12/01/10. STUDENT NAME: STUDENT id #: NOTE: Clearly write out solutions and answers (circle the answers) by section for each part (a., b., c., etc.

Transcription

1 GENERAL PHYSICS PH -3A (Dr. S. Mirv) Tet 4 (/03/07) Key /0/0 STUDENT NAME: STUDENT id #: ALL QUESTIONS ARE WORTH 0 POINTS. WORK OUT FIVE PROBLEMS. NOTE: Clearly write ut lutin and anwer (circle the anwer) by ectin r each part (a., b., c., etc.) Iprtant Frula:. Mtin alng a traight line with a cntant acceleratin v aver. peed [dit. taken]/[tie trav.]s/t; v aver.vel. Δ/Δt; v in d/δt; a aver. Δv aver. vel. /Δt; a dv/δt; v v + at; /(v +v)t; v t + / at ; v v + a (i 0 at t 0). Free all tin (with pitive directin ) g 9.80 / ; y v aver. t v aver. (v+v )/; v v - gt; y v t - / g t ; v v gy (i y 0 at t 0) 3. Mtin in a plane v v cθ; v y v inθ; v t+ / a t ; y v y t + / a y t ; v v + at; v y v y + at; 4. Prjectile tin (with pitive directin ) v v v cθ; v t; a ( v inθ cθ)/g (v inθ)/g r y in y in ; v y v y - gt v inθ - gt; y v y t - / gt ; 5. Unir circular Mtin av /r, Tπr/v 6. Relative tin v P A v P B + v B A a a PA PB 7. Cpnent ethd vectr additin

2 A A + A ; A A + A and A y A y + A y ; A A + A y ; θ tan - A y /A ; The calar prduct A a b a b c φ a b ( a ˆ ˆ ˆ) ( ˆ ˆ ˆ i + a y j + a zk b i + b y j + b zk ) a b a b + a yb y + a zb z The vectr prduct a b ( a iˆ + a ˆj + a kˆ) ( b iˆ + b ˆj + b kˆ) y z y z iˆ ˆj kˆ a y a z a ˆ ˆ a a z ˆ a y a b b a a a y a z i j + k b y b z b b b z b y b b b y z ( a b b a ) iˆ + ( a b b a ) ˆj + ( a b b a ) kˆ y z y z z z y y. Secnd Newtn Law af net ;. Kinetic rictin k μ k N; 3. Static rictin μ N; 4. Univeral Law Gravitatin: FGM/r ; G N /kg ; 5. Drag ceicient D C ρ A v 6. Terinal peed v t g C ρ A 7. Centripetal rce: F c v /r 8. Speed the atellite in a circular rbit: v GM E /r 9. The wrk dne by a cntant rce acting n an bject: W F d cφ F d 0. Kinetic energy: K v. Ttal echanical energy: EK+U. The wrk-energy there: WK -K ; W nc ΔK+ΔUE -E 3. The principle cnervatin echanical energy: when W nc 0, E E 4. Wrk dne by the gravitatinal rce: W g d cφ g

3 . Wrk dne in Liting and Lwering the bject: Δ K K K W + W ; i K K ; W W i a g i a g. Spring Frce: F k (H k' law ) 3. Wrk dne by a pring rce: W k k ; i 0 and ; W k i i 4. Wrk dne by a variable rce: W F ( ) d W d W 5. Pwer: P avg ; P ; P F v cφ F v Δ t d t 6. Ptential energy: Δ U W ; Δ U F ( ) d 7. Gravitatinal Ptential Energy: Δ U g ( y y ) g Δ y ; i y 0 a n d U 0 ; U ( y ) g y i i i i i 8. Elatic ptential Energy: U ( ) k 9. Ptential energy curve: du ( ) F ( ) ; K ( ) E e c U ( ) d 0. Wrk dne n a yte by an eternal rce: F ric ti n i n t in v lv e d W h e n k in e tic ric ti n rc e a c t w ith in th e y te Δ E d th k W Δ E Δ K + Δ U e c W Δ E + Δ E e c th. Cnervatin energy: W Δ E Δ E + Δ E + Δ E e c th r ilated yte (W 0) Δ E + Δ E + Δ E 0 in t e c th in t Δ E. Pwer: P avg ; P Δ t de d t ; 3. Center a: r r n c i i M i 4. Newtn Secnd Law r a yte particle: F net M a c 3

4 . Linear Mentu and Newtn Secnd law r a yte particle: P M v and F c net dp dt t. Clliin and ipule: J F ( t ) d t; J F Δ t; t i avg when a trea bdie with a and n n Δ peed v, cllide with a bdy whe pitin i ied F avg Δ p Δ v Δ v Δ t Δ t Δ t Ipule-Linear Mentu There: p p i J 3. Law Cnervatin Linear entu: P P r cled, ilated yte 4. Inelatic clliin in ne dienin: p + p p + p i i i 5. Mtin the Center Ma: The center a a cled, ilated yte tw clliding bdie i nt aected by a clliin. 6. Elatic Clliin in One Dienin: v v ; v v i i Clliin in Tw Dienin: p + p p + p ; p + p p + p i i iy iy y y 8. Variable-a yte: Rv rel v v v M a (irt rcket equatin) i r e l M i ln (ecnd rcket equatin) M S 9. Angular Pitin: θ (radian eaure) r 0. Angular Diplaceent: Δ θ θ θ (p itiv e r c u n terclc k w ie r tatin ) Δ θ d θ. Angular velcity and peed: ω avg ; ω (p itive r c u n tercl ck w ie rtati n ) Δ t d t Δ ω. Angular acceleratin: α avg ; α Δ t d ω d t 4

5 ω ω + α t θ θ ( ω + ω ) t. angular acceleratin: θ θ ω t + α t ω ω + α ( θ θ ) θ θ ω t ω t. Linear and angular variable related: I r d v π r π θ r ; v ω r ; a t α r ; a r ω r ; T r v ω 3. Rtatinal Kinetic Energy and Rtatinal Inertia: K I ω ; I iri r bdy a a yte dicrete particle; r a bdy w ith cntinuuly ditributed a. 4. The parallel ae there: I I c + M h 5. Trque: τ rf r F rf in t φ 6. Newtn ecnd law in angular r: τ net I 7. Wrk and Rtatinal Kinetic Energy: α W θ θ i τ dθ ; W τ ( θ θ ) r τ cnt; i dw P Δ K K K I ω I ω W dt ; i i w rk energy there r rtating bdie v c ω R K I cω + v 8. Rlling bdie: a c α R g in θ a c + I / M R c c r r llin g th ly d w n th e ra p 9. Trque a a vectr: τ r F ; τ r F inφ r F r F 5

6 l r p ( r v ) ;. Angular Mentu a particle: l r v in φ r p r v r p r v dl. Newtn Secnd law in Angular Fr: τ net dt 3. Angular entu a yte particle: L τ net n l i i 4. Angular Mentu a Rigid Bdy: L I ω 5. Cnervatin Angular Mentu: L i L (i la te d y te ) F net 0; τ net 0 6. Static equilibriu: i all the rce lie in y plane F 0; F 0; τ 0 7. Elatic Mduli: tre dulu train F Δ L 8. Tenin and Cprein: E, E i the Y ung' dulu A L F Δ L 9. Shearing: G, G i the hear dulu A L Δ V 0. Hydraulic Stre: p B, B i th e b u lk d u lu V et dl dt net, net, y net, z. Siple harnic tin: t + v t + a t + c( ω φ ); ω in( ω φ ); ω c( ω φ ) k. The Linear Ocillatr: ω, T π k 3. Pendulu: T T π I k, trin pendulu π L g, i ple pendulu T I π, phyical pendulu g h 6

7 . Daped Harnic Mtin: bt k b ( t ) e c ( ω ' t + φ ), ω ', E ( t ) k e 4 bt. Sinuidal wave: y (, t ) y in( k π ω ω λ ω t ), k,, v λ λ π T k T 3. Wave peed n tretched tring: v τ μ 4. Average pwer tranitted by a inuidal wave n a tretched tring: P avg μ v ω y 5. Intererence wave: y '(, t ) [ y c φ ] in ( k ω t + φ ) 6. Standing wave: y '(, t ) [ y in k ] c ω t v v 7. Renance: n, r n,,3,... λ L B 8. Sund wave: v, ρ Δ L φ π ( π ) r 0,,,3..., cntructive intererence λ 9. Intererence: Δ L φ π ( + ) π r 0,,,3..., detructive intererence λ 0. Sund Intenity: P P I, I ρ v ω, I A 4 π r. Sund level in decibel: β I ( 0 db ) l g, I 0 W / I. Standing wave pattern in pipe: v n v λ L, n,,3,..., r pipe pened r bth end v n v λ 4 L, n,3,5,..., r pipe cled at ne end and pened at the ther 3. Beat: beat 7

8 vr. The Dppler eect: ' ( ± ) v und;(v 33/); ' v E v v ± vr ' general Dppler Eect v v E, v R the peed the receiver; v the peed the + r receiver appraching tatinary eitter, - r receiver ving away r the tatinary eitter;, v E the peed the eitter, v the peed the und, - r eitter appraching tatinary receiver, + r eitter ving away r the tatinary receiver; 8

9 9

10 . A iple pendulu length.0 i ued by a tudent t deterine the acceleratin gravity. The pendulu wing back and rth thrugh 0 cplete wing in.. What value g i btained? L Fr a iple pendulu T π g 0 wing in. ean that T (. /0). 4π 4π. L g 9.6 / T. 0

11 3. A tranvere traveling inuidal wave n a tring ha a requency 00Hz, a wavelength 0.040, and an aplitude.0. What i a) the aiu velcity in / any pint n the tring? b) the peed the wave? The ablute value the aiu velcity any particle n a tring i v ωy π y π(00 Hz) (0.00 ).3 / pa v λ (0.04 ) (00 Hz) 4 / wave

12 4. I the length a pian wire ( given denity) i increaed by 5%, what appriate change in tenin i neceary t keep it undaental requency unchanged? TL T.05L v L L (.05 L) T T.05 (.05) T (.05) T T T T(.05 ) 5% increae T T

13 5. 3

14 6. Fr AC> BC AC r AC<; BC AC 0.55 () BC + AC () ()-() AC.7485 AC 0.9 4

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16 8. A urce eit und with a requency 000Hz. It i ving at 0/ tward a tatinary relecting wall. I the peed und i 340 /, what i the beat requency heard by an berver pitined at ret directly behind the urce? v ± vr ' general Dppler Eect v v E ' '' Statinary receiver hear beat requency beat, v Hz v v ' where i a requency E heard by a tatinary receiver r appraching eitter. v Hz v + v '' where i a requency heard by a tatinary receiver r the urce relected r the wall and ving away r the receiver. beat Hz E 6