s4 - PHYS 260 Problem Set 4 1. A K meson (rest mass = 494 M...

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Unformatted text preview: PHYS 260 Problem Set 4 1. A K meson (rest mass = 494 M eV/c2) travelling through the laboratory decays into two F mesons (rest mass = 137 M eV/cz). One of the 7r mesons is left at rest. (a) What was the kinetic energy of the K? (b) What is the kinetic energy of the remaining 7r meson? “ ‘35iiiléii?i v_ _, fl, ., raga, “-7 WV : , I . r, .. _’ ETTfifmjifiWWw7.im l .7 : i : ; Q i ‘ 3 1 i 1 5 f i 3 j ‘ ‘ s v ‘ ‘ , ‘ ~e4%x m»%¢$wmqaeeeflwkmkmtu»h 1 l t : : 4 Awawwaqu'umaegwmm kgi- , A) i . i ' 2. A particle of rest mass m0 and kinetic energy xmocz, where a: is some number, hits an identical ' . particle which is at rest. The result is single particle of rest mass M0. (a) What is M0? ‘ (b) What is the momentum of the new particle? ‘ ; a x \— ‘ -—. . 7 l ‘ l 1 . y , i i l I . 7 w: ,7. ‘ , 2 ‘ w . ‘ ‘ y I i l ‘ l ; :l ' 'R 1 l 3 l ’i ‘ l ! 1 ! L l l : é l l I; 37 ., he 3,5, a i 1 ,L ,1" ; L l 3 y J ‘fl 1 r l l l ’i . 1 ‘ l l : j ‘ ‘ 1 I , + ,7 I 1 l E l ‘ 3 l l 11 ‘ 1 I ; : i i 1 : g Y : i t l 3 l ‘ l i ‘ g j l ’2 3 i W 17."? 1 "T i ‘1‘ a 7 E "Em-i, “‘- 1 hi “T H 7Q z s l P l . “F I l r (/P , l ii i ; . + 2—1 l 1 i 7/ 3. Two inertial coordinate systems 5 and .5" move with speed 0/2 with respect to one another. ‘ Draw a Minkowski diagram relating these two systems. (Let the axes of x and ct for S be at right angles in your drawing.) (a) Draw calibration hyperbolas that'allow you to define unit distances along the axes of ac, 33’, . ct and ct’. (b) Plot the following point events on the diagram: A 1 :r l,ct osc’=1,ct’=1 '; ‘ '1 o$’=2,ct’=0 g 2 v~——,.———~rr (c) From your diagram" determine the coordinates in S" or S corresponding to the above events ,7 ‘ (ie in the frame for which they are not already given). -, A ,,,, ,, - Imar.,%e=,-t:elfiw , x NW A. w w , :1; WI ,s—WM 1 w ; v l r e ‘ ; ' " 1;: iii we we.) ’* emmwa . mm jt: X/u— at: x/m UV ,Sd veil} V I 7 "' 4 r:-.~r"+ 4:??féiiiiifi” ~ ‘ ,, i """ '1' . 3 j ‘ < ‘ 5 4 t z c ‘ ' * '5 'm ~ , Té"/v-ei~hs~.cews«e~x+<» aflmm m. as: awmzm : [ ,X’Q 7856‘ 7; E #53 ; 153%? =1: 1;; :2 ’ 9+ m ) ~ + , .k ,, ,, ; 1 _f . 7, W, , \ I} ‘ -l , i 9 i ? , V r. w ‘ ...
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s4 - PHYS 260 Problem Set 4 1. A K meson (rest mass = 494 M...

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