of the orbit? Additional integral of motion for Coulomb central field (LL end of 15). I = [v M ] + r r = const There are integrals of motion: (1) total energy; (2) angular momentum; and why now there is (3) if for the description of motion you need only two coordinates (r,) two and equations of motion? Particles decay (spontaneous decay) in CMS: Eint 0 = Eint1 + 2 p0 p2 + Eint 2 + 0 2m1 2m2 v01 , v02 are fixed in CMS = Eint 0 Eint1 Eint 2 > 0 = 2 2 p0 1 1 p0 + = 2 m1 m2 2m disintegration energy (usually known) reduced mass Laboratory reference system LS: v ( LS ) = V (CMD in LS) + v0 (CMS ) v 2 + V 2 2vV cos = v0 v = v(cos ) in Lab v0 and V are fixed 3 9/18/2008 CMS and LS angles are related by v = V + v0 What is min and max velocity in the Lab? Distribution functions in CMS the distribution of secondary particles is isotropic dN = N d 0 4 d = dN = const d 0 d = d d cos dN N d 0 = d 0 4 d 0 dA R2 d dN 0 d 0 = N = dN dN d d cos = const d 0 d cos 4 9/18/2008 Angular distribution in CMS dN d0 2 sin 0 d 0 d cos 0 = = = N 4 4 2 dN N = = const d cos 0 2 angular distribution in CMS Kinetic energy distribution in Lab (e.g. for final particle 1) 2 from v 2 = v0 + V 2 + 2v0V cos 0 d cos 0 = cos d (v 2 ) 2v0V dT1 dN = N 2m1v0V or dN N = = const dT1 2m1v0V energy distribution in LS Lets plot this uniform distribution dN dT Tmin = N 2mv0V T Tmax Tmax m1 (v01 V ) 2 2 m = 1 (v01 + V ) 2 2 Tmin Check that integral of this distribution = N ? What will happen if LS system will coincide with CMS system? 5
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