WYSE Academic Challenge 2004 Sectional Physics Solution Set

Transcription

1 WYSE Acadec Challenge 004 Sectnal Physcs Slutn Set. Answer: e. The axu pssble statc rctn r ths stuatn wuld be: ax µ sn µ sg (0.600)(40.0N) 4.0N. Snce yur pushng rce s less than the axu pssble rctnal rce, the rctnal rce s equal t yur pushng rce: 4.0N. The blck wll nt ve.. Answer: d. Snce yur pushng rce nw exceeds the axu pssble statc rctn rce, the blck wll be vng, s we need t use the knetc cecent rctn t nd the aunt rctn. µ N µ g (0.400)(40.0N) 6.0N 3. Answer: a. knetc K K The su rces n the wan ust equal the prduct her ass and acceleratn: F a Fnral upward + Fweghtdwnward + Fcentrpetalnward v r nward Fnral upward + (53.0 kg)(9.80 /s ) dwnward + Fcentrpetalnward Fnral upward + (59 N) dwnward + Fcentrpetalnward (34 N) nward F upward + F nward (34N) nward (59 N) dwnward nral centrpetal Fnral upward + Fcentrpetalnward (34N) nward + (59 N) upward 4. Answer: d. [Trque] [r F] [r][ass][acceleratn] (L)(M)(L/T ) 5. Answer: e. ML /T (5.0 /s) (53.0 kg) 35.0 Inerta s a easure hw dcult t s t accelerate an bject r a gven rce. Fr a gven F rce, the greater the ass (r nerta), the saller the acceleratn wll be: a. 6. Answer: a. By dentn. nward 004 Sectnal Physcs Slutn Set

2 7. Answer: c. The zer t the let the decal place s csetc, whle the zer edately t the rght the decal place s just a place hlder, s nether s a sgncant gure. The sgncant gures are thus 34. Snce the reanng part the decal ( ) s re than halway t, the s runded t. It s usually easer t deterne the nuber sgncant gures by rst cnvertng the nuber t scentc ntatn. Thus, ( ) 0 (34) Answer: a. F 40.0 N east 4.00 kg a 0.0 /s east 9. Answer: e. () () 5.00 kg 0.0 kg 60.0 N 60.0 N 5.00 kg 0.0 kg () () 5.00 kg N N 0.0 kg 60.0 N 60.0 N N N 5.00 kg 0.0 kg In ether case, the agntude the acceleratn the syste wll be: 60.0 N a 4.00 /s. 5.0 kg Applyng Newtn s nd law t the 5 kg bject n case (), N Applyng Newtn s nd law t the 0 kg bject n case (), N (0.00 kg)(4.00 /s ) 40.0 N. Thus, N /N (5.00 kg)(4.00 /s ) 0.0 N. 004 Sectnal Physcs Slutn Set

3 0. Answer: b. () 60.0 () 60.0 () () Only crd () has a cpnent rce n the vertcal drectn. Fvertcal Tsn(60.0 ) 50.0N 0 T 57.7 N.. Answer: b. v 5.0 /s ω 78.rad/s r N. Answer: c. 43 N θ Trque r F rfsn(80 θ) 80.0 N (0.300 )(43 )sn( θ) θ Answer: b. ω ω + α θ ( θ ) ω ω α θ ( θ ) ( 3.0π) 0 4. rad/s 0.94 rad/s 4. Answer: b. (.0 kg)( 0.0 ) + (.0 kg)( 6.0 ) + (.0 kg)( 6.0 ) x c kg +.0 kg +.0 kg Y kg.0 kg X.0 kg Sectnal Physcs Slutn Set

4 5. Answer: d. Usng Krchh s Current Law, I I. n ut A -5 A Nte n and ut are dened by the drectn the arrws. n s tward the junctn. ut s away r the junctn. I 3 (A) + (-5A) + (I 3 ) 0. I 3 3 A. 6. Answer: c. F qvbsn(θb ) ( 6.6µ. )( 43/s)( 3.T) sn( N 0.0 ο 43 /s 3.0 T 7. Answer: c. () I 0 0. Ω The 60 and 30 h resstrs n dagra () are replaced by a 0 h equvalent n dagra (). 80 V I Ω 30. Ω The 0 and 0 h resstrs n dagra () are Replaced by a 30 h equvalent n dagra (3). () I 0 0. Ω Usng Oh s Law n dagra (3), 80V I0 6A. 30Ω 80 V 0. Ω I 0 In dagra (), the sae current, I 0, lws thrugh the 0 h equvalent resstance. Therere, the vltage acrss the 0 h equvalent s ( 0Ω )( 6A) 0V. Ths sae vltage derence exsts acrss the 30 and 60 h resstrs that were replaced by the 0 h equvalent. Therere the current n the 60 h resstr 0V s: I 60.0A. 60Ω (3) I 0 80 V 30. Ω 004 Sectnal Physcs Slutn Set

5 8. Answer: e. Usng Snell s Law, n sn( θ) n sn( θ).70sn(30 ).00sn(30 + θ) θ 8. vlet ray 30 ο ar 60 ο 30 ο 30 ο θ lnt glass 60.0 ο 9. Answer: a. Fr cnstant acceleratn, v v a( x x). Slvng r a: v ( x x) ( 0.0 /s) -( 0.0 /s) v a.5/s (0) 0. Answer: a. Fr cnstant acceleratn, ( x x) ( ) v + v 0 x x t t 8.00s v + v 0.0/s /s ( ) ( ). Answer: b. Knetc energy s prprtnal t the square the speed. I the speed trples, the knetc energy ncreases by a actr 9.. Answer: c. The hrzntal cpnent velcty reans cnstant. The te t travel 50.0 hrzntally at a cnstant hrzntal velcty 0.0 /s s gven by x x 50.0 t.50s v 0.0/s x The vertcal tn s ree all wth an ntal vertcal velcty cpnent that s zer because the ntal velcty s hrzntal: ( ) ( )( ) y y y y + v t+ a t s /s.5s Sectnal Physcs Slutn Set

6 3. Answer: b. The unversal law gravtatn s F G F r r d F F F 80 N 0 N r r r d 4. Answer: e. The relatnshp between wrk and the change knetc energy s ( 3 ) ( )( ) ( )( ) 3 W KE KE KE v v 70.0kg 5.0/s 70.0kg 5.0/s J 5. Answer: c. Ipulse s the area under the rce versus te graph. Usng that the area a trangle s ne-hal base tes heght r the te between 0.0 s and.0 s results n an pulse ( )( ) I.0s 5.0 N.5 N s Frce 5.0 N 4.0 N 3.0 N.0 N.0 N 0.0 N Usng the area a rectangle s the base tes the heght r the te between.0 s and.0 s results n an pulse 0.0 s.0 s Te.0 s I (.0s)( 5.0 N) 5.0 N s The ttal pulse s I I+ I.5 N s N s 7.5 N s 6. Answer: e. Ipulse s the area under the rce versus te graph. Usng that the area a trangle s nehal base tes heght r the te between 0.0 s and.0 s results n an pulse ( )( ) I.0s 5.0 N.5 N s The pulse n an bject s equal t ts change n entu: p I.5kg /s 7. Answer: a. The ptental energy stred n the sprng s 3.0 kg PEsprng kx ( )( ) 500 N/ J 004 Sectnal Physcs Slutn Set

7 8. Answer: c. The ttal rce n the ass s F ttal F + F sprng gravty F ttal kx g Settng the ttal rce t zer: F ttal kx g 0 x g k ( 3.0kg)( 9.80 /s ) ( 500 kg) c At the ntal pstn, the sprng s cpressed 0 c, s the ass wll be at equlbru a dstance 8.0 c abve the ntal pstn. 9. Answer: b. The perd the sple harnc tn a ass attached t a sprng sprng cnstant k s gven by ( 3.0 kg) ( 500 N/) T π π 0.8s k 30. Answer: d. The law cnservatn entu:.00 kg 5.00 kg v + v v + v v v v v Because ths cllsn s perectly elastc, knetc energy s cnserved: v + v v + v v v v Dvdng the let and rght sdes the secnd equatn by thse the rst equatn results n v + v v + v Usng ths equatn and the rst equatn, the nal velcty the secnd ass s v v + ( ) v (.00 kg)( 3.00 /s) + ( 5.00 kg.00 kg)(.00 /s) + ( 5.00 kg +.00 kg).9 /s 004 Sectnal Physcs Slutn Set

8 3. Answer: a. The lud s ncpressble s the speed the lud ust be greater at pnt B than at pnt A. Bernull's prncple apples under the gven cndtns s the pressure ust be greater at pnt A than at pnt B. 3. Answer: d. The te dependence actvty, A, s gven by () ( ) ( )( ) (.5 hr ) t/ t /.0 hr At A 0.0 C 7.07 C 0 A B 33. Answer: e. By the deal gas law, PV N T V T V T T PV N T V V T The lar specc heat a natc deal gas at cnstant pressure s 5R/. The heat necessary added s 5R 5 Q ncp T n ( T T) nrt I ne des nt recall that the lar specc heat a natc deal gas s 5R/. One ay d ths prble usng the rst law therdynacs. The change n nternal energy the gas s The wrk dne by the gas s 3 U nr T W P V nr T Usng these expressns n the rst law therdynacs: U Q W Q U + W nr T + nr T nr T nrt 004 Sectnal Physcs Slutn Set

9 34. Answer: c. Usng east as the pstve drectn, the velcty easured by bserve, u, s related t the velcty easured by bserver, u, by u u v 0.40c 0.50c 0.75c uv ( 0.40c)( 0.50c ) c c where v s the velcty bserver relatve t bserver. 35. Answer: e. The lnear agncatn,, s related t the bject and age dstances by sl s s s We are gven that the dstance between the bject and the age s 00 c. Ths ples ( ) s + s 00 c s + s 00 c 5.0s 00 c s 0.0 c The bject dstance, s, age dstance, s, and cal length,, the thn lens are related by Slvng r the cal length, + s s ( ) ( c) ( [ ])( ) ss s c s + s s c 004 Sectnal Physcs Slutn Set