WYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E]

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1 WYSE Aaem Challenge 0 Setnal hss Exam SOLUTION SET. Crret answer: E Unts Trque / unts pwer: [ r ][ ] [ E] [ t] [ r ][ ][ t] [ E] [ r ][ ][ t] [ ][ ] [ r ][ t] [ ] m s m s. Crret answer: D The net external re (an therere the mpulse atng n the tw blk sstem s zer. r example, the upwar nrmal re that the surae exerts n eah blk s equal an ppste t the gravtatnal re n eah blk. The re that the sprng re exerts n the.00 kg blk s equal an ppste t the re that the sprng exerts n the.00 kg blk. Therere the mmentum the tw blk sstem must be nserve. ( m + ( m ( m + ( m (.00 kg. m/s + (.00 kg 0.00 m/s (.00 kg kg kg, nt 0.70 m/s kg kg, nt kg kg, kg kg,. m/s.00 kg.00 kg.00 kg.00 kg. Crret answer: E There are n external res that wrk n the sstem nsstng the tw blks an sprng. Therere the energ that sstem must be nstant. Thus the ntal knet energ the.00 kg blk must be equal t the knet energ the tw blks n the state plus the elast ptental energ n ths state. In equatn rm: m m + m + kx kg kg, nt kg, kg,. Crret answer: C At the tp ts trajetr, the prjetle has nl a hrzntal mpnent velt. Ths hrzntal mpnent velt s nstant sne there are n res atng n the prjetle n the hrzntal retn. Thus the hrzntal mpnent velt at the tp s the same as at launh: ( 6.0 m/s s( 6..6 m/s. hrz S /.6 / tp launh

2 0 Setnal hss Exam Slutn Set. Crret answer: D Usng nservatn energ, the sum gravtatnal ptental energ plus knet energ s nstant. GE + KE GE + KE 6. Crret answer: A ntal ntal 6.0 J J 7.0 J + KE GE h 8.0 J KE m.66 m/s GE ntal 6.0 J (.00 kg( 9.80 m/s 7.0 J J 0.88 m (.00 kg mg h 7. Crret answer: A A hrzntal B ur res at upn the lner, the tensn (T n the tensn, T gravt R strng pullng t the let at B, the rtnal re ( at D C atng alng the plane as shwn, the nrmal re (N N mg the plane at D atng alng a lne rm D t C, an the gravtatnal re (mg atng wnwar at C. Wth D hrzntal β respet t a lne perpenular t the page thrugh pnt C, N an mg nt prue trques sne ther lnes atn pass thrugh pnt C. s the nl res prung trques wth respet t C are the rtnal re an the tensn. Sne the lner s n stat equlbrum, the sum these tw trques must be zer. w + R sn( 90.0 ΣTrqueswrt, C RT sn 90.0 w 0 RT w R w RT w R w RT R 8. Crret answer: B Reslvng all res alng the nrmal (t the plane retn: Nrmal: N s( 0 N β β T C β mg gravt rtn: s( 90 0 Tensn: T sn(β mg s β Weght: hrzntal D N β The sum res n the nrmal retn must be zer. N mg s ( β T sn( β 0

3 0 Setnal hss Exam Slutn Set 9. Crret answer: D Applng Newtn s n Law t the allng mass an lettng wn be pstve: mg T ma T m g T ( a (.0 kg( 9.80 m/s.00 m/s T.N, where T s the tensn n the rpe..0 kg Applng the rtatnal rm Newtn s n Law t the wheel: τ Iα, (where τ trque, I mment nerta, anα angular aeleratn. RT Iα Ia / R I R T / a 0. Crret answer: A ( 0. m (.N /(.00 m/s 0.96kg m 0. m A B A ρ ρ Dg D D (.00 atm + ρntghnt + ρmantg( D + H (.00 atm + ρ g( H + H + D + ρ g( H ghnt + ρmantg( D + H ρntg( Hmtn + Hnt + D + ρmantg( H ghnt + ρmantg( D ρntg( Hmtn + Hnt + D ( ρmant ρnt ρntg( Hmtn + Hnt Hnt ρnt ( Hmtn + Hnt Hnt ρnt ( Hmtn ρnt ( Hmtn ( ρmant ρnt ( ρmant ρnt ( ρmant ρnt.87( 6. km ( 0.8 km (..87 nt nt B nt mtn nt mant Cntnent.87 g/m Mantle. g/m A Rt B D H Muntan 6. km. km Depth Cmpensatn. Crret answer: E Usng Newtn s n Law: ma rgnal rgnal N +. Crret answer: C atnal rgnal atnal atnal.00 kg (.00 m/s ma ( j N 0.0 N.00 kg ( j m/s ( j N a + a 000 m m 600 s 600 s 9.0 m.8m/s

4 0 Setnal hss Exam Slutn Set. Crret answer: B t vert hrz gt g vert t hrz 7.0 m g vert 7.0 m.0 m 9.80 m/s 8.87 m/s.0 m 7.0 m. Crret answer: B Let { } ente mass energ nt energ { H} + { H} + { He} + { 0n} + energ { H} + { H} { He} + { 0n} + energ release. Crret answer: E energ nt energ release ({ H} + { H} { He} { 0n} 8 ( m/s ( ( u m / s ( kg/u.76 0 J 9 (.76 0 J / (.60 0 J/e 7.Me u E average kt 6 (.8 0 J/K( + 7. K.77 0 J 0 6. Crret answer: C + ( 0 m ( 0 m ( 0 m + + ( s( θ let + sn( θ up let + up 6 ( 0 m up 6 ( 0 m ( πε e e.60 0 up ( 0 m ( 9 C an ε up + up + let let / C.0 0 /( N m..00 mm N, where.00 mm θ.00 mm

5 0 Setnal hss Exam Slutn Set 7. Crret answer: E. 0.0 m s m π A s x + ( π t λ π. π, λ m λ m π, s s π 8. v λ m/s. v T ρ T v 8. Crret answer: B mm h h 6. mm h h 9. Crret answer: D 8. x + s 8. ρ m/s. 000 mm t ( 70 mm 9. mm (.67 0 kg/m 6.mN The mtn s nstant aelerate mtn wth an aeleratn 9.8 m/s vertall wnwar. Usng upwar as the pstve retn an the at that the greatest heght s reahe when the vertal velt s zer: v v 0 0 ( 0.0 m/s v v 0 a m 7.9 m a 9.8 m/s 0. Crret answer: B The mtn s nstant aelerate mtn wth an aeleratn 9.8 m/s vertall wnwar. Usng upwar as the pstve retn, v v 0 + at 0.0 m/s 9.8 m/s (.0 s 0. m/s

6 0 Setnal hss Exam Slutn Set. Crret answer: D There are tw perpenular mpnents t the ar s aeleratn, the entrpetal aeleratn, a, an the tangental aeleratn, a t : a v a + at + at R. Crret answer: E re ( 9.00 m/s 70. m + ( 0.00 m/s 0.00 m/s Wrk s the area uner the re versus pstn graph between the lmts the mtn. The re at pstn x.00 m s (.00 N/m(.00 m6.00 N. The re at pstn x.00 m s (.00 N/m(.00 m.00 N. The wrk s the area the trapez wth base.00 m an the rst heght 6.00 N an sen heght.00 N. The wrk s stn W (.00m 8.0J (.00N N. Crret answer: C Applng mpulse equals hange n mmentum an usng a rnate sstem wth pstve x twar the nrth: Impulse mv mv. Crret answer: B Impulse m v v 80.0N s ( 0.0 m/s ( 0.0 m/s.60 kg As the velt the blk s nstant, the net re n the bjet s zer. Cnserng the hrzntal mpnents re: rtn 60 Ns Ns 0 6.N rtn Cnserng the vertal mpnents re: nrmal mg + 60Nsn nrmal mg 60Nsn 0.0 ( 0.0 kg( 9.8 m/s 60Nsn N µ µ rtn k nrmal k rtn nrmal 6.N 69. N 0.0. Crret answer: B Applng Newtn s Sen Law an usng vertall upwar as the pstve retn: net ma a net m 00N 0N sn kg ( 8.00 kg( 9.8 m/s. m/s

7 0 Setnal hss Exam Slutn Set 6. Crret answer: C I τ α ( 9.00N m (.00 kg m.80 ra/s ( θ θ ( π / 0 0 θ θ 0 + ω0t + αt an ω0 0 t. s α.80 ra/s 7. Crret answer: E N s/kg J 8. Crret answer: E Applng nservatn energ: ( 6.00 kg (.00 m/s (.00 m/s 0 ( 0.00 m mv mv mv + kx mv + kx k x x 9. Crret answer: A Applng the parallel axs therem: 88.N/m I I m + m I I m m ( 8.0 kg m ( 0.0 kg m.00 m.00 kg 0. Crret answer: C Applng nservatn angular mmentum: L rtr + L b I ω L rtr rtr ω I + L rtr rtr. Crret answer: B Reatane b + I + I b b ω I b rtr ω + I b ω I rtr ω rtr + I b b (.00 0 kg m (.00 0 ra/s + (.00 0 kg m ( 0 (.00 0 kg m + (.00 0 kg m ω 9. ra/ s. Crret answer: A R.00 Ω The equvalent resstane the 6.00 Ω an the.00 Ω restrs s R eq +.00 Ω 6.00 Ω.00 Ω Ths equvalent resstane s n seres wth the.00 Ω, resultng n a net resstane 6.00 R eq.00 Ω R eq.00 Ω R eq.00 Ω +.00 Ω. 00 Ω 6.00

8 0 Setnal hss Exam Slutn Set Usng Ohm s Law, the urrent lwng thrugh ths net equvalent resstane s 6.00 I.00 Ω.00 A Ths wll als be the urrent thrugh equvalent resstane R eq, resultng n a vltage arss R eq, I R.00 A.00Ω.00 eq eq Ths wll als be the vltage arss the rgnal.00 Ω resstr, resultng n a urrent thrugh the.00 Ω resstr I (.00 (.00 Ω.00 Ω. Crret answer: E. A (.00 sn(.0 sn(.0 n snθ n snθ n snθ n.9 snθ. Crret answer: C σ AT T σ AT σ AT T. Crret answer: C prtn ( ( (.00 W 6.0 W