( ) WYSE ACADEMIC CHALLENGE Regional Physics Exam 2009 Solution Set. 1. Correct answer: D. m t s. 2. Correct answer: A. 3.

Transcription

1 YSE CDEMIC CHLLENGE Regnl hyscs E 009 Slutn Set. Crrect nswer: D d hrzntl v hrzntl t s t s t d d d ll ll ll gt 9.80 s 0.63 ( s). Crrect nswer: ( ) ( 3 /s) t ( 4. 0 /s ) ( 4. 0 /s ) 8. 0 /s 3. Crrect nswer: v t ( ) ( 3 /s)( t) ( 4. 0 /s )( t) ( t 0.50s) ( ) ( 3 /s)( 0.50s) ( 4. 0 /s )( 0.50s) ( t 0.00s) ( ) ( 3 /s)( 0.00s) ( 4. 0 /s )( 0.00s) ( t 0.50 s) ( t 0.00 s) ( 55) ( 70 ) ve 30. / s 0.50 s 0.00 s 0.50 s 4. Crrect nswer: Let nrth, suth - Δt v v t ( ) ( ) ( 40.0 N ) Δt ( 00. kg / s) ( Δt 0.0 s 5. Crrect nswer: C t 300. kg / s KE knetc energy, GE grvttnl ptentl energy ) ΔEnergy ΔKE ΔGE drver drver. 0 ( ) g( y y ) ( 58.0 kg)( 0 4 ) / s g( y y ) 4 J drver drver drver gy drver drver gy

2 009 Regnl hyscs Slutn Set 6. Crrect nswer: E ( ) 0 ( ) ( 5) 7. Crrect nswer: D 4 / s.54 / s The chnge n entu syste s equl t the ttl pulse ctng n the syste. Ipulse Σ Δt 8. Crrect nswer:, sys, sys The unversl lw grvttn s credted t Newtn. 9. Crrect nswer: ccrdng t the unversl lw grvttn, the gntude the grvttnl rce between tw pnt sses s prprtnl t the prduct ther sses, nd nversely prprtnl t the squre ther seprtn dstnce. 0. Crrect nswer: D n pprprte unt esure r pressure s scl.. Crrect nswer: E ccrdng t the specl thery reltvty, n bserver wuld bserve tht clck vng reltve t the bserver runs t slwly. Let Δt prper the te ntervl seen by n bserver vng wth the clck. Let Δt prper the te ntervl seen by n bserver wh sees the clck vng wth speed v. c dentes the speed lght. Then: Δt prper Δtprper v c. Crrect nswer: C ecuse the net eternl rce ctng n the syste s zer, the entu the syste wll be cnserved. The knetc energy the syste wll be less ter the cllsn snce se energy s used t dent the pucks.

3 009 Regnl hyscs Slutn Set 3. Crrect nswer: KE KE 4 8 ( 4 ) 4. Crrect nswer: E Sung trques wth respect t the center the ruler: Στ Στ C CC c c (. g 5.0 g) 980 ( 50.0c 0.0c) sn( 90 ) ( M 5.0 g) 980 ( 75.0c 50.0c) sn( 90 ) 00 s s M 75 g 5. Crrect nswer: up ulcru ulcru ulcru dwn stck g hlder g ( 0.50 kg) g ( 0.00 kg) g ( 0.50 kg) g ( 0.050kg) g ( 0.50 kg) g ( 0.00 kg) ( kg)( 9.8 / s ) 5.39 N 6. Crrect nswer: C net kg 000 g s Crrect nswer: D y b rse y ntercept run 50 s y 3000 T ( 54 g) N 3 s s R 3 50 s g

4 009 Regnl hyscs Slutn Set 8. Crrect nswer: E The rble s vng wth the crt bere t s prjected nd thus hs cnstnt hrzntl speed t the rght s seen by n bserver n the lb. hen the rble s prjected upwrd, t stll hs the se hrzntl speed t the rght, but nw t ls hs vertcl cpnent tn. The cbntn these tw tns yelds prblc pth, E, s shwn. C D E 9. Crrect nswer: E Usng cnservtn energy: X k v N J k gy N 3.3J 70 v.43 / s gy k ( 0. ) (.5 kg) 9.8 ( 0.3) (.5 kg) v gy s v s ( 0.3) (.5 kg) 9.8 ( 0.4 ) (.5 kg).4 s v k gy v 0. Crrect nswer: Gven : ˆ80N cs( 55 ) ˆ80 j N sn( 55 ) ˆ7.5N ˆ33.8 j N nd such tht : ˆ33.8 j N ˆ33.8 j N ˆ7.5N ˆ33.8 j N ˆ33.8 j N ˆ7.5N 3 r. Crrect nswer: D τ τ w. r. t. w. r. t. r r r r ( )[ C ] 3r( 3 )[ CC ] ( 9 )( r )[ CC ] 7r[ CC ]

5 009 Regnl hyscs Slutn Set. Crrect nswer: C Snce n eternl trques ct n the syste 3 pnt sses nd ssless rd, the ngulr entu the syste s cnserved. th respect t pnt, the ntl ngulr entu the vng pnt ss s vr(c). The ntl ngulr entu the rd nd ttched sses s zer. Therere the ttl ntl ngulr entu s vr(c) 0 vr(c). terwrd, the rd nd ss syste spns wth cnstnt ngulr speed. In ters ths ngulr speed, ω, the trnsltnl speed the sses t dstnce r r s uter (r)ω, whle the trnsltnl speed the ss clsest t s nner rω. S the ttl nl ngulr entu the syste s: ( uter )(r)(c) ( uter )(r)(c) ( nner )(r)(c). v r r r Replcng nner nd uter nd splyng ne btns: (rω)(r)(c) (rω)(r)(c) (rω)(r)(c) 9r ω (C). Settng the ttl ntl ngulr entu equl t the ttl nl ngulr entu, ne hs: vr(c) 9r ω(c). Slvng: ω v / (9r). 3. Crrect nswer: E In the precedng stutn, whch physcl qunttes re cnserved n the syste 3 pnt sses nd rd? Snce n eternl trques ct n the syste 3 pnt sses nd ssless rd, the ngulr entu the syste s cnserved. Knetc energy s nt cnserved snce se energy s lst t het durng the nelstc cllsn. Lner entu s nt cnserved becuse the pn t eerts n eternl pulse n the rd t keep t r trnsltng. 4. Crrect nswer: π π π ω π T 48s 4s 5 π ωt cs 0 3 π π 4s t 8.00s 3ω 3 π 0 c ωt g h j 5 c 5. Crrect nswer: C T π k Snce perd depends upn ss nd sprng cnstnt, nd nt pltude, the perd des nt chnge. T 48.0 s.

6 009 Regnl hyscs Slutn Set 6. Crrect nswer: τ I α I R T R TR I R T T I R / s (.500 kg ) 4.69 N ( ) T T.50 kg 7. Crrect nswer: eternl 4kg &6kg syste ( 6.00kg) g ( 4.00kg) g ( 0.00kg)(.60 / s ) g 8.00 / s T T T Sttnry supprt T OR 4.00 kg T n 4 kg ss ( 4. 00kg) 4 kg ss T ( 4.00kg) g ( 4.00kg)(.60 / s ) (4 kg) g (6 kg) g 6.00 kg n 6 kg ss ( 6. 00kg) 6 kg ss ( 6.00 kg) g T ( 6.00kg)(.60 / s ) ddng these tw equtns yelds the equtn bve, resultng n the se nswer. 8. Crrect nswer: D Cnsderng the pulley: T T n pulley T 8.00 kg g 9. Crrect nswer: C bt reltvet erth / E θ sn T T ( 4.00 kg g 4.00kg.60 / s ).8 N pulley pulley 0 [ Sˆ ] ( 8.50k / h)[]?ˆ ( 5.00k / h)[ Eˆ ] bt reltvet rver rver reltve t erth ( west suth) 8.5 ( 8.50k / h) θ ( 5.00k / h) Ŝ / E Ê

7 009 Regnl hyscs Slutn Set 30. Crrect nswer: C T blnce the dwnwrd rce grvty, the gnetc rce ust be drected upwrd. qv qv suth est qv up gnetc Due suth s the crrect respnse. ( ) ( ) ( ) 3. Crrect nswer: The ptentl derence crss the 4.00 kω resstr s gven by Oh s Lw. 4k Ω (5)(4kΩ) kω.00 kω Thus the vltge crss the seres cbntn cnsstng the.00 kω nd 3.00 kω resstrs s ls 0. The current thrugh the.00 kω nd 3.00 kω cbntn s: 0 I k Ω r 3kΩ 4. kω 3kΩ Thus the ptentl derence crss the 3.00 kω resstr s: k (4)(3kΩ) 3 Ω 4.00 kω 3.00 kω 3. Crrect nswer: E 8 3 slpe 8 3 (equtn the prcess lne) rk re under 'curve' rk (verge pressure)(chnge n vlue) rk ( 8 3 ) Crrect nswer: ( 5 )( 5 ) ( 3 )( 3 ) T nrt nrt nrt nrt T.78T 9 nrt 5 nrt 9

8 009 Regnl hyscs Slutn Set 34. Crrect nswer: D hen the ptentl derence crss the cpctr s 4.00, the ptentl derence crss the resstr s Usng Oh s Lw t deterne the current n the resstr t tht nstnt (whch s ls the current n ech the seres eleents), ne hs 5.00 I Snce ths s ls the current n the cpctr t ths nstnt, ne hs.50kω q cp C Δcp Δq Δt C Δt 35. Crrect nswer: I C s r t N s 0.5 wvelength. S there re 5 tes 0.5 wvelengths n the ppe. 5 L λ 4 4L λ 5 N N N.5 / L λ 4L / 5