Exam 1 Special Relativity
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1 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Eam Speial Relaiiy Do NOT wrie yor name on his eam. Wrie yor lass ID nmber on he op righ hand orner of eah problem page. Do NOT wrie yor lass ID nmber on his page. Grading breakdown: Problem Problem Problem 3 Problem 4 Problem 5 35 poins 40 poins 0 poins 0 poins 0 poins Toal poins 35 poins
2 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem Shor answer problem (35 poins oal 5 poins eah) () Wha was he eher? () Define an inerial referene frame. (3) Sae Einsein s Poslaes of Speial Relaiiy. (4) Wha is a proper ime ineral? (5) A ligh sore is known o emi ligh wih a waelengh of nm while a res (in he lraiole region). While in moion, we obsere he ligh o be Doppler shifed o 366 nm. Is he sore approahing s or reeding from s. Jsify yor answer. (6) Skeh a graph of he Lorenz faor () erss eloiy (in nis of ). (7) In parile aeleraors, elerons are aeleraed o ery high speeds. In a single graph, skeh he aqired eleron eloiy (in nis of ) erss (a) he relaiisi kinei energy and (b) he non-relaiisi kinei energy.
3 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem Era Workspae.
4 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem (40 poins) Alpha Cenari, a nearby sar in or galay, is 4.3 ligh-years away. This means ha, as measred by a person on Earh, i wold ake ligh 4.3 years o reah his sar. A roke leaes for Alpha Cenari a a speed of 0.95 relaie o he Earh. Assme ha he Earh and Alpha Cenari are saionary wih respe o one anoher. (a) Work o he disane o Alpha C., as measred by Earh obserers, in km? (5 poins) (b) The disane allaed in (a), is i a proper disane? Jsify yor answer. (5 poins) () Aording o he asronas, how mh did hey age (in years) dring heir jorney? (0 poins) (d) Aording o he asronas, how far (in km) did hey rael? (0 poins) (e) One of he asronas, sing a meer sik, measres he lengh and diameer of he ylindrial spaeraf o be 8 and m, respeiely. Assming ha he spaeraf is oriened wih is long ylindrial ais in he direion of moion, wha are he dimensions of he spaeraf, as measred by an obserer on earh? (0 poins)
5 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem Era Workspae.
6 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem 3 (0 poins) A 0-year-old poliial prisoner named Bob is eiled o rael spae for 35 Earh years. By a srange wis of fae, his dagher is born he ery day ha he leaes o sere his senene. How fas wold he need o rael so ha, when he arries bak on Earh, he s he same age as his dagher?
7 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem 4 (0 poins) A physis professor laims in or ha he reason he wen hrogh he red ligh (λ 650 nm) was ha, de o his moion, he red olor was Doppler shifed o green (λ 550 nm). How fas was he going? Usefl reminder: The relaion beween freqeny, f, and waelengh, λ, is gien by λf.
8 PHYS40 (Spring 00) Eam # (Friday, Marh s, 00) Problem 5 (0 poins) The parile aeleraor a Sanford Uniersiy is hree kilomeers long and aeleraes 3 elerons ( m eleron 9.0 kg ) o a speed of , whih is ery nearly eqal o he speed of ligh. (a) Wha is he res energy (in MeV) of he elerons? ( ev Joles) (b) Find he magnide of he relaiisi momenm of he elerons. Comparing i wih he nonrelaiisi ale, is i bigger, smaller? By wha faor? () Compe he eleron s oal energy (in GeV).
9 PHYS40 (Spring 00) Eqaion Shee for Eam # (Friday, Marh s, 00) Lorenz Transformaions ) ( ) ( z z y y where Veloiy Transformaion, y y, z z Time Dilaion 0 0 Lengh Conraion 0 0 L L L Doppler Shif ( ) ( ) obserer f sore f +, approahing sore Momenm m p Energy res oal E KE m E + ; m E res E oal E res m m KE ; ) (m p E oal +
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