Classical Mechanics PHYS 3210
Popular in Course
Popular in Physics 2
This 4 page Class Notes was uploaded by Ubaldo Jacobson on Monday September 21, 2015. The Class Notes belongs to PHYS 3210 at University of Virginia taught by Julian Noble in Fall. Since its upload, it has received 6 views. For similar materials see /class/209752/phys-3210-university-of-virginia in Physics 2 at University of Virginia.
Reviews for Classical Mechanics
Report this Material
What is Karma?
Karma is the currency of StudySoup.
Date Created: 09/21/15
PHYS 321 Lecture 10 20 September 2002 Y9k a l1 R 1 uneasequot x2 h Thls ls the equataon for an e elllps Xarcose y esme more lnformanon ls posted on the Lecture Notes page Example ofan elllpucal orblt Halley39s eomet htt neo lnasa ovorblts s arch Halley Setthe applet to December 1 1986 and play forwardto wateh the eometmove along lts penhellon Notlee Halley39s eomethas a path Why ls thls7 Rutherford Scattering Panicles randomly placed uniform in size 0 a O A Avea O a Ernest Rutherford with the help of many students graduate and English majors discovered this scattering by sending a beam of particles through a thin sheet of gold The idea is to make the sheet thin enough so that only by luck it has atomsithat is there will be no overlapping of atoms Then send in a beam of particles photons xparticles etc and with the right equipment you will nd that particles are being scattered out the other side These particles are loose valence electrons knocked out of the gold shell by the incoming particles They are seen as sparks against a backboard by a careful observer So how many targets do we see The average number is determined by Average nVslab where n number density and Vslab the volume of the slab tested which can also be written as Vslab Adz making the equation Average nAdz Let s look at it this way imagine instead that the slab is instead pizzas set out on the ground in a square array or round whatever and it begins to rain on them What s the area of rainfall What you need to do is not only count all of the raindrops falling but the number that land on the pizzas which is GllAdz dphn O39 area of one pizza A dphit is the probability of the pizzas hit Now going back to the slab the change of radiation intensity behind the slab is then 11 dphita Here the number of hits is equivalent to one hit times the number of times a hit was tried This leads us then to dN aAt d1 41pm IaAt where a area of target and IaAt N 11 lle I 111 o ndz gt In I o ndz constant I 10 emquot Ioe39m39 where o n 11 and I mean free path Son cl3 and O39 12 1 length 39T h r F r lead blocks are bestfor blockmg radrauon llke xrrays attlne nosprtal Ifwe pretendtlnatlottenes are 100 fan for exam le tlne elnane wrn eould be 1 rn arnrllron Let39s say tlnat tlne lottery pays halfamllllon wrn you shouldbuy all rnrllron uekets But lf eaelr ueket eosts one dollar tlnen yo e tlnat you wrll To be sure you u go ahead and play more but don39tpay out too much For rnstanee lfyou buy ve uekets you rnerease your elranees by flve trrnes for only ve dollarsl So for every Nelnanee betteryou want you needto t Numesithus tlne earlrerrnenuoned srtuauon Where tlne nurnber ofhlts rs really one luttrrnes tlne nurnber of urnes you tned nrng 1mm oyertne whole It39s much more srrnpler andrn rnany eases Just as aeeurate or as so Mev Ithey luttlre sernullaung sereen tlne atorns are exerted andrelease lrglnt as they settle to aground state Take our teleyrsron or eornputer rnonrtor ltreleases not only a lot of yrsrble lrglnt butxrrays as well The harmful erays however are redueed l b Also sereen rnereases tlne elnanee tlnattlre partreles wrll lnrt and seatter off of arr rnoleeules Besrdes arparucles usually pass tlnrouglr substancesithey are harmful lf swallowed elose to you So lets get back to tlne errpenrnent tlnat leadto tlne drseoyery ofRuLherford Seattenng You take a substanee llke Radrurn and put rtrn alead box wrtln a srngle nole lnlt Frmlhlh L n h 01P ll 39 L dlfferentwavelengths ofthe partreles seen rn tlne serntrllatron Mostly you wrll notree attlne parueles wrll seatter off axls Ofcourse no one noueed tlnrs lmmeddatelymosdy due to tlne ousand partreles wrll make rt tlnatlnrglr Rutherford ofcourse foundthls odd so rn orderto aboye Arnazrnglyrt worked Lnlateryearstlne Gerger eounter beearne more useful when rt earne to rernoyrng bras Well rst of all along the zraxxs alpha 9 1 2 1 WWW cam classlcal lmpact parameter dlstance from me axls ofthe atom Ifthe force F ls attractmg Ann muti anal Why are me two b39s me same397 Beeause the path looks the same no matter wlnen However on me macroscoplc level thls ls not always posslbleillke an egg unbrealnngquot The gure above ylelds two equatlons d2 17 and Pg 3 dt ow does the scattering angle mm Regardless ofthe slgn othe angle the So affectls the same