Physics 111. Exam #2. February 23, 2018

Transcription

1 Phyic Exam # February 3, 08 ame Pleae read and fllw thee intructin carefully: Read all prblem carefully befre attempting t lve them. Yur wrk mut be legible, and the rganizatin clear. Yu mut hw all wrk, including crrect vectr ntatin. Yu will nt receive full credit fr crrect anwer withut adequate explanatin. Yu will nt receive full credit if incrrect wrk r explanatin are mixed in with crrect wrk. S erae r cr ut anything yu dn t want graded. Make explanatin cmplete but brief. D nt write a lt f pre. Include diagram. Shw what ge int a calculatin, nt jut the final number. Fr example p m v " 5kg ( ) ( m ) 0 kg m Give tandard SI unit with yur reult unle pecifically aked fr a certain unit. Unle pecifically aked t derive a reult, yu may tart with the frmula given n the frmula heet including equatin crrepnding t the fundamental cncept. G fr partial credit. If yu cannt d me prtin f a prblem, invent a ymbl and/r value fr the quantity yu can t calculate (explain that yu are ding thi), and ue it t d the ret f the prblem. All multiple chice quetin are wrth 3 pint and each free-repne part i wrth 9 pint Prblem # /4 Prblem # /4 Prblem #3 /4 Ttal /7 I affirm that I have carried ut my academic endeavr with full academic hnety.

2 . A ma pectrmeter i an analytical intrument ued t identify the variu mlecule in a ample by meauring their charge-t-ma rati q m. The ample i inized and the pitive in are accelerated thrugh a ptential difference ΔV, and then enter a regin f unifrm magnetic field. The magnetic filed bend the in in t circular trajectrie, but after jut half a circle they either trike the wall r pa thrugh a mall pening t a detectr. A the accelerating vltage i lwly increaed, different in reach the detectr and are meaured. Cnider the ma pectrmeter hwn belw with a magnetic field B 00mT and a d 8.00cmpacing between the entrance and exit hle. a. What accelerating ptential difference i required t detect CO + in? Sme atmic mae are hwn in the table n the right. Element Atmic ma (amu) C O F b qv B mv R v qrb m edb m W qδv eδv mv ΔV m f e v m f e ΔV ed B 8m C 0.08m u kg u edb m ( ) T ( ) ( ) ed B 8m 0.V b. Suppe that yu wanted t ee + in rather than the CO + in. + ha nminally the ame ma a a CO + in but becaue f mall but meaurable difference in the accelerating vltage the tw in pecie are eaily eparable. T ee the + in the acceleratin vltage needed wuld. need t decreae frm the value ued fr the CO + in.. remain unchanged frm the value ued fr the CO + in. 3. need t increae frm the value ued fr the CO + in. 4. be unable t be determined frm the infrmatin given in the prblem.

3 c. Suppe that intead f the ma pectrmeter etup yu had a unifrm magnetic field that pint alng the z-axi with a value f B 30mT. An electrn enter the magnetic filed with a peed v m at an angle 300 abve the x-y plane a hwn in the figure n the right. What i the radiu f the circular rbit abut the magnetic field line and the ditance between the winding f the helix, called the pitch, p? F b qv B mv R v p T p v T v R mv eb kg m in m C T π R v vcφ vinφ π R π R tanφ π m m tan60 d. Suppe intead f electrn in an external field yu had the fllwing etup in which a wire f cntant linear ma denity λ ma i held between the ple length f a magnet in the plane f the page. The magnet are bth circular with radiu r. If an ideal battery prvided the current in the circuit, what i the initial acceleratin f the wire? a Rλ int the page. VB a Rλ ut f the page. VB a VB int the page. Rλ a VB ut f the page. Rλ V R S

4 . Of magnetic field, airplane and helicpter a. Suppe yu had the tw circuit hwn n the right, where circuit # i n the left and circuit # i n the right. A ditance d eparate the right and left ide f circuit # and #. At the midpint between the tw circuit, which f the fllwing give the net magnitude f the magnetic field? Aume that up the page, ut f the page and t the right are the pitive directin.. B net B net B net B net µ π d µ π d µ π d V R + V R V R V R.. V V R. R b. Suppe yu had tw circular cil each f radiu r eparated by a ditance d. They are held in place that their face are parallel t each ther. Their center lay n a line that i perpendicular t bth face. If each ha a current I flwing in the directin hwn, the magnetic frce n the upper lp due t the lwer lp trie t make. the upper lp maller and pull it dwnward.. the upper lp maller and puh it upward. 3. the upper lp larger and pull it dwnward. 4. the upper lp larger and puh it upward.

5 c. The Earth magnetic field ha cmpnent that pint nrth parallel t the grund ( B.µT ) and vertically dwn int the grund ( B 5.6µT ). A Being 737 airplane ha a wingpan 40m ~ 0 feet and i flying parallel t the grund at a peed v 35.5 m mi ~ 500. A the plane flie nrth, what ptential difference i hr induced acr the wingtip and which wingtip becme negatively charged? ε Blv T 40m 35.5 m 0.49V and a the plane flie nrth, the magnetic frce n the charge puhe the electrn t the right. S the right wingtip becme negatively charged. d. Suppe that yu have a metal bar f length L 3m rtating abut ne end with angular velcityω Δθ radian 47 thrugh a magnetic field B Δt 5.6µT perpendicular t the face f the bar pinting int the grund. What ptential difference i induced acr the bar? Hint: A the bar rtate it weep ut an angle Δθ. Out f π radian, what fractin f the area f the circle i wept ut in a time Δt by the bar? x x x x x x x ω x x x x x x x x x x x x x x pivt ΔA Δθ π π L ε B ΔA Δt B Δθ πδt π L BL ω T 3m ( ) 47 radian 0.0V

6 3. The tudy f light i fundamental t the wrking f many device, uch a lene. a. Suppe that light trike a plane bundary between tw material with different refractive indice. Which f the fllwing cannt ccur?. There i a reflected beam, but n tranmitted beam.. There i a tranmitted beam, but nt reflected beam. 3. There are bth tranmitted and reflected beam. 4. The peed f light increae when the light enter the ecnd material frm the firt. 5. The peed f light decreae when the light enter the ecnd material frm the firt. b. Cnider the cm thick lab f material belw that ha an unknwn index f refractin. Light frm a 0.5mW laer pinter i incident at angle θ 45 0 with repect t the nrmal t the ide urface. The light prpagate thrugh the material and exit at an angle θ 76 0 with repect t the nrmal t the bttm urface. What i the index f refractin f the material? Hint:in 90 φ ( ) cφ. θ β α cm α β θ Left urface: n inθ n m inα Bttm urface: n m inβ n m in 90 α ( ) n m cα n inθ. Dividing the tw exprein: n m inα n m cα n inθ n inθ tanα inθ inθ in45 in76 α 36.0 n m inα n inθ n m n inθ inα in45 in36..

7 c. Suppe that yu have an arrangement f lene placed uch that the len n the left ha a fcal length f 7mmwhile 5mm t the right f thi len a ecnd len with fcal length 48mm i placed. Thi cmbinatin f lene i ued t image the mtin f an bject mving at 0.7 mm. If the image f the bject i prjected nt a creen lcated.7m t the right f the ecnd lend, what wuld be the velcity in mm f the bject n the creen? Object ditance fr len : + d 0 d i f d 0 f d i 48mm 70mm d 49.9mm 0 Image ditance fr len : d 0 + d i D d i D d 0 5mm 49.9mm 0.mm Object ditance fr len : + d 0 d i f d 0 f d i 7mm 0.mm d 34.mm 0 The peed i given by the magnificatin: v creen M M v 0 d i d i v 0.mm mm 70mm 49.9mm d 0 d 0 nt t cale 0.7 mm 4. mm d. Suppe that yu have a cnverging len and the arrangement f clred bject hwn belw. Which f the fllwing are true? There may be mre than ne crrect anwer. f c f c. Only a real image f the bject will be prduced.. Only a virtual image f the bject will be prduced. 3. Bth real and virtual image will be prduced. 4. Whether real r virtual image are prduced, the magnificatin will be greater than unity. 5. Whether real r virtual image are prduced, the magnificatin will be le than unity. 6. There i nt enugh infrmatin n the ize f r lcatin f the bject t anwer thi quetin.

8 Phyic Equatin Sheet Electric Frce, Field and Ptential Electric Circuit Light a a Wave F k Q Q r F E q E Q k Q r ˆr PE k Q Q r V ( r) k Q r E x ΔV Δx F qvbinθ F IlBinθ B µ I 0 πr ε induced ˆr W qδv q V f V i Magnetic Frce and Field Cntant g 9.8 m e C Δφ B Δt k m C 4πε ε C ev J µ 4π 0 7 Tm A c m h J m m e kg 0.5MeV c m p kg 937.MeV c m n kg 948.3MeV c amu kg 93.5MeV c A Ax + Bx + C 0 x B ± Δ( BAcθ ) Δt Blv B 4 AC A Light a a Particle & Relativity hc E hf pc λ KE hf φ ev max Δλ γ v c p γmv E E E I ΔQ Δt neav ; n ρ A d M V IR I R erie R parallel ttal ttal ret KE h m c e mc ( cφ) KE + E p c ret + m c ( γ ) mc γmc 4 tp Circle : C πr πd A πr Triangle : R i i ρl A A bh Sphere : A 4πr V 4 3 πr3 i R i P IV I R V R Q CV κε A 0 d V ( κc 0 )V PE QV CV Q C Q charge ( t) Q max e t RC Q dicharge C parallel C erie Gemetry ( t) Q max e C i i i C i t RC c f λ ( ) S t ε µ energy time area cε E t I S avg cε E max P Frce Area S S c θ v θ inc θ refl εµ c n S c S c n inθ n inθ f + d d i M h i h d i d M ttal E binding ( ) ( ) M i i c B max µ 0 ( ) ( c B t) µ 0 ( Zm + m m ) Δ λ Δt λt A t A e m t m e ln t λ p λt Mic. Phyic 0 Frmulae F Δ p Δt Δ( mv) m a Δt F k y F C m v R r ˆ W ΔKE m v f v i PE gravity mgy PE pring ky x f x i + v ix t + a xt v fx v ix + a x t v fx v ix + a x Δx uclear Phyic n ( t) ret e ( ) ΔPE c λt