Physics 111. Exam #1. January 26, 2018

Transcription

1 Physics xam # Januay 6, 08 ame Please ead and fllw these instuctins caefully: Read all pblems caefully befe attempting t slve them. Yu wk must be legible, and the ganizatin clea. Yu must shw all wk, including cect vect ntatin. Yu will nt eceive full cedit f cect answes withut adequate explanatins. Yu will nt eceive full cedit if incect wk explanatins ae mixed in with cect wk. S ease css ut anything yu dn t want gaded. Make explanatins cmplete but bief. D nt wite a lt f pse. Include diagams. Shw what ges int a calculatin, nt just the final numbe. F example p m v " 5kg ( ) ( m s ) 0 kg m s Give standad SI units with yu esults unless specifically asked f a cetain unit. Unless specifically asked t deive a esult, yu may stat with the fmulas given n the fmula sheet including equatins cespnding t the fundamental cncepts. G f patial cedit. If yu cannt d sme ptin f a pblem, invent a symbl and/ value f the quantity yu can t calculate (explain that yu ae ding this), and use it t d the est f the pblem. All multiple chice questins ae wth 3 pints and each fee-espnse pat is wth 9 pints Pblem # /4 Pblem # /4 Pblem #3 /4 Ttal /7 I affim that I have caied ut my academic endeavs with full academic hnesty.

2 y. Hydchlic acid is a mdeately stng acid cmpsed f a hydgen in ( H ) and a chline ( Cl ) in cvalently bnded tgethe. This cnfiguatin is called an electic diple and the sepaatin between the hydgen and chline ins is s 0.7nm. H P Cl - x a. Suppse that a Cu in wee placed at the pint P (x, y) (0,5)nm. What ae the net electic field and net electic fce that the Cu in wuld feel? The electic field fm the in wuld pint away fm alng the line jining the pint and while the electic field due t the in wuld pint twad the in alng the line jining the in and the pint. Since these chages cay equal magnitudes f chage and ae equidistant fm the pint the vetical cmpnents f the electic field (and hence electic fce) vanish by symmety. Thus thee is nly an x-cmpnent t the electic field and fce. x kq csθ kq kq kq csθ csθ m C 3 kqs s C m m ( ) m ( ) kqs C F x q x e x C C b. Hw much wk wuld be dne t bing in the Cu in fm vey fa away and place it at the pint P (x, y) (0,5)nm? V P V q V q kq kq 0V W qδv e 0V 0V 0J

3 c. Assuming that each f the thee chages in the distibutin abve ae bught in fm vey fa away and placed in thei espective lcatins, the electic ptential enegy f the assembled chage distibutin is given by. U q Cu k q H. U kq Cu 3. U kq Cu 4. U ke s. 5. U 0. q H q H q Cl q Cl q Cl 4ke. ke ke.. d. Suppse that the Cu in wee eleased fm est at the pint P (x, y) (0,5)nm. The mtin f the in wuld mst likely be. t mve dwn alng the y-axis twad igin.. t mve up alng the y-axis away fm igin. 3. t mve t the left alng the x-axis and then twad the H in. 4. t mve t the ight alng the x-axis and then twad the Cl in. 5. t mve alng the x-axis and keep mving alng the x-axis until the Cu in is vey fa fm the H and Cl ins.

4 . Cicuits a. Cnside the esist cicuit n the ight in which a cllectin f esists is wied in cmbinatin t a battey. The battey is ated at VB 0V and each esist is R 00Ω. What is the equivalent esistance f the cicuit and the ttal cuent pduced by the battey? Assume that the switch S is clsed f this questin. Resists R3, R4, R5, and R6 ae in seies and thei equivalent esistance is R3456 R3 R4 R5 R6 400Ω. Resists R7 and R3456 ae in paallel and thei equivalent esistance is R R Ω. R7 R Ω 400Ω 400Ω Resists R, R, R34567, and R8 ae in seies and thei equivalent esistance is Req R34568 R R R34567 R8 380Ω The ttal cuent is I ttal V 0V 0.06 A. Req 380Ω b. What is the ttal pwe develped by the battey and what is the enegy dissipated acss esist R7 if the cicuit is enegized (cnnected t the battey) f minute? Assume that the switch S is clsed f this questin. The pwe develped by the battey is given by V P IV I R ( 0.06 A) 380Ω 0.57W 57mW. R T detemine the enegy dissipated acss R7 we need t detemine the pwe lst acss R7 and then t multiply this by the time. The ptential diffeence acss R, R, and R8 is given by VR VR VR I ttal R 0.06 A 00Ω.6V. The ptential diffeence acss is 8 given by V V V V34567 V8 V34567 V7 V (V V V8 ) 0V.6V 3.V. Theefe the enegy dissipated is given by V7 (.V ) 7 60s.9J. P7 7 P7t t t R7 00Ω

5 c. Suppse that the switch S in the cicuit abve wee left pen. In this case the ttal cuent and the pwe pduced by the battey wuld. Bth the ttal cuent and the pwe develped by the battey wuld incease.. The ttal cuent wuld decease and the pwe develped by the battey wuld incease. 3. Bth the ttal cuent and the pwe develped by the battey wuld emain cnstant at thei iginal values. 4. The ttal cuent wuld incease and the pwe develped by the battey wuld decease. 5. The ttal cuent wuld decease and the pwe develped by the battey wuld decease. d. Suppse that yu wanted t build a esist-capacit cicuit utilizing the equivalent esistance yu calculated in pat a. Yu decide t build yu ai filled capacit ut f tw paallel metal plates f aea A and sepaatin between the plates d. Yu calculate the capacitance t be C and yu chage the capacit with a battey f ptential diffeence V at which pint yu emve the battey fm yu capacit. Afte yu built and chaged this capacit yu decide that yu want a diffeent value f the capacitance. Instead f ebuilding fm scatch a new capacit yu ealize that yu can get the desied value f the capacitance yu want by gabbing ne f the capacit plates and pulling it away fm the the plate s that the new sepaatin between the plates is s, whee s > d. This capacit has a capacitance C n. The wk yu did n the capacit is given by. W Q ( ε 0 A s d ).. W Q ( ε 0 A d s ). 3. W Q ( ε 0 A s d ). 4. W Q ε 0 A d s ( ). 5. nne f the abve.

6 3. Speaking f capacits, a paallel plate capacit is cnstucted ut f tw cicula metal plates f diamete D 0.5m. The plates ae sepaated by d 5mm and an unknwn dielectic mateial has been inseted between the plates. a. If the capacit wee chaged by a battey such that a chage f Q 4.6 µc wee placed n each plate and an eclectic field 7500 C wee pduced between the plates. What is the value f the dielectic cnstant f the unknwn mateial placed between the plates f the capacit? κε A κε A Q CV 0 V 0 d κε 0 A d d κ Q ε 0 A C C m π ( 0.5m) 7500 C 96.3 b. Suppse that the fully chaged capacit fm pat a was cnnected t the fllwing cicuit whee the esistances ae all identical light bulbs each with esistance R. When the capacit is cnnected t the cicuit, the capacit begins t dischage thugh the light bulbs. Which f the fllwing is/ae tue?. The light bulbs light and each f the light bulbs emain at a cnstant bightness at all times.. The light bulbs light and the bightness f each f the light bulbs deceases with time. 3. The light bulbs light and light bulbs and 3 ae bighte than light bulb. 4. The light bulbs light and light bulbs and 3 ae less bight (dimme) than light bulb. 5. Thee is nt enugh infmatin t detemine the bightness f the bulbs and what happens t the bightness ve time. 3

7 Cnside the setup n the ight whee tw sets f capacits ae used. The capacit n the left is called the acceleat and has a ptential diffeence ΔV a acss the plates while the capacit n the ight is called the deflect and has a ptential diffeence f ΔV d acss its plates. In pats, c and d, the actual values f bth ΔV a and ΔV d ae unknwn. A chage q is acceleated fm est in the acceleat and then entes the deflect. The chage q is deflected in the y-diectin ve a distance Δy y by the electic field between the deflect plates and the deflect plates ae sepaated by an amunt d, whee d > y. c. T detect the acceleated ins fm the acceleat, the ptential diffeence acss the deflect ΔV d is changed until a signal is seen in the in detect. When this signal is seen, it is detemined that the y-cmpnent f the velcity f the ins is v fy. In tems f q, y, d, v fy, and the mass f the chage m, what is the expessin f the ptential diffeence acss the deflect and which deflect plate, the uppe lwe, is at the highe electic ptential? The wk dne n the chage in the deflect egin is given by ( ) mv i W qδv y mv mv m v v f i fy fx, whee ΔV y is the ptential diffeence ve which the chage is acceleated in the electic field. Since thee ae n fces in the hizntal diectin, v fx v ix v i. Thus W qδv y mv mv mv f i fy. q ΔV a ΔV d v f q in detect The electic field between the deflect plates is cnstant s we can elate ΔV d t ΔV y thugh ΔV y y ΔV d d ΔV y y d ΔV d. The diffeence in ptential acss the deflect plates is theefe W qδv y q y d ΔV d mv ΔV fy d mdv fy qy. d. Which f the fllwing expessins belw give the angle, with espect t the hizntal, at which the in detect was set?. tanθ y ΔVd. d ΔVa. tanθ ΔV d ΔV. 3. tanθ d. 4. y tanθ ΔVd. ΔV a ΔV a d ΔVa

8 Physics quatin Sheet lectic Fces, Fields and Ptentials lectic Cicuits Light as a Wave F k Q Q F q Q k Q ˆ Magnetic Fces and Fields F qvbsinθ F IlBsinθ τ IAB sinθ µb sinθ P µb csθ B P k Q Q V ( ) k Q x ΔV Δx µ 0I π ε induced Δφ B ˆ W qδv q V f V i Cnstants 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 ) B 4 AC A ttal I ΔQ V IR I R seies R paallel 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 chage ( t) Q max e t RC Q dischage C paallel C seies max γ v c p γmv K h m c mc ( t) Q max e t C i i i C i ( csφ) K p c m c ( γ ) mc 4 RC Light as a Paticle & Relativity hc hf pc λ K hf φ ev Δλ ttal est Gemety e est stp γmc Cicles : C π πd A π Tiangles : A bh Sphees : A 4π V 4 3 π3 c fλ S θ ( t) cε ( t) I S P v θ n sinθ n ε µ S S cs θ inc f d d M S c enegy time aea c εµ n i d sinθ mλ a sinφ m' λ cε Fce Aea sinθ hi di M h d ttal avg efl binding ( ) ( ) i M i max Bmax c µ ( m ) λ 0 B c µ ( Zm m m ) Δ λ λt A t A e m t m e ln t λ p λt Misc. Physics 0 Fmulae F Δ p Δ( mv) m a F k y F C m v R ˆ W ΔK m v f v i P gavity mgy P sping ky x f x i v ix t a xt v fx v ix a x t v fx v ix a x Δx uclea Physics n ( t) est e ( ) ΔP c λt ( t) 0