1. (25pts) Answer the following questions. Justify your answers. (Use the space provided below and the next page)

Transcription

1 Phyi 6 xam#3 1. (pt) Anwr th foowing qution. Jutify your anwr. (U th pa providd bow and th nxt pag) a). Two inrtia obrvr ar in rativ motion. Whih of th foowing quantiti wi thy agr or diagr on? i) thir rativ pd; th pd of ight in vauum; i th tota nrgy of a moving parti; iv) th ombind quantity (E p ) whr E i th tota nrgy and P i th inar momntum of a moving parti; v) th duration btwn two tik of a ok. b). Suprman i running at high pd on a traight highway toward a pdtrian bridg whih i orintd prpndiuar to th highway. Whih of th foowing ngth maurmnt wi b ontratd aording to Suprman? i) th ngth of th bridg; th hight of th bridg abov th highway; i th ditan to th bridg aong th highway. ). In a phototri fft xprimnt, no phototron ar obrvd to b jtd by an inidnt bu ight. Wi th xprimntr obrv jtd phototron if th bu ight i rpad by a rd ight within th am xprimnta tup? d). In a Compton attring xprimnt, inidnt Xray ar attrd from a tationary tron. Whih of th foowing ar th poib hang for th wavngth of th attrd Xray: i)inra; tay th am; i dra? Anwr: a) i) agr; agr; i not agr; iv) agr; v) not agr b) i) not ontratd; not ontratd; i Lornz ontratd. Lngth i Lornz ontratd ony in th dirtion of th rativ motion. ) Sin rd ight wi hav owr frquny than bu ight, rd ight wi hav owr nrgy. If bu ight i not nough to jt phototron, a owr nrgy rd ight wi not b ab to jt phototron ao. d) By th onrvation of nrgy, th attrd Xray annot hav a highr nrgy than th inidnt Xray in th attrd tron an hav it kinti nrgy argr than or qua to zro. Thu, th attrd Xray an hav th am (φ0) or a ongr wavngth but it annot hav a hortr wavngth in th nrgy of a photon i invry proportiona to it wavngth. 3/7

2 Phyi 6 xam#3. ( pt) A ditan gaaxy i about ightyar in diamtr. Th tarhip Entrpri ntr th gaaxy with a pd v i) How ong do th Entrpri tak to ro th gaaxy from our viwpoint (tationary with rpt to th gaaxy)? How ong do th rw on Entrpri think th journy tak? i How wid i th gaaxy (aong th dirtion of th motion) aording to th rw of th Entrpri? i) From our viwpoint, th 10 ightyar i th ditan th Entrpri ha to trav and it pd i 0.99 o that th tim that it tak to ro th gaaxy i: Lp 10 ight yar t yar v 0.99 Th tim intrva maurd by th arth obrvr i not propr. Sin th Entrpri i atuay xprining th two vnt (ntring and aving th gaaxy) whih dfind thi tim intrva, it maurd tim intrva i th propr tim. Thn, from th tim diation formua, th Entrpri houd maur a hort tim intrva a ompard with th tationary obrvr. t v tp whr γ γ yar yar 1 (1 ) 1/ i In th Entrpri moving fram, th diamtr of th gaaxy aong th dirtion of motion i Lornz ontratd: L L v p 1 whr γ (1 ) 1/ γ 10 ight yar ight yar So, in it viwpoint, th tim that it tak to ro th ontratd gaaxy i: L ight yar tp yar v 0.99 Thi agr with tim diation argumnt in part ii. /7

3 Phyi 6 xam#3 3. ( pt) An untab parti with a rt ma of kg i initiay at rt and i obrvd to day into two mar fragmnt with ma m 1 and m. Th voiti of th two fragmnt ar maurd in th aboratory fram to b (in th + x dirtion) and (in th x dirtion). a) Uing th onrvation of rativiti nrgy and rativiti inar momntum, find th vau of m 1 and m. b) I th rt ma a onrvd quantity in thi pro? Conrvation of E: kg g 1m1 + g m 1 1 whr g 1 v g v So, w hav kg 6. m +. 01m (1) 1 Conrvation of inar momntum: g m v g m ( ). 01m m 0. 8m 1 1 m v Subtitut thi ration into (1), w hav, m m kg kg b g Not that 7 7 m + m kg < kg o that ma i not onrvd in thi pro. 1 /7

4 Phyi 6 xam#3. ( pt) In a phototri fft xprimnt, whn a grn ight from a mrury amp ( λ 6.1nm ) i hind on a mta urfa, a topping potntia of 0.387V i ab to top th photourrnt ompty. i) What i th work funtion for thi mta? With th am tup a bfor, a yow ight from a odium amp ( 87. nm ) i ud in pa of th grn ight. What wi th nw topping potntia in thi a b? [xpr nrgy in unit of V] i) KE DV hf f max h V f h f V J m 1V I f. V. m HG. J K J f 189. V hf DV DV DV h hf f f J m 1V I. V. m HG. J K J V hf 6/7

5 Phyi 6 xam#3. ( pt) A photon with a wavngth of λ 0.10nm oid with a tationary tron in a Compton attring xprimnt. Aftr th oiion, th photon roi bakward and th attrd tron mov in th forward dirtion. S th diagram bow. i) What i th wavngth λ of th roid photon du to Compton hift? What i th nrgy of th roid photon? i What i th kinti nrgy of th attrd tron? [xpr nrgy in unit of V] bfor aftr λ 0 λ i) i h λ λ0 + (1 o180 ) m + (1+ 1) λ λ0 λc λ 0.10nm nm λ 0.186nm 0.1nm E ( m) 3 8 h J V hf 9 19 λ E 8.01kV Conrvation of nrgy rquir that m J hf + m hf + KE + m KE hf hf 1 1 KE h λ0 λ V KE J ( m) nm 0.1nm J KE 60V 7/7