WYSE Academic Challenge Regional Physics 2008 SOLUTION SET

Transcription

1 WYSE cdemic Chllenge eginl 008 SOLUTION SET. Crrect nswer: E. Since the blck is mving lng circulr rc when it is t pint Y, it hs centripetl ccelertin which is in the directin lbeled c. Hwever, the blck is ls speeding up lng the rc, s it hs tngentil ccelertin in the directin. The sum f the centripetl nd tngentil ccelertins wuld be in directin in-between (represented b rrw e).. Crrect nswer:. t pint Y, the clindricl shell eerts nrml push rdill inwrd n the blck. Grvit cts dwnwrd. 3. Crrect nswer: D. g X t Z the frces n the blck re the nrml frce frm the shell, which pushes upwrd, nd grvit, which cts dwnwrd. Thus the ccelertin f the blck must be in the verticl directin since ll f the frces cting n it re in the verticl directin. The fct tht the blck is mving lng circulr rc with curvture upwrd mens tht the blck hs n upwrd centripetl ccelertin. c e Y Z Digrm fr Questins, nd 3 b. Crrect nswer:. st drpped sphere nd drpped sphere st drpped sphere 5. Crrect nswer: C. (9.8 m/s )(t) (9.8 m/s )(t nd drppedsphere ( 9.8 m/s )( t ) st drpped sphere nd drpped sphere r t s, s) ( 9.8 m/s )( t -s) (9.8 m/s )(t) (9.8 m/s )(t s) 9.8 m/s, fr t s st drpped sphere nd drpped sphere ( 9.8 m/s )( t) ( 9.8 m/s )( t s) ( 9.8 m/s )() t.9 m/s 008 eginl Slutin Set

2 6. Crrect nswer: D. cnstnt ( s) gt ( s) g (s) 9.6 m/s 9.6 m/s 0.5 Therefre, 78. m/s. 7. Crrect nswer:. [ ] [ rise] [ run] [ perid] s s kg kg [ length] m m kg m kg/s N slpe 8. Crrect nswer: C. [] τ [ r sinθ ] [][ r ][ sinθ ] ( m)( N )( ) 9. Crrect nswer: C. Nte tht the sme frce,, cts n bth bjects ver the sme displcement, d. W ΔKE W d KE 0. d W n, finl KE, finl n d KE, finl 0. KE, finl d KE, finl kg M M d Strt inish 008 eginl Slutin Set

3 0. Crrect nswer:. : :. M t t f i i M + v t + f. f i + vitf + f Md Md f t f tf d 0 + (0)t + d 0 + (0)t + M M t f t f t f t f Md Md. Crrect nswer: C. [ ] [ wrk] [ time] [ frce][ displcement] [ time] s Nm pwer. Crrect nswer:. stne The initil crdinte f the stne is - 0 m. s defined b the crdinte sstem, dwn is psitive, thus the initil cmpnent f velcit is + 8 m/s sin(30 ) + 9. ( ) m/s 0. m m/s grvit ls, since dwn is psitive, the ccelertin due t grvit is m/s. Thus, 0 m m/s t +.9 m/s t. ( ) ( ) 8 m 3. Crrect nswer: D. Wrpping fingers f the right hnd in the directin f the rrws rients the thumb ut f the pper (the z directin). Z, ut f pge. Crrect nswer: E. Let ωf ω0 δω, ω i ω0 v v v ωf ωi ω0 δω zˆ ω0 zˆ α ( ) ( ) ( ) δω zˆ δω ( zˆ ) 008 eginl Slutin Set

4 5. Crrect nswer: C. Let f δ, v v v f i tn i ( δ) 6. Crrect nswer: D. ˆ ˆ δ ( ˆ ) v 37 m/s Est 37 m/s Suth 37 m/s.87s.87 s (.89 m/s ) Nrthest 8. m/s Nrthest 7. Crrect nswer:. ( Est Suth) (.89 m/s )( Est + Nrth).80 N kg 9.80 m/s chnge in mmentum f bll (0.837 kg)(5.0 m/s West) (0.837 kg)(5.0 m/s Est) cntct time s (0.837 kg)(5.0 m/s West) + (0.837 kg)(5.0 m/s West) N West s mbll v n bll The frce n the wll is equl in mgnitude, but ppsite in directin. 8. Crrect nswer: E. Cnsider the frces cting n the knt. rigid wll 0.0 N N Σ hrizntl 50.0N 0.0 N cs(0.0 ) T T.3 N 9. Crrect nswer: E. 0 Unknwn weight 0.0 due t weight N sin(0.0 ) T N Unknwn weight T due t weight 008 eginl Slutin Set

5 0. Crrect nswer: C. Since the sstem is frictinless, the tensin in the crd is everwhere the sme. Thus, frce f T pulls up n the lwer pulle, nd frce f (30.0 kg)(9.80 m/s ) pulls dwn n it. Since tht pulle is in equilibrium, the sum f frces n it is zer. T - (30.0 kg)(9.80 m/s ) 0. Thus, T 7 N.. Crrect nswer:. Since the crte is mving t cnstnt speed nd nt ccelerting, the sum f frces must still equl zer. Thus the tensin in the crd is still 7 N kg T. Crrect nswer: D. k ) k 5 N/m ( 0.05m) ( 0.05 kg)(.80 m/s 3. Crrect nswer: D. The bject strts t the rigin. t pints thrugh just befre C, the bject hs psitive velcit nd is thus mving in the psitive is directin, frther nd frther frm the rigin. fter pint C, the bject hs negtive velcit nd is thus mving in the negtive is directin, bck twrd the rigin. S the crrect nswer is d.. Crrect nswer: D. elcit C time On velcit versus time grph, the ccelertin is btined frm the slpe f the tngent t the curve. Pint D (respnse d.) hs the gretest negtive slpe nd thus the gretest mgnitude f ccelertin. D E 5. Crrect nswer:. Using cnservtin f mmentum, since the net eternl impulse n the tw cr sstem is zer: M + M M (8/7) + M ( ther ) ther -8/7 6/7. 6. Crrect nswer: E. P 0 W 80 N 7.0 m/s 008 eginl Slutin Set

6 7. Crrect nswer: C N 3 blck sstem m/s 8kg blck kg blck kg blck Mttl.00 kg Σ 7.00 N - kg, 8 kg cntct 8.00 kg n 8kg blck 8kg blck Mf 8 kg blck kg, 8 kg cntct 3.00 N m/s.00kg.00kg 8.00kg 7.00N 8. Crrect nswer:. Σ3 blck sstem N μ(.00 kg)(9.80 m/s ) μ(.00 kg)(9.80 m/s ) μ(8.00 kg)(9.80 m/s μ Crrect nswer: E. Plnets mve in ellipticl rbits with the sun t ne fcus. ) 30. Crrect nswer:. 35 KE i sstem KEi + KEi (3M)(3) + (M)() M The initil mmentum f the sstem equls the finl mmentum f the sstem, since there is n net eternl impulse cting n the sstem. Thus, (3M)(3) + (M)( ) (5M). S the finl speed f the linked blcks is: KE f sstem KEf + KEf (5M)() M lck KE f sstem 5M / lck M KE 7.0M 35M / i sstem 3. Crrect nswer:. The mmentum f the sstem is cnserved. v v v v p i + pi p f + pf v v v v pi pf p f - p i v v pf p v v i - p - p f i 008 eginl Slutin Set

7 3. Crrect nswer: D. The imge will be finter since fewer rs rech ech imge pint. 33. Crrect nswer: E. v v v Since mgnetic qv ( )(right) (in) dwn, there will be dwnwrd mgnetic frce n the free electrns in the metllic rd which cuses them t be piled up t the bttm end f the rd. Therefre, the bttm end f the rd will hve net negtive chrge while the upper end will hve net psitive chrge. Since electric field lines pint frm psitive chrge nd twrd negtive chrge, the electric field is dwnwrd inside the rd. ++ E v Crrect nswer:. L The wvelength f the nth hrmnic is given b λ n. Therefre, the frequenc f the n v nv nth hrmnic is fund frm fn. In this prblem, we re given the frequencies f λn L tw djcent hrmnics, s let s cnsider the nth hrmnic nd the (n+)th hrmnic. v nv v (n + )v The frequencies re fn nd fn+. Nw let s tke the difference λn L λn+ L (n + )v nv v between the tw frequencies. Δf fn + fn L L Slving, v (8. / s)()(.350 m) 7.3 m/s. 35. Crrect nswer:. ( θ) ( 3.μ C)(.00 0 ) N/Cest 0 Σest, west 0.3N sin west+ θ 0.3N θ sin 6 ( 3. 0 )(.00 0 ) 0.3 qe (3.μ C) (.00 0 )N/C 5.9 m g 008 eginl Slutin Set