Physics 111. Exam #1. September 28, 2018

Transcription

1 Physics xam # Sepember 8, 08 ame Please read and fllw hese insrucins carefully: Read all prblems carefully befre aemping slve hem. Yur wrk mus be legible, and he rganizain clear. Yu mus shw all wrk, including crrec vecr nain. Yu will n receive full credi fr crrec answers wihu adequae explanains. Yu will n receive full credi if incrrec wrk r explanains are mixed in wih crrec wrk. S erase r crss u anyhing yu dn wan graded. Make explanains cmplee bu brief. D n wrie a l f prse. Include diagrams. Shw wha ges in a calculain, n jus he final number. Fr example p m v " 5kg ( ) ( m s ) 0 kg m s Give sandard SI unis wih yur resuls unless specifically asked fr a cerain uni. Unless specifically asked derive a resul, yu may sar wih he frmulas given n he frmula shee including equains crrespnding he fundamenal cnceps. G fr parial credi. If yu cann d sme prin f a prblem, inven a symbl and/r value fr he quaniy yu can calculae (explain ha yu are ding his), and use i d he res f he prblem. All muliple chice quesins are wrh 3 pins and each free-respnse par is wrh 9 pins Prblem # /4 Prblem # /4 Prblem #3 /4 Tal /7 I affirm ha I have carried u my academic endeavrs wih full academic hnesy.

2 . Pin Charges a. Alex he pin charge has a mass m and a charge +q. Samanha, her siser, has a mass f 3 4 m and a charge q. Since hey have ppsie signs fr heir charges hey arac. Which is araced mre he her and by hw much?. Alex is araced mre Samanha and by wice as much.. Samanha is araced mre Alex and by wice as much. 3. Alex is araced mre Samanha and by fur imes as much. 4. Samanha is araced mre Alex and by fur imes as much. 5. Alex and Samanha arac each her by he same amun. b. Suppse ha pin charges Alex and Samanha were iniially very far away frm each her. If each was brugh in frm very far away and was frced sand a disance L apar, hw much wrk was dne assemble he cllecin f w pin charges? Wrk dne place Alex: W A q A ΔV 0 Wrk dne place Samanha: W S q S ΔV A q ( ) kq L 0 kq L The wrk dne build he disribuin f charges: W ne W A +W S kq L

3 c. Suppse ha pin charges Alex and Samanha were a he fllwing lcains; Alex is a he pin ( x, y) ( 0,0)m while Samanha is a he pin ( x, y) ( L,0)m. In his cnfigurain, pin charges Alex and Samanha sar arguing wih each her. w, suppse ha a hird pin (le s call her Mm) is placed a a pin ( x, y) ( 0, L )m. Wha frce wuld Mm feel because f Alex and Samanha? Assume ha Mm has a mass m and a charge 4q. F ne,x F M,S csθ kq Q M S csθ 8kq 5 r M,S 4 L 5 64kq 5 5L 5.7 kq L F ne,y F M,A F M,S sinθ kq Q M A kq Q M A sinθ 6kq r M,A r M,A L F ne F ne,x φ an F ne,y F ne,x + F ne,y ( 5.7) + ( 3.) kq L 3. an kq L 8kq 5 4 L 5 3.kq L

4 d. Suppse ha pin charge Mm has had enugh f pin charges Alex and Samanha and decides leave her psiin and mve very far away. A her frmer psiin, he elecric field due pin charges Alex and Samanha (sill in heir riginal lcains) wuld have a magniude and a direcin given by which f he fllwing?. The magniude f he elecric field wuld be given by F and he direcin 4q wuld pin in he same direcin f he ne frce n pin charge Mm.. The magniude f he elecric field wuld be given by F and he direcin 4q wuld pin in he ppsie direcin f he ne frce n pin charge Mm. 3. The magniude f he elecric field wuld be given by F and he direcin q wuld pin in he same direcin f he ne frce n pin charge Mm. 4. The magniude f he elecric field wuld be given by F and he direcin q wuld pin in he ppsie direcin f he ne frce n pin charge Mm. 5. The elecric field in bh magniude and direcin wuld be zer because pin charge Mm is n lnger a he pin in quesin.

5 . Circuis a. Cnsider he resisr circui n he righ in which a cllecin f resisrs is wired in cmbinain a baery. The baery is raed a VB V and each resisr is R 00Ω. Wha is he equivalen resisance f he circui and he al curren prduced by he baery? Assume ha he swich S is clsed fr his quesin. R7, R8, and R9 are in series: R789 R7 + R8 + R9 00Ω + 00Ω + 00Ω 300Ω. R5, and R6 are in series: R56 R5 + R6 00Ω + 00Ω 00Ω. R4, R56, and R789 are in parallel: R Ω R Ω R4 R56 R789 00Ω 00Ω 300Ω 600Ω R, R, R3, and R are in series: Req R R + R + R3 + R Ω + 00Ω + 00Ω Ω 354.5Ω. The al curren prduced by he baery: V IT Req IT V V 0.06A 6.mA. Req 654.5Ω b. Wha is he al energy dissipaed as hea and ligh acrss he prin f he circui cnaining resisrs R4 R9 if he circui is energized (cnneced he baery) fr 3s? Assume ha he swich S is clsed fr his quesin. VR V VR VR VR VR V IT R IT R IT R3 VR V 3IT R VR V ( 3 0.6A 00Ω ) V 8.6V 3.4V Δ VR ( 3.4V ) P 0.W Δ R Ω Δ PΔ 0.W 3s 6.67J

6 c. Suppse ha he swich S in he circui abve were lef pen. In his case he al curren and he energy per uni ime prduced by he baery wuld change accrding which f he fllwing?. Bh he al curren and energy per uni ime prduced by he baery wuld increase.. The al curren wuld decrease and energy per uni ime prduced by he baery wuld increase. 3. Bh he al curren and energy per uni ime prduced by he baery wuld remain cnsan a heir riginal values. 4. The al curren wuld increase and energy per uni ime prduced by he baery wuld decrease. 5. The al curren wuld decrease and energy per uni ime prduced by he baery wuld decrease. d. We have alked abu resisrs in class and we have said ha elecric currens flw hrugh a resisr while elecric penial differences ccur acrss a resisr. Cnsider par f a circui shwn in he figure belw where he elecric curren eners he resisr frm pin A. Fr his siuain, is he elecric penial higher a pin A r a pin B and is he elecric curren greaer a pin A r pin B?. The elecric penial is higher a pin A han pin B and he elecric curren is greaer a pin A han a pin B.. The elecric penial is higher a pin B han pin A and he elecric curren is greaer a pin A han a pin B. 3. The elecric penial is higher a pin A han pin B and he elecric curren is he same a pin A as i is a pin B. 4. The elecric penial is higher a pin B han pin A and he elecric curren is he same a pin A as i is a pin B. 5. The elecric penial is higher a pin A han pin B and he elecric curren is lwer a pin A han a pin B. 6. The elecric penial is higher a pin B han pin A and he elecric curren is lwer a pin A han a pin B.

7 3. Capacirs A 54 µ F capacir is cnneced a 0000Ω resisr and his resisr-capacir cmbinain is cnneced a swich S and a baery wih penial V as shwn belw. a. A ime he swich S is clsed and he iniially uncharged capacir begins charge. In fracins r muliples f he ime cnsan, a wha ime des he penial acrss he resisr equal hree-quarers f ha acrss he capacir? In her wrds, a wha ime des VR 43 VC? V VR + VC VR + V e RC VR Ve RC RC 3 RC RC VR VC Ve V e e RC ln τ n τ b. Suppse ha afer a lng ime has passed, he capacir is fully charged and ha a his pin he swich S is pened and he baery and resisr are bh remved frm he circui. If he plaes f he capacir are hen squeezed geher s ha he disance beween he capacir plaes is ne-half f is riginal disance. In his scenari, which f he fllwing describes he change in he elecric field beween he capacir plaes and he wrk dne pushing he plaes geher? In he answers belw, le C and V be he riginal capaciance f he sysem and penial difference acrss he capacir plaes respecively, befre yu pushed he plaes.. The elecric field wuld increase and he wrk dne pushing he capacir plaes geher wuld be given by W 4 CV.. The elecric field wuld increase and he wrk dne pushing he capacir plaes geher wuld be given by W + 4 CV. 3. The elecric field wuld remain cnsan and he wrk dne pushing he capacir plaes geher wuld be given by W 4 CV. 4. The elecric field wuld remain cnsan and he wrk dne pushing he capacir plaes geher wuld be given by W + 4 CV. 5. The elecric field wuld decrease and he wrk dne pushing he capacir plaes geher wuld be given by W 4 CV. 6. The elecric field wuld decrease and he wrk dne pushing he capacir plaes geher wuld be given by W + 4 CV.

8 c. A ligh bulb is cnneced in series a swich, a baery, and an uncharged capacir. A ime 0, he swich is clsed. Which f he fllwing bes describes he brighness f he ligh bulb as a funcin f ime? In an experimen called he phelecric effec, ligh is shwn n a meal surface and if here is sufficien energy in he ligh, elecrns can be ejeced frm he meal surface. T measure he maximum energy f he emied elecrns, a secnd plae is placed abve he meal surface and is kep negaive enugh s ha he elecrns are jus repelled frm he upper plae as shwn n he righ. d. If barium meal is illuminaed wih ulravile ligh ejecing elecrns, wha was he maximum speed f he ejeced elecrns and wha elecric field was beween he barium surface and he upper plae if Δy cm? The specrscpic infrmain fr barium is 37 Ba. 56 W ΔK qδv mv mv qδv mv f i i v i qδv m ( ) 3.0V C kg ( ) m s ΔV Δy 3.0V 0V 0.0m 0m 30 V m r 30 V in he psiive y-direcin. m

9 Physics quain Shee lecric Frces, Fields and Penials lecric Circuis Ligh as a Wave F k Q Q r F q Q k Q r ˆr Magneic Frces and Fields F qvbsinθ F IlBsinθ τ IAB sinθ µb sinθ P µb csθ B P k Q Q r V ( r) k Q r x ΔV Δx µ 0I πr ε induced Δφ B Δ ˆr W qδv q V f V i Cnsans g 9.8 m s e C k m C 4πε ε C ev J µ 4π 0 7 Tm A c m s h Js 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( BAcsθ ) Δ B 4 AC A al I ΔQ Δ V IR I R series R parallel R i i ρl A i R i P IV I R V R Q CV κε A 0 d V ( κc 0 )V W U QV CV Q C Q charge ( ) Q max e RC Q discharge C parallel C series max γ v c p γmv K h m c mc ( ) Q max e C i i i C i ( csφ) K + p c + m c ( γ ) mc 4 RC Ligh as a Paricle & Relaiviy hc hf pc λ K hf φ ev Δλ al res Gemery e res sp γmc Circles : C πr πd A πr Triangles : A bh Spheres : A 4πr V 4 3 πr3 c fλ S θ ( ) cε ( ) I S P v θ n sinθ n ε µ S S cs θ inc + f d d M S c energy ime area c εµ n i d sinθ mλ r a sinφ m' λ cε Frce Area sinθ hi di M h d al avg refl binding ( ) ( ) i M i max Bmax c µ ( m + ) λ 0 B c µ ( Zm + m m ) Δ λ Δ λ A A e m m e ln λ p λ Misc. Physics 0 Frmulae F Δ p Δ Δ( mv) m a Δ F k y F C m v R r ˆ W ΔK m v f v i P graviy mgy P spring ky x f x i + v ix + a x v fx v ix + a x v fx v ix + a x Δx uclear Physics n ( ) res e ( ) ΔP c λ ( ) 0