ǰλãҳ >> >>

״Ԫ֮·һܸϰ¿α2


ٲ顤 𰸽 1 һ ˶ ȱֱ˶о ٲ(һ) ˶Ļ

1𰸣D 2 GPS λϵͳоλZҪ˶IJ죬Կ ʵ㣻϶\̬ʱ״ܺԣܿʵ㣻ƹ˶Ա ƹתתܺԣܰƹ򿴳ʵ㣻о

Խһɽ ʱʱ迼ǻ𳵵ijȣ𳵲ܿʵ㣮A ȷ 𰸣A 3·̲ͬλͬA 󣻡 ۡһУ족ָʱ䣬㡱ָʱ̣ B C ȷоĺʱʱĴСԺԣܱΪʵ㣬D ȷ 𰸣CD 4 A ˶ C λ A C ߶Σ䷽ A ָ C ѡ D ǴģλƴСΪ (3R)2R2 10Rѡ AB Ǵģ˶ 3 5R ·̵ R 2R ֻѡ C ȷ 4 2 𰸣C 5ڼΪοϵǾֹģԱΪοϵ˶ģ ôΪοϵһ˶ģȷѡΪ B. 𰸣B

6. ϵĺΪ x ᣬΪ y ᣮ㷨иļ λZȻֱλZ˶켣ͼʾ˵˶ һֱߣ ˻ͨͬһ㣬 ѡ A B ԭ㣬 յ(2,2) 2 2 λƴСߵijλƴСΪ 2 2 m2 2 mѡ C ȷ ˵ƽٶȴСΪ 1 m/sѡ D 𰸣C 7ٶٶȶʸʾٶٶȵķٶٶȷ ෴˶ 1 s ٶȼС vat1 m/sٹ 1 s ٶȱΪ 5 m/sѡ AC ȷ 𰸣AC 8ٶǷӣٶȵ޹أֻٶٶȵķǷͬ v أ A ٶȱ仯Խ족ָٶȵı仯 Խ󣬼ٶ a ԽB t ȷٶȷ򱣳ֲ䣬ٶȷܱ䣬Ҳܲ䣬ֱ˶ʱv0 Ժͷ˶ C ˶Уٶȵķٶȷͬ ٶڱСڼ٣ֱٶ a0ٶȾʹﵽˣ D 𰸣B

9˶ԱλƶͬҶʫõʱ̣˵ٶȴ 200 Ӿ˶·̳ʱƽʣԱѡ D. 𰸣D 10ס˵ڲοϵѡͬģA B ԣ ˶һҪѡοϵC οϵѡȡԣѡȡʱҪԷΪԭ D 𰸣B 100 11(1)ĩٶ vt100 km/h m/s27.78 m/s 3.6 vtv0 27.780 ƽٶ a m/s26.61 m/s2. t 4.2 vtv0 27.780 (2)ʱ t s9.26 s. a 3 2 𰸣(1)6.61 m/s (2)9.26 s 2 12 ·ϵƽٶΪ v·Ϊ s 3 1 s 3 1 ǰ s ʱt1 3 20 2 s 3 2 ں s ʱt2 v 3 ȫ̵ƽٶΪ s 40 km/h v80 km/h s 2s 60 3v 2s ɽ֪λļƻں ·ƽٶӦ 80 km/h. 3 𰸣 80 km/h 13ѡˮΪοϵСľǾֹģˮԴСٶ˶ ׷ϡСľ飬˶ʱȣΪ 1 Сʱ 2 СʱʱڣС ˮ˶׷ϡСľ飬Сˮ˶λΪ 5 400 mʱΪ 2 С ʱ x 5 400 m v 0.75 m/s. t 23 600 s 𰸣0.75m/s ٲ() ȱֱ˶Ĺ

1 1 ٶΪ a Сڵ 5 s ڵλ s5s5s4 a(52 2 9 9 42) a 18 a a4 m/s2. 2 s ĩٶ v2at28 m/sѡ A 2 2 ڵ 5 s ڵλƴС 18 m˶ʱ 1 sƽٶ 18 m/sѡ B 1 1 ڵ 2 s ڵλ s2s2s1 422 m 412 m6 mѡ C 5 2 2 1 s ڵλ s5 452 m50 mѡ D ȷ 2 𰸣D 2ٶʱͼ֪εĵױΪʱ 10 s ߾ٶȣεǰľ 15 mԸ

1 ļ㹫ʽ 10 sv15 mٶ v3 m/sѡ B ȷ 2 𰸣B 3 ʱ T1 s s10.2 m s30.8 m s3s12aT2 ɵã a0.3 m/s2 ѡ A B ȷʵ 1 ʱ̼Ϊ t0⣬t0.5 sʵ v0.2 m/sԵ 1 ʱʵٶ v1vat0.2 m/s0.3 m/s20.5 s0.05 m/s 2 ʱʵٶ v2vat0.2 m/s0.3 m/s20.5 s0.35 m/sѡ CD 𰸣B ɣȱֱ˶壬ʱڵλƲ㶨 sm sn(mn)aT2 ɿٶȣҲǴֽij÷

4. 򶫵ķΪ򣬸ɻ˶ٶʱͼͼʾ ֪ ǰ 5 s ٶӵ v 5 s ٶȼС 0 Ȼټٵ v ټС 0 ?? ˶ٶȴСʱʱ䷽һֱ򶫣 C ȷ 𰸣C 5ڼٺͼٹ vma1t1a2t2ɴ˿ɵ a1a212AD vm 󣻼ٺͼٹеƽٶȣ B ȷٺͼٹλ֮ 2 x1x2t1t221C ȷ 𰸣BC 6ս˶߶Ϊ h ʱٶΪ vʱɡʼȼ ˶ʱٶȸպΪ 5 m/sսڿ˶ʱ̣ v22ghv2 t v22a(Hh) h125 m v50 m/s Ϊʹսȫŵأ չɡʱĸ߶Ϊ H h224 m125 m99 mѡ AB 5 m/s ٶŵʱ൱ڴ hߴ vt2 25 2 £ vt 2gh䣬 h䣽 m1.25 mѡ D C ȷ 2g 210 𰸣C v2 202 1 0 7 s m40 m ֹͣ˶ xv0t at2 ã37.520t 2a 25 2 1 5t2 t3 s(һֵ)ѡ A ȷ 2 𰸣A 8⿼ȱֱ˶Ĺɣͨһ 60 m ƽٶΪ v1 x1 мʱ̵ļʱٶȣ 5 s ĩٶ v1 v16 m/sͨڶ 60 m t1 x2 ƽٶΪ v2Դмʱ̵ļʱٶȣ 13 s ĩٶ v2 v210 m/s. t2 2 v2v1at a0.5 m/s .ٽ 6 s ǰ 6 sȵʱ䣬 x aT2 x60aT2 x78 m. 𰸣A 1 1 2 9˶ѧɵ s1 a1t2 1s2 a2t2va1t1a2t2C ϸʽ 2 2 2?s1s2? s1 t1 s1 s2 s1s2 v ɵ A ȷ κɵ v BD ȷ s2 t2 t1 t2 t1t2 2 t1t2 Ӧѡ C. 𰸣C 10γʻٶΪ v˾ڷӦʱ˶λΪ x1 ɲȼٽ׶ελΪ x2 x1vt

2ax2v2 dx1x2 ٢ڢʽ v30 m/s γʻٶΪ 30 m/s. 𰸣30 m/s 11ڵһʱĩ(ʱ t0)ٶΪ vһʱʻ ·Ϊ s1ٶΪ aڵڶʱʻ·Ϊ s2.˶ѧʽ vat0 1 s1 at2 2 0 1 s2vt0 (2a)t2 0 2 ʱ t0 ٶΪ v䣬 ڵһ ʱʻ·̷ֱΪ s1䡢 s2. ͬ v䣽(2a)t0 1 s1䣽 (2a)t2 0 2 1 s2䣽vt0 at2 2 0 סʻ·̷ֱΪ ss ss1s2 s䣽s1䣫s2 ϸʽãסʻ·֮Ϊ s 5 . s 7 5 𰸣 7 12(1)ȡΪС ٶ v010 m/sٶ g10 m/s2Կ ţٵڶɿɵ mgFma ݵ a2 m/s2 辭ʱ tС N ˴Сĸ߶ 1 h1v0t gt2 2 1 չĸ߶ h2 at2 2 h1h2L 1 1 v0t gt2 at2L 2 2 ݽ t14 st21.5 s(ȥ) 1 (2)СijٶȴСΪ v0䣬չܾʱ t䵽棬 H at2 2 2H t䣽 8 s a 1 С tʱĸ߶Ϊ hv0t䣫 gt2 2 Сڵ 64 mh88 m ã32 m/sv0ܣ29 m/s СijٶȴС 29 m/s 32 m/s Χڣ 𰸣(1)4 s (2)29 m/sv032 m/s 2 13ˮ A B ȼֱ˶ v2 Bv12gh ɵãvB 17m/sɵ

1 1 λʱͨˮȣɵãv1td2 vBtd2 4 1 4 2 ãd20.98 cm B ȷ 𰸣B ٲ() ˶ͼ ׷

1t1 ʱ֮ǰ a b ǰ棬 t1 ʱ b ׷ aA t2 ʱ a x ˶b x Ḻ˶߷෴ B ȷ xt ͼбʱʾʣ ͼ֪ b ȼСӣһֱ a Ĵ󣬹 C ȷD 𰸣BC 2 A xt ͼ󣬹˵˶ 0 ֻص 0 㣬ص ʼλZ A ԣB vt ͼλƲΪ 0˵˶岻ص ʼλZB ȷģC D vt ͼ󣬵λƶ 0ΪͼʱΧɵ ʱϡ¶ȣ CD ҲDzԵģ 𰸣B 3ڱУvt ͼϸ㴦б(ôߵб)ʾٶȵĴС ͼΧͼεġʾλƣͼ t1 ʱ̵бʽСԼ ٶȱʵʵСѡ A 0t1 ʱڣߵġϴ󣬱ʾλƽϴ󣬸 x ƽٶȹʽ v ֪ ߼ƽٶȱʵʵĴ ѡ B ȷ t1 t t2 ʱڣ ߵġС ߼λƱʵʵС ѡ C t3 t4 ʱڣˮƽֱߣбΪ㣬ٶΪ㣬߷ӳ˶ѡ D 𰸣B 4vt ͼбֵʾٶȣΪߵߵбֵӦٶȵ v1v2 Сt1 t2 бֵСʼٶȲϱС A ƽٶ v 2 v1v2 ֱ˶Уͼֱߣ v ʾֱ˶ƽ 2 v1v2 ٶȣʾλƴС֪ƽٶ v < BC D ȷ 2 𰸣D 10 5 B ȼ˶ٶΪ 0 ʱʱ t1 s5 s˶λ 2 2 2 0vB 10 xB m25 mʱ A λ xAvAt145 m20 mȻ 2a 22 û׷ϣ˺ B ֹ׷ʱΪ t 4tx25 m t8 sѡ B. 𰸣B 6 vt ͼУͼʱΧͼεġʾλƣߵ Ϊٶȵʱ̣ ͬһ ͼӰֵġͱʾ ٴǰ룬 A ȷ 𰸣A 1 7 ӿʼɲٵ v0 ĹУ гȱֱ˶ λƴСΪ v0t0 2 vt 1 vt v0t0v0(tt0)ãv0 . 2 1 t t0 2 𰸣C

8ΪͬʱܣȻֱ˶˶ st ϵ ͼǾԭбֱߣ vt ϵͼƽںֱߣ Ȼ ѡ D ⣬һʱҵλƴ󣬱ʾٶȽϴst ϵͼбʽϴ ѡ A B ȷΪҵٶȽϴѡ C 𰸣B

9. vt ͼ⣮ ͼʾ ͬһ vt ͼзֱͼ(ע v ָʣ\ʾ·)⣬»ijٶȾΪ㣬 ʼʱB ļٶȽϴͼбʽϴָݻеغ㶨ɿ֪ǵĩҲ ͬȻΪʹ·ͬ\ͬȻ tA>tB.Ϊ A. 𰸣A 10֪ AB ٶʱͲ ҳijٶΪ v1ҳٶȴﵽ׳ٶ v2 ʱΪ tӦʱΪ t0ٶ Ϊȱ˶ʽv2v1atݿɵ t3 s. 1 У׳˶ľ x2v2(tt0)21 mҳ˶ľ x1v1t0 (v1v2)t 2 39 m˶λƲ xx1x218 m<20 mԣײ 𰸣ײ 11ʯµ׵ʱΪ t1Ϊ v1 1 2 x1v0t1 a1t1 v1v0a1t1 2 ֵ t120 sv116 m/s 19 s ʱڷλΪ 1 2 x2 a2t2 90.25 m 2 ٶΪ v2a2t29.5 m/s پʱ t3ʯ׷ 1 v1t3x2v2t3 a2t2 2 3 2 ֵ t326t33610 <0޽⣮ ʯ޷׷˾ܰȫ룮 𰸣˾ܰȫ 12ʱ tֱ˶λΪ 1 y ףvAt gt2. 2 ֱ˶λΪ 1 y ң gt2. 2 ֱľΪ yHy ңy ף ˮƽλΪ xvBt. ֮ľΪ L x2y2 ϸʽ L ?103t?2?4t?2. 6 t s ʱ̣֮̾ L8 m. 5 6 𰸣(1) s (2)8 m 5 13⿼ţ˶ɺ˶ѧ֪ʶ۹ƽıΣ СԵ۹˶ļٶȣ Сÿе˶ɷΪΣ

ελȣٶҲȣΪ˶ p ʼ˶һιǽϴ p ڿʼһιм˶ʱٶȽϴںһιм˶ʱٶȽС p ˶ƽٶȱ q ƽٶȴ p ȵܿڣ A ȷ Ѷеȣ 𰸣A ٲ() ʵ飺оȱֱ˶

1𰸣ABD 2ڡоȱֱ˶ʵУӦȽͨԴٷſֽA ȵʱͨλ xMxN(MN) at2֪(x6x1)(x2x1) 5 B xAC B ٶΪ A C мʱ̵ٶ vB C ԣڵļ֮ 2t 仹 4 ûлʱΪ 0.1 sD 𰸣C 3ڴ¼㡰05ĹУֽʱֽͬλС ֽλƣ v ף v ңѡ A B ԣڼʱȣҵٶȱ ø죬 a ףa ңѡ C D ԣ 𰸣BD 4(1)ɱݿԿСٶȵʱ ķΧȣСȼֱ˶ (2) x ıʽԿͬѧÿ 0.1 s ڵijٶȼֱ˶λ ֮ͣӦʵʵȼ˶λСΪʹλƵС 05 Ĺ v0v5 еƽٶȳʱλƸʣ x t ܣ 2 𰸣(1)ȼֱ (2)С 05 ĹеƽٶȳʱλƸ v0v5 ʣ x t 2 b b 5(1)ٶȣv1 v2 t1 t2 2 1 ? v2 b2 1 2v1 a ? . 2d 2d??t2?2 ?t1?2? b (2)ƬԽС Խӽ˲ʱٶȣƬ d Խv2 v1 Խ t ڼСʵ 1 b2 1 𰸣(1) ??t ?2?t ?2? (2)BC 2d? 2 1 ? 6⿼оȱֱ˶鿼ͼݵ (1)OD Ϊ 1.20 cm. 1 (2) s at2 ֪ͼбΪٶȵһ룻 2 0.028 ͼ֪б k m/s20.466 m/s2. 0.06 𰸣(1)1.20 (2)ٶȵһ 0.466(0.4640.468 ) 7⿼ʵݵĴڿѧѧ̬ȼӦͼ 1 s 1 ݵķ svtt at2 ɵ vt atɴʽ֪ٶȴСΪͼбʵ 2 2 t 2 1.991.02 a2 m/s22.0m/s2. 1.0

s 1 1 𰸣(1) atvt(д s at2vtt Ҳ) t 2 2 s (2) t ͼͼʾ t

(3)2.0( 1.82.2 Χ) 8(1)M 봥ͷӴڼ䣬ӦִԴڣʵԴֱԴͽ ԴɣA ʵҪͨСײ M Ͽ·ͷһС򣬹 M ڵ ·B ȷСĸ߶ӦΪ¶˵ M ֱȥСֱC û M ˲䣬С 1 ʼ䣬ӦͬʱʼʱD ȷ 1 1 T ?2 (2)H gt2 g? 2 2 ?10? 200H 2001.980 g 2 m/s29.4 m/s2 T ?6.5?2 1 T1 1 T2 t?2 H2 g? t?2 (3) H1 g? ? ? 2 ?n 2 ?n 2n2? H1 H2?2 ɵ g ˿ȥ t Ӱ죮 ?T1T2?2 (4)Сĸ߶Ȼظʵ飬ȡƽֵΪIJʹʵ С 𰸣(1)BD (2)9.4 (3) (4)Сĸ߶ȣڶظʵ飬ȡƽֵ ڶ ໥ ٲ()

1A ȭ˶ԱһȭȻֶ˶ԱʩӵȻ 壬 Ϊκ໥ã ûʩDz ģȭ˶ԱȻûлж֣ȴ˿ϣǿ A ȷģB в໥Ӵ֮ҲԴȷģΪ̫û Ӵ֮ȴãɼеҪֱӽӴC е˵ ҲȷģΪЧǰЧģǰıʶģ Ħѹ֧ЧD ͬһ бܵˮƽܵȵģ бѹˮƽ ѹDzͬģ D ԣ 𰸣BC 2бǵΪ ȣСļٶ a0 ʱֻ a ֧ 0<a<gtan ʱab ֧ agtan ʱֻ b ֻ֧ ѡ D ȷ 𰸣D k1L 3еȿɵ b ɵ쳤Ϊ P ƶľΪ k2

k1 L Lѡ B ȷ k2 𰸣B 4ǰ׳ԺṩǰĦãǰ˶ ׳ܵĦģ׳Եˣѡ B ȷͬɵѡ C ȷ 𰸣BC 5𰸣BC 6.

⿼龲Ħķжϣ Ū˶ƵķǽĹؼ ˶ƷжѶȽϴˣǿü跨жϣ O1 Ƥ Ħã O1 ˳ʱתʱO1 Ƥ佫򻬣ʱ C 㽫 A ˶ʵϣO1 Ƥûд򻬣ɼ C A ˶ƣ֮A C ˶ƣ ݾĦķ˶Ƶķ෴ ֪ C A ܵľĦ FCFA ķֱ¡ϣͬǿԵõ BD ܵľĦ FBFD ķֱϡ£ӶABCD ܾĦ ķͼʾӦѡ C  𰸣C 7һΪо󣬸պôھֹ״̬ʱ mgsinȣmgcosȣ tan ̣Ӧѡ B  𰸣B 8 a ܵϵ F ã򵯻 N ض״̬ F Ga ʱM شѹ״̬ A ѡȷ FGa ʱ M ڲ첻״̬ D ѡȷ FGa ʱ M 쳤״̬ a ϵ F ã N ڲ첻״̬M شѹ״̬ a ϵĵ C ѡܲѹ N ѹ״̬Dzܵģ B ѡ 𰸣AD 9ѹڸֽϵʱƽ̨ϱܵѹ±ܵ ̨ϱܵ ±ܵѹ ӦڳIJøֽӹ̣ Ӧ D ʾķZʽ 𰸣D 10ľ崦ˮƽ״̬ʱɱ죬ܵľĦã̧ ľҶˣʹĹУĦľ¼СΪ֮󣬷 󣮹ѡ A ȷ 𰸣A 11嶼ھֹ״̬ AB һ壬 BC һ Ħ忴һ壬 C һĦ AB ȿܴ ĦҲܲĦ BD ȷģ 𰸣BD 12 P Q ֱ˶ʱQ ܵĦΪ mgң ӼСΪ mg P ãP ˮƽĸãһ ҵ F ãǵĦãСΪ 2mgܵ Q ĦãСΪ mgӶãСΪ mg ʴµʽ F4mg A ȷģ 𰸣A 13ȡ B Ϊоͼʾƽ 2mgsinFN1FN2

Aƽ FN2䣽FN2mgcos AB 壬ƽ FN1䣽FN13mgcos 1 ɢ٢ڢ۵ ̣ tan 2 1 𰸣 tan 2 14.

ְٶ v1 ˶ԵȴٶԸְƶΪ v1䣬ͬ ʱ屻Ҳһٶ v2ڸְ˶ٶӦ v1 v2 ĺϳɣ ͼеٶ v. Ħ谭ߵ˶Ħ Ff v ķ෴Ҫʹ ˶ʩӵֻ Ff һ F1 ƽ⣬ FF1Ff sinFf. 𰸣C ٲ() ĺϳֽ

1ƽʱĺССȣ ĺΧΪ 3 NF11 NABC Χڣֻ D е 15 N Χ D Dzܵģ 𰸣D 2ϸΪ mgԺֱµ mg BC бϵ mg ĺ䷽غֱָǽСҲһ mg m Խֱµ mg BC бϵ mg ĺԽ ҲԽ ʹ C λZߣ BC εԵ mg.ѡ C ȷ 𰸣C 3Сͼƽıζ֪ a е b 2 k1x1 x1 2k2 2k2x2 ѡ C ȷ x2 k1 𰸣C 4 L ȡ F1F2 ķF1F2 L Ϸ֮ѡ A ȷ 𰸣A 4 5ÿϸֱļнΪ ȣɼ֪ʶ֪ cosȣ ƽ 5 5 3FcosȣG F Gѡ A  12 𰸣A 6 A ƽ״̬֪ FT ܺȣF һƽļнǣнԽ󣬺ԽСC ȷ 𰸣C

7. B ͼʾ BFF뼸 ABO ֪ F ܵ F䣬ܵ G F1F2C ȷ 𰸣C 8.

Сͼʾb ʱתиı仯ͼƽ ıλα߳ı仯 a 𽥼٣ b ȼС F1 F3F2. 𰸣AD 9ζж A ȷ 𰸣A 10 F O Чɰ F ֽΪ OAOB F1 F2ͼʾ

F ɶԳԿ֪ F1F2 . A ͼʾ ƽã FTF1 sin 2 2cos 2 F tan . 2 2 F 𰸣 tan 2 2 11(1)ǰƽ״̬Ϊ㣮Ϊо󣬽 ֧ĦˮƽֱΪ ϵֽⷨɵ F1cos45 (mgF1sin45 ) mg F1 100 2 N. cos45 sin45 (2)ˮƽļнΪ ȣֽⷨˮƽֱƽⷽ mg Fcosȣ(mgFsin)F . cosȣsin mg ȣarctan ʱF СֵֵΪ Fmin 60 5 N. 12 Ըͬѧñ F1 СǰСΪ 60 5 N. 𰸣(1)100 2 N (2)ܣ60 5 N 12 PQ ССܹ⻬˵֧ӵƽ һƽ֧ǴֱڸϵģӵҲǴֱڸӵģ

ɼιϵֱ֪ļнȣȣ F1F211. 𰸣B ٲ() ƽ

1 A ǡò뿪棬 A ѹĦ A ܵ F B A ĵãA ȷ 𰸣A 2ʱɶϵĵ F 20 N AƽF mgsin300F fɵС F15 N AƽFF mgsin30 f֪С F55 NҪʹƶСӦ 15 N A ܣ 𰸣A 3 5 3ƽ˶СĵС F ?mg?2? mg?2 mgѡ 4 4 D ȷ 𰸣D 4ͼʾˮƽ FFTcos60 ֱ FTFTsin60 Gʽ F(2 3)GFT2(2 3)GȷѡΪ A.

𰸣A 5 B ΪоͼףƽãF1(FGB)tanȣF2 FGB FGB .ţٵɵ F2F2䣽 F1F2 F A Ϊо cos cos ͼңF3 Ϊ FN Ff ĺƽãF3 F2 GA ĺF3 F ѡ C ȷ

𰸣C 6ÿʯΪ G 13 ʯΪ F31 12 ʯ Ϊ F21Ե 1 ʯΪоͼʾƽɵ F31cos 37 4 F21 F21F31cos 37 .ȷѡΪ C. 5

𰸣C

7. ͼ OA ֧ FA OC FC ĺС Gͼ֪OC СȼСѡ C ȷ 𰸣C

8С򼰵 B Ϊ FA 1 xA FCFAsin30 FAkxA 21 21 D ȷABC FC sin30 xC 𰸣D 9 A ƽ֪СΪ Fmgsin30 B ƽ 2F 2 mBgʽɵ mB mѡ A ȷ 2 𰸣A 10ֱΪһ壬ֱе֧ N Ͷߵ ƽ N(Mm)gţٵɵãˮƽĵС N䣽 mg (Mm)gѡ A ԣֱͼ(ƽɵ T2 ѡ D tan mg mg ֱĵС F ǽĵ T1T2 ѡ B sin tan

𰸣A 11 Mm Ϊоƽã ˮƽFcos30 FN0 ֱFNFsin30 Mgmg0 3 ɢ٢ڵạ̃ . 5 m Ϊоƽã Fcos30 FTcosȣ0 Fsin30 FTsinȣmg0 ɢۢܵãȣ30 . 3 𰸣30 5 12(1)ͬѧϸ˷ôСΪ F ϰѣϰѵֱˮ ƽֽ⣬ƽ FcosȣmgN Fsinȣf ʽ N f ֱΪذϰѵѹĦĦ fN

٢ڢʽ F mg sinȣcos (2)ϸ˷öʹϰѴӾֹʼ˶Ӧ FsinȡܦN ʱʽ㣮٢ʽ mg sinȣcosȡܦ F ֿʹʽ ǵȡֵΧע⵽ʽұǴ㣬ҵ F ޴ʱ Ϊ㣬 sinȣcosȡ0 ʹʽ ȡܦ0 0 ٽǣ ȡܦ0 ʱ ϸ˷öƲϰѣٽǵΪ tan0. mg 𰸣(1) (2) sinȣcos 13.

bO ӳͼcosd/Ld Ϊ˼룬L Ϊ ĴС ab λZ޹أˣ b ƹУƶ ĴС䣬FT 䣬 A ȷ 𰸣A ٲ() ʵ飺̽뵯쳤Ĺϵ ֤ƽıζ

1ɵ쳤ָ쳤ijȼȥɵԭ C ʵʱ Ҫͬһ D ȷѡΪ AB. 𰸣AB 2ͼебʱʾϵ֪ a ľϵ b ĴB ȷ l Ľؾʾԭ a ԭ b Ķ̣A 𰸣B 3Ƥ̶㵽 O ߷Ǻ߷ O 䶯 ôĴСҪ仯Ͳ֤ƽıζ򣬹 A ѡC ѡ Уһɲ̣ͨһɲƤ O ʱÿ һɲƶ̣ܳ𻵣׼ C ѡɽǶȵ ĺϳɣƽıζǶȶãس 90 ǣ D ѡ 𰸣ACD 4𰸣(1)L5 L6 (2)6.85 (6.846.86) 1405(14.0414.06) (3)L7L3 7.20 (7.187.22) ?d1d2d3d4? (4) 1.75 44 (5)28 3.00 5 (1)ɵľϵ k N/m53.8 N/m (2)ɳӶΪ 2.10 (3) 5.5810 2 ƽıζͼõ F ϣ3.3 N. 𰸣(1)ͼͼ 53( 2 ڶ)

(2)2.10(Чλȷ 0.02 ڶ) (3)3.3( 0.2 ڶ) 6(1)ķ BΪ B вƲ׶㣻 (2)ͼ󾭹㡢߼ɣǷͼ󲻹ԭ㣬˵Ϊ 0 ʱĦ һĴСԭûпľ f 3.5 N1.5 N (3)Ϊ fNǿƳ f̦NʶĦΪ ̣ 0.25. N 8 N0 N 𰸣(1) Bͼй̶ɲƣľ˶׿ ٶȣʹʾȶ׼ȷ (2)ϵͼͼʾѹ F ©ľ

(3)0.25 7 𰸣 (1)Ʒˮƽڹ⻬ˮƽϣ ûֱֽµΪˮƽ 6 (2)F210 x(N) ƽĵ С ţ˶ ٲ() ţ˶

1ѡ AB ˵ȷ٤ʵĿģʵĿ Ҫ˵˶Ҫά֣ѡ C ȷD 𰸣C 2 F ǽڶѹͬһϣСȡ෴ һֱϣһƽѡ A F ϣǽڵ ѹǽϣܳΪƽѡ B ֱ ֱ£ǽڶľĦֱϣ崦ƽ״̬ һƽѡ C ȷǽڵѹǽڶѹ ໥һ뷴ѡ D ȷ 𰸣CD 3г٣г˶ٶȱСˣСΪйԣҪ ԭֱ˶״̬ С˶ٶҪڴг˶ٶȣ С

ҪԴгǰ֮гʱг˶ٶȱˣ СΪйԣ Ҫԭֱ˶״̬ С˶ٶҪСڴг ˶ٶȣСҪԴгϷ֪ѡ BC ȷ 𰸣BC 4ˮƽԶˮƽľѹ A Ħ СȣCD ֪ţٵڶ a3a2a1A B ȷ 𰸣B 5ţٵڶɣ m1Fm1a1 m2Fm2a2 m1m2F(m1m2)a a1a2 a D ԣ a1a2 𰸣D 6˶Աˮƽ򻹾봬ֵٶȣӦѡ A. 𰸣A

7. λ A СΪоͼʾʱ쳤Ϊ x 2h mg Уkxmgtan30 x 3hãk AB ͬС tan30 3h 22h h ɵõkx cos30 mgsin30 maͬʱ x 3h tan30 ãag C ȷD 𰸣C 8бĽǶΪ ȣз mgsinȣmgcosȣma sinȣcosȣa/g F ţٵڶɵ(mgF)sinȣ(mgF)cosȣma1 mgsinȣmgcosȣFsinȣFcosȣma1 maFsinȣFcosȣma1 FsinȣFcosȣF(sin cos)Fa/g Fa/g 㣬 ʽ֪ a1 a.齫Դ a ļٶȼ» ֻ ѡ C ȷ 𰸣C 9СΪоֱٶΪ㣬Ϊ㣬 ֱ(С)Ϊϸֱнȣ ȣ F1䣽F1. F1sin ԼͼѡСΪоţٵڶɵ a ͼѡСΪо M F1sin ţٵڶɵ a䣽 . m F1F1䣬Mm a䣾a. ֪ѡ B ȷ 𰸣B 10Ƥ ֱܵµãţٵڶɣ mgkv ƤеļٶȴС a Ƥٶ v СٶȼС m ٶ v0 ʱٶ agat ͼһƽ t ֱߣC ȷAB D 𰸣C

11͵뿪ᶥʱΪ v0͵ԴʱҲˮƽٶ v0 Եƽ˶͵䵽ϵʱΪ tʱ͵ˮƽλΪ x1v0tˮƽ 1 1 λΪ x2v0t at2 x1x2͵ O ҷ O xx1x2 at2 2 2 2h a t x h. g g a 𰸣 h g 12ֱͼʾӵĸ˸ֱϵ Ħ FfţٵɣӦһֱµĦ Ff䣬ֱ ͼʾ Mg֧ FN Ħ Ff䣬ƽ ֪FNMgFf䣬FfFf䣬ţٵɿɵӶԵѹΪ FN䣽FN FN䣽MgFf.

𰸣MgFf 13(1)ˮƽСĵΪ㣬Сûжʱܵ F mg ͵ɵĵ T öƽ״̬ƽã ֱFcosȣmg ˮƽFsinȣT ãTmgtanȣ10 N. (2)Сֱƽ⣬ˮƽ֧ƽ Nmg ţٵڶɵãTNma a8 m/s2 𰸣(1)10 N (2)a8 m/s2

14. СΪ mˮƽнΪ Ϊ Tţٵڶ g ɣˮƽ maTcos٣ֱ mgTsinڣ tan a Ϊоţٵڶɵ Fcos£(Mm)aFsin£(Mm)g tan g £ A ȷ a 𰸣A ٲ(ʮ) ţ˶ɵӦ

1ʱڴʧ״̬ؼƵѹСˣ ûиı䣬 A ѡ ؼƵѹؼƶ֧һ 뷴СһȣB ѡֱΪУmgFma a g ֱ£ٶȷֱϣҲֱ£C ѡD ѡ 5

ȷ 𰸣D 2 m FsinȣmaFcosȣmg. M FfFsinȣMa FNMgFcos. Ħ Ff(Mm)aFN(Mm)gagtanȣжϣAB ȷ 𰸣AB 3ľˮƽֻĦٶ a f m mg g2 m/s2D СٶȲȣĦΪĦľ m f mg ٶ a g2 m/s2B û˶ٶҼٶС m M g2 m/s2A ԣ˶ľٶ ag2 m/s2Сٶȴľ ٶȣC ԣ 𰸣AC F 4ͼףţٵڶɣٶ a1 B A mAmB mBF B N1 mBa2 ͼңţٵڶɣļٶ a2 mAmB F?mAmB?gsin F gsinȣ B УN2mBgsinȣmBa2ãN2 mAmB mAmB mBF .֪ a1>a2N1N2. D ȷABC mAmB 𰸣D Fmg 5赯ɳȱ䳤 m1 ܵµĵٶ a >g m mgF m2 ܵϵĵٶ a <g߼ٶȲȣܱ m mgF ȶ ˲쳤 ѹ m1 ܵϵĵ ٶ a <g m Fmg m2 ܵµĵٶ a >g߼ٶȲȣܱ m ȶ˲ѹ m1 m2 ΪֵɳȾ䣬D ԣ 𰸣D 6() Mgkv2Ma mgFNma ʽɵãٶȵFN 󣮵 a0 ʱ FN ﵽ FNmaxmgC ȷ 𰸣C 7a1t1vmaxa2t2 a12a2 t1t212B ȷ»ٶ vmax 2s 2 v 8 m/sA t ٹ mgFf1ma1ٹ Ff2mgma2 a18 m/s2a24 m/s2 Ff1Ff217C ȷٹٹ̵ƽٶȣλ x1 v t1 x2 v t2x1x2t1t212D 𰸣BC 8С뵲֮䵯Ϊʱ룬ʱСļٶΪ aţٵڶ 2m?ga? 1 ɺ˶ѧɵ mgkxmax at2 t A ȷСٶʱ 2 ka mg Ϊ㣬x D ȷ k

𰸣AD

9. Fmg 1 ľˮƽܵĦãţٵڶ a F m m 1 gϼٶ a F 仯ͼaF бʴ ͼ Q бʴ󣬼 m1>m2 m ĽؾǣgͼӳõؾͼQ ؾֵ˵ 2>1 B ԣ 𰸣B 10⿼ţٵڶɺٶͼڿ鿼Ӧţٵڶ ɲ vt ͼʹģ͵СԵٶΪʱ t1 ʱ̣뿪 A Զt2 ʱ̣СԴʹֹʱԴʹԴӿʼ˿̣ Դʹľ.0t2 ʱڣСܵĦΪĦʼ ңС䣮t2 ʱԺԴʹֹʲĦãB ȷ 𰸣B 11(1)ļٶ amg2 m/s2 Fmg Сļٶ aM 1 m/s2 M (2) amt1v0aMt1 t12 s 1 (3)ڿʼ 2 s Сλ s1 amt2 4 m 2 1 2 s ĩٶ vamt14 m/s ڽ 1 s СԾֹһ˶ F Ҽٶ a 1.2 m/s2 Mm 1 1 s ڵλ s2vt at2 4.6 m 2 2 ͨλ ss1s28.6 m. 𰸣(1)2 m/s2 1 m/s2 (2)2 s (3)8.6 m 12(1)ϵͳʼ˶ʱٶΪ a1ţٵڶ Fmg2ma1 a11 m/s2 A 򾭹 P ʱٶΪ v1 v2 12a1(L/2) v12 m/s. (2) AB PQ ȼ˶ʱٶȴСΪ a2 2mg2ma2 a2g2 m/s2 A 򾭹 P ʱ F ȥ ϵͳУ 赱 B Q ʱеľΪ x1 ٶΪ v2 x1xPQL0.5 m 2 v2 2v12a2x1 v2 2 m/s Ϊ v2>0֪ B ͨ Q 㣬ȼֱ˶ʱٶȴСΪ a3. mg2ma3 a31 m/s2 ϵͳ x2 ֹ 0v2 22a3x2 ɵ x21 m A ֹʱ Q ľ xxPQx1x23 m 𰸣(1)2 m/s (2)3 m

13(1)ڸ˶Уʼʱ˶ٶȵӸ ճӣ¸ܵĺСԼٶȼСռٶΪ㣬 ˶ (2)˶ʱܸF 0gV ճ F mgţٵڶɵã mgF Fma g V g0V g6ЦvrV 2 ֵãv8.210 3 m/s. (3)ٶʱٶΪ V g0V g6Цvmr0 ֵãvm210 2 m/s. 𰸣(1)ٶȱСļ˶˶ (2)8.210 3 m/s (3)210 2 m/s

14 ܵĦбϣţٵڶɵ fmgsinȣmacos mgcosȣFNmasin 1 ֪ FNf a gˮƽң A B ȷͬɵ 7 Ħбʱa7gˮƽ󣬹 C D ȷ 𰸣BD ٲ(ʮһ) ʵ飺֤ţ˶

1ʵͬʱ仯овÿƱͨԱ С䣬ֻıСоԹɳٶȡ֮Ĺϵͨ ԱС䣬ֻıСоԵóٶȡ֮Ĺϵ D ȷ 𰸣D 2(1)С˶ֽ֧ܵľСĦ ϸã Ϊʹϸ߶ССܵĺ Ӧľһ˵ ʵĸ߶ȣʹֽ֧ĦĺΪ㣬С˶ ڽһʱӦɰͰСӦֽAC B ȷ (2)ӵײʵɰɰͰɰͰ ˶ٶȴСΪ a Tm(ga)ɰͰļٶȺСʱT Ƶ mg ʵӦʵ ʹɰͰļٶȺС ֻеСԶɰɰͰ ʱСɰͰļٶȲźСŽƵɰɰͰC ȷ (3) ʱ T 0.1 s x aT2 a ?sFGsEFsDE??sCDsBCsAB? ݽ a0.42 m/s2. ?3T?2 𰸣(1)B (2)C (3)0.42 3𰸣(1) ƽС˶ܵĦ (2) 0.99 1.0 (3)AD 4(1)ڵɰתƵͰУͱ֤ Mm 䣬ϵͳ䣬 F mg 1 оϵͳa ɼ aF ͼбʵ .ϵͳĺ Mm Mm Mm ͵ɰͰ mg M?m

(2)Сӻȥɰӣ Ǹıϵͳ Mm ϵͳĺԵ ɰͰ mg֤˺䣮ͼ󷨴ʱԼٶ a Ϊᣬ Ӧ Mm Ϊᣮ 1 𰸣(1) ں ۷Ϊʵоϵͳϵͳܵĺ Mm ͵ mg (2)Mm 2L 5𰸣 2 ı бһʱٶ޹ 10 agsin t 2 ˶ 뺽 ٲ(ʮ) ˶ ˶ĺϳֽ

1𰸣C 2ͼ֪ vy0𽥼СֱΪ㣬ṩѡ֪ D ԣ 𰸣D 3ٶʸ8 m/s ٶ 4 m/s ٶȽкϳɣٶȴڵ 4 m/s Сڵ 12 m/sĸѡУֻѡ A ĴΧڣϣ ѡ A ȷ 𰸣A 4 FyFxtan Fx Fy ĺ F v ͬһֱϣʱʵֱ FxFycot FxFy ĺ F x ļн £ʵ x һ ˶ȷѡΪ D. 𰸣D 5.

ٶ v1 ɷֽΪٶ vκ vͣͼʾ vΪ ٶȣ С B ٶ v2 vΪƶתٶȣ v2vΣv1cosȣ vͣv1sinȣ Ϊ˵ļнǣ A 붨ֵˮƽλZʱȣ90 vͣ v1 vΣ0ʱ v20. 𰸣D 6Ӿ˶ԱںӾʱͬʱ˶һDZˮΣ зĻ˶ӾķˮķѡˮΪοϵAB ˶Ա ֻһ˶֮߶̣ѡ A. 𰸣A 7 F1F2F3 ֱ˶ F3 F1F2 ȴ򣬵 F3 С䣬ı 90 ʱF1F2 ĺСΪ F3ı F 2F3 F3 нΪ 90 F ϣ 2F3ٶ a ֪ԭٶȷ F m m ķĹϵ BC ֿܣ 𰸣BC 8 x ٶͼ֪ x ļٶΪ 1.5 m/s2 Fx3 N y λͼ֪ y ֱ˶ٶΪ vy4 m/s Fy0ʵ

ijٶΪ 5 m/sA ѡȷܵĺΪ 3 NB ѡȷȻʵٶȷ 򲻴ֱC ѡ2 s ĩʵٶӦΪ v 6242m/s2 13 m/sD ѡ 𰸣AB 9.

˵ٶȷΪɡָ 3 m/s ٶ v1 2 ֱµٶ v24 m/sͼʾζ˵ĺٶΪv v1 v2 25 m/s v1 3 tan 37 .ɼɡӦбֱ 37 ǣ v2 4 𰸣бֱ 37 10ⷨһ(ٶȺϳɵ˼·)

ͼʾнٶ v12 m/s A ٶ v210 m/sٶȼн Ϊ .ڲиٶΪ v3⣬ΪʹиIJΪΣҪ v3 ֱ v1 A Բ˶(v3)ͲԵص˶(v1)Ƿ˶ A Եص ʵ˶ v2 Ϊ v1v3 ĺ˶ͼ֪ v1 1 1 cos arccos . v2 5 5 1004 24 0.98.v3v2sin9.8 m/s. 10 5 d 9 ɼиʱΪ t s0.92 s. v3 9.8 ⷨ(ٶȷֽ˼·) sin

ΪʹߴֱߣҪ A ٶ v2 v1 ϵķ v1 A v1 벣ͬˣ v2 ֱ v1 ķ v3 ΪԲиٶȣ v2 ķֽͼͼʾĽͬⷨһ 1 𰸣벣˶ļнΪ arccos 0.92 s 5 11(1)˶еʱĹϵΪ ? ?x3.0 t m ? ʱ t10 sɵã 2 ?y0.2 t m ? x3.0t3.010 m30 m y0.2 t20.2102 m20 m t10 s ʱλZΪ(30,20) ? ?x3.0 t m (2)˶еʱĹϵʽ? 2 ?y0.2 t m ?

xv0t ? ? Ƚ˶ѧʽ? 1 2 ? ?y2at ãv03.0 m/sa0.4 m/s2 t10 s ʱvyat0.410 m/s4.0 m/s 2 2 2 v v2 0vy 3.0 4.0 m/s5.0 m/s vy 4 tan vx 3 ٶȷ x нΪ 53 . x ᷽˶ y ᷽ȼ˶a0.4 m/s2 y 𰸣(1)(30,20) (2)5.0 m/s x нΪ 53 0.4 m/s2 y 12AB ٶȵķֽͼʾ֪ȣ30 ˶ĺϳ ֽ

vAsinȣvBcosȢ AB ɵϵͳеغ㣬 l 1 1 mg mv2 mv2 2 2 A 2 B 1 1 ɢ٢ڽ vA 3glvB gl. 2 2 1 1 𰸣 3gl gl 2 2 ٲ(ʮ) ƽ˶

1Ĺؼٶȷˮƽļн ֵ tan ʱ t vy g g Ĺϵʽƽ˶Ĺɿɵ tanȣ tΪ Ϊֵ tan t ȣ v0 v0 v0 𰸣B 2AB ƽ˶ˮƽϾкͷɻͬˮƽٶȣAB ͬһֱϣ A B · A ʱ B ǰ 1 s B t s A (t1) s. 1 1 1 1 ֱyA g(t1)2yB gt2 AB yyAyB g(t1)2 gt2 2 2 2 2 1 gt gy t ı仯仯󣬹 D ȷ 2 𰸣D 1 3ѡ Aƽ˶ֱϵķ˶Ϊ˶ h gt2 ֪ 2 ʱɸ߶Ⱦhbha a ķʱ b Ķ̣A ͬb c ķʱ ͬB ԣٸˮƽλ xv0t֪ ab ˮƽλ xaxbҷʱ tbta v0av0bC ͬɵ v0bv0cD ԣ 𰸣BD 4Сľˮƽֱ˶ֱϵȼֱ˶ ˶Ĺ켣Ϊ B.

𰸣B 5AB ڵһǰֱ˶ʱ l 1 g ʱ A ˮƽ׳ijٶ v0 h gt2 v0l ֻҪ A ˮƽٶȴ v0A t 2 2h B ͿڵһǰA ȷ AB ڵһǰײط l ĹУ A ҵˮƽٶȱֲ䣬Ե A ˮƽλΪ l ʱ t ʱ v0 l AB һ t ʱAB ߵ㣬Ҳֱ߶ h еκλZ v0 B C D ȷ 𰸣AD 6 A ֱٶΪ vAvAv0gtA tA1 s B ֱٶΪ vB vBv0tan60 gtB tB 3 sС򾭹 AB ʱΪ tBtA( 31) s A vAvB ȷB AB ĸ߶Ȳ hAB t10 m C ȷD 2 𰸣AC 7⿼ƽ˶е⣮ƽ˶˶ʱֱĸ߶ 2h t a ĸ߶ b 2 ta 2tbD ȷˮƽľɸ g 2h ȺͳٶȾ xv0 a ˮƽλ b 2 ֪ va 2vbB ȷ g 𰸣BD 8С˶ɷֽΪˮƽֱ˶ֱ˶ǡ xˮƽ ˵ֱ׷˶ǡôﵽߵ㣬˶ʱΪ t ߶ hv vˮƽ 1 2 t gt ãv 6.8 m/sѡ C ȷ 2 𰸣C 9ս˶켣ߣˮƽֱ˶ʱֱȼ x 2y ֱ˶ս B ʱˮƽٶȴС vx ֱٶȴС vy ٶ t t 2 2 x 4y 2 СΪ v vx v2 D ȷ y t 𰸣D 10(1)ͬʱأ˵ˮƽ˶˶ֻ˵ֱΪ ˶ (2)ֱ A ϶Ӧˮ棬ܵõȶϸˮ 𰸣(1)ͬʱأ˵ˮƽ˶˶ֱ˶˶ (2)ֱ A ϶Ҫˮ 11(1)xv0t 1 y gt22h 2 yx2/2h 4h2 ãt . 2 v0gh 1 (2) C h gt2,2hvtãv 2gh. 2 B B Ϊ(xh)߷̣hx2/2h x 2h. 1 xvth gt2 2

ãv gh. ٶӦ㣬 ghv 2gh. (3) BC ϣ 1 Ek mv2 mgh 2 0 ãv0 1.1gh. 1 1 OB ϣEk mv2 mghh gt2 2 0 2 4h2 t v2 0gh ãv0 0.6gh. 4h2 𰸣(1) 2 v0gh (2) ghv 2gh. (3) BC ϣv0 1.1gh OB ϣv0 0.6gh 12(1) A ϻĹУţٵڶɵã mgsinȣma ݵãa6 m/s2 辭 t ʱ B A 壬˶ѧʽ0v1at ݵãt1 s. (2)ƽ B ˮƽλƣ 1 x v1tcos37 2.4 m 2 x ƽٶȣv2 2.4 m/s. t (3) AB ĸ߶Ȳ 1 1 h v1tsin37 gt26.8 m. 2 2 𰸣(1)1 s (2)2.4 m/s (3)6.8 m 13AB ˶еĹ켣ͬ AB ֱʱAB ߳ A B ˮƽλƲ x ֱλƲ y. (x)2(y)2AB2 ⣮ AB ˮƽλƲΪ xv0t4.50.8 m3.6 m 1 1 AB ֱλƲΪ y4.8 m g(tA0.8)2 gt2 2 2 A tA0.2 s tBtAt1 s. 𰸣1 s 14С׳ƽ˶Բİ뾶Ϊ RС˶ʱ 1 1 2 ֱΪ t1t2 A Rsinv1t1Rcos gt2 1. B Rcosv2t2Rsin gt2. 2 2 v1 ãСٶ֮Ϊ tan tanѡ C ȷ v2 𰸣C ٲ(ʮ) Բ˶ĹɼӦ

v2 1 1ڼa a ˵ٶȵĴСֲ䣻a r r r a2r˵ٶȵĴСֲ䣮 𰸣AD

2ͻȻͣʱB B ԵСA Ұڶ Բ˶ͻȻֹͣʱA λZΪԲ˶͵㣬ɴ˿ʱ A v2 Ϊ FAmgm 3mg FBFA13C ȷ L 𰸣C 3С˶Сĺһظָ O 2L СΪ mL2 m ʸͼͼмιϵɵ sinȣ ѡ A ȷ g 𰸣A 4.

ͼʾҪʹĦΪ㣬ʹ·֧ĺṩ v2 v2 m mgtanȣ ȣarctan B ȷ R gR 𰸣B 5ļٶ a2rC Ĺ뾶ļٶA ȷܵľĦ Ffm2r FfAFfC2FfBB 󣻵תʱ CAB ͬʱC D ȷ 𰸣AD 2rP 2rQ 6P TP v 0.14 sQ TQ v 0.08 sΪʱ ڵѧ֪ʶ0.14 0.08 СΪ 0.56Ծ ʱСΪ 0.56 s ABC D ȷ 𰸣D O1O10 7ӵİ뾶 r 0.2 mٶ أ2n8 rad/ sԵٶľ 18 v ˶ٶȣvr1.6 m/sľ˶ʱλƷֱΪ t1 1 sx1 g v2 L x2 0.8 m˶λ x2O1O10 x12.4 m˶ʱ t2 v 1.5 s 2g 2 ľ屣ˮƽ״̬˶ʱ tt1t22.5 s. 𰸣D 8ǰסСԲ˶ɾĦĺ ҾĦﵽĦΪСͬһԲתʽٶ ͬʱеΪ FTԼףFfmFTm2R ףңFTFfmm2R ң ʱFT0ܵĦСҪ˶Ȼˮ УܵľĦСֱҪȣʼԲһԲ ˶ѡ D ȷ 𰸣D 9(1)ˮֱķ˶Ϊ˶ 1 2h h gt2 t1 . 2 g (2)֪ˮʱڣԲתĽǶӦΪ nУԽٶ Ϊ n g أ n (n1,2,3?) t1 2h (3)ڶˮԲϵˮƽλΪ 2h x2v 2t12v g

ˮԲϵˮƽλΪ 2h x3v 3t13v . g ڶˮϵλͬһֱԲʱ ľ 2h xx2x35v . g 2h g 2h 𰸣(1) (2)n (n1,2,3?) (3)5v g 2h g 10(1)ľĦľԲ˶ 2?2 fm? ?T? R (2)ľԲ˶벣ʱĦﵽ 2 vm fmmgm R ľ벣ֱ˶ 1 h gt2 2 ˮƽ˶ˮƽλ xvmt x s뾶 R Ĺϵͼʾ

ͼɵ s2R2x2

s2R2 ϸʽľ벣ĶĦ ̣ . 2hR 2?2 s2R2 𰸣(1)m? R (2) ?T? 2hR

11. (1)СͼʾСֱûмٶȣֻ ˮƽ O1 ΪԲԲ˶FN ˮƽ F1 ṩ F2FNcosȣmg F1FNsinȣmr2 0 rRsin 2g ϸʽ 0 . R (2) ٵ أ(1k)0 ʱʽ Fnmr2 ֪ ԽҪ Fn Խ󣬴 ʱ F1 ṩˣҪ˶Ħã鲻

ޱ˶Ħķعޱ£ͼʾ f зֽ⣬

ʱ FN ˮƽ F1 f ˮƽ f1 ĺṩ F2f2mg FnF1f1mr2 3k?2k? üιϵݴ f mg. 2

ڵ أ(1k)0 ʱʽ Fnmr2 ֪ ԽСҪ Fn ԽСʱ F1 ҪˣҪ˶Ħã鲻عޱ ˶Ħķعޱϣͼʾ f зֽ⣬ʱ FN ˮƽ F1 f ˮƽ f1 ĺṩ F2f2mg FnF1f1mr2 3?2k? üιϵݴ f mg. 2 3k?2k? 2g 𰸣 (1) (2) أ (1 k)0 ʱ f mg أ (1 k)0 ʱ f R 2 3k?2k? mg 2 12ľԲ̵Ħ͵㣬ʱĦָԲģ ĦԲ̵ķĺṩľԲ˶ mgcosȣmgsin mr2ٶΪ أ2 rad/sѡ B ȷ 𰸣B ٲ(ʮ) 뺽

GMM FR2 1Ϊ M䣬 Mg FMg M䣽 ѡ A R2 GM ȷ 𰸣A

2. ͼʾ⡰ֲȵǶԿΪ㡱֪ 洦ǶԵ󾮵ײ֮ĻβֵΪ㣬洦ٶΪ g Mm1 Ϊ Mɵ m1 ܵƵ m1gG 2 ٽ R ײڵȡ󾮵ײٶΪ g䣬Ϊ M䣬뾶 Mm2 4 rRd ͬɵÿ󾮵ײ m2 ܵ m2g䣽G 2 MVѡR3 r 3 g 4 d M䣽V䣽ѡ(Rd)3 1 A ԣ 3 g R 𰸣A

vr GMm mv 3 2 M ֪ r ̫2109r أ v ̫7v أ M 0.981011M r r G ̫ѡ B ȷ 𰸣B 4𰸣AD 5ɴ칬һͬһϣɴʱ˶Ӷԭ ޷ʵֶԽӣ÷ɴϵ͵ĹȻٶм٣ʵֶԽӣ 𰸣C 6⣬ڲ֪ԴڣԲ֪ͬڣA 1 ѡ󣻾ǵ 2 M䣽2M뾶ǵ뾶 R 2 1 GM RУg 2 g䣽8gǵ 8 B ѡȷ 2 R GM GM v ֪һٶǵ 2 C ѡȷ v ֪ R r 뾶ͬʱǵٶǵ 2 D ѡ 𰸣BC 2 7תڡ1 \T ǰ뾶޹أɴ˿֪ C ȷ 𰸣C 8϶ڽԲʱٶСڻ 7.9 km/sA ϶ v2 Mm ͼлԲԲ˶ ṩã G 2 m ã R R M 1 4 v G 7.9 km/s 1.8 km/sB ȷ½м½ R 81 1 ״̬C СڵܵǷʧ أD 𰸣B T ?R?3 3 9ݿյ ? ? 18 76.4 T أ1 ꣬ T 76 2 T ?R?2 ꣬´ηɽĴ 1986762062 ꣬Ϊ C. 𰸣C 10 b ķٶС 11.2 km/s(ڶٶ)A ͬǣ ĸ߶ԽߣҪķٶԽ󣬻еҲԽB c ٣ ԭĹ˶ b ԽӣD a b ٴõʱΪ t GM 2 atbt2У bأa ɵãt C ȷ (2R)3 GM 3 8R 𰸣C 11(1) O Ϊ MA Ϊ mɺţ Mm 42 ڶɵ G 2 mR0 2 R0 T0 42R3 0 M GT2 0 (2)֪AB ʱB A Ӱÿ t0 ʱ t0 t0 B Ϊ TBУ 1 T0 TB T0t0 TB t0T0 MmB 42 B ǵΪ mB˶Ĺ뾶Ϊ RB G 2 mBRB 2 RB TB

2

2

3 t0 2 ɢ٢ܢݵãRBR0 ? ? t0T0



3 42R3 T0t0 t0 2 0 𰸣(1) (2) R0 ? ? 2 GT0 t0T0 t0T0 12(1)ɴ½УԷɴṩУ 2?2 Mm G mR? ?T? R 42R3 M . GT2 (2)Сƽ˶ˮƽֱ˶Уsv0t 1 ֱ˶Уh gt2 2 2?2 Mm 棬СܵƵG 2 mR? ? T ? mg R 22Rs2 Сʼ׳ʱصĸ߶ȣh 2 2 T v0 42Rs (3)Сʱٶȵֱvͣgt 2 T v0 42R 42Rs 164mRs ˲ʱʣPmgvͣm 2 2 4 . T T v0 T v0 2 3 2 2 4 4 R 2 Rs 16 mRs 𰸣(1) (2) 2 2 (3) 4 2 GT T v0 T v0 13ͬǵ˶תͬٶͬ 13 ݹϵʽ vr a2r ֪ v1<v3 a1<a3 Ǻ͵ͬǶΧƵת m v2 Mm GM M ܵĵṩ G 2 m2r ma ɵ v aG 2 r r r r GM أ ɼ뾶ٶȡļٶȺͽٶȾС v2v3a2a3 r3 23Ƶ渽Բ˶(߶Ⱥ)ٶȾǵһٶȣ v2vļٶȵٶȣ a2g vv2v3v1ga2a3a12 31Ϊ Fma F2F3F1ɼѡ ABC D ȷ Ϊ D. 𰸣D еܼغ㶨 ٲ(ʮ)

1ݹĶ֪ a b ĵ b b a ĵ a ѡ D ȷ 𰸣D 2С̺½пȫп СΪ W 製W ϣW £Ffh(Ffh)2Ffh. 𰸣C 3𰸣D 4 P ܵľĦбϣԶ P ˶ P ĹΪ㣬 BCD 𰸣A 5ϳ֮ǰǣĦ֮ܵĦ f

СΪǣ F ֲ䣬佫ȼֱ˶ٶȴСΪ a(F f)/mԭĹʲ˶ PFv ֪ǣٶ СٶȴСҲ a(Ff)/m 𽥼Сɼ׳ٶȽϴ ׳ǰҳ󣮱Ϊ A. 𰸣A 6 m ҶˣСľλΪ L/2 m ֪ FFTmg M ֪FTmgĹΪ mgLѡ A.Ҫעеǹ⻬ģ 治⻬ M ĶĦҲΪ ̣ȷ𰸾ѡ B ˣ 𰸣A 7ͼԿǰ 2 s ķ˶ķͬ徭һ ļ˶ͼٶ𽥼Сļ˶ 2 s ĩ F ٶȷ 򲻱䣬 2 s ʵ뻹󣬹 A 󣻵 2 s ĩ F ٶȷ򲻱䣬Ҫ˶Ե 2 s ĩʵٶ󣬶󣬹 B ȷ 01 s ڣٶ F 󣬸˲ʱ PFv F ˲ʱһֱ12 s ڣٶ󣬵ʱٶ F ʱС죬 F ˲ʱ мСḶ́ C 04 s ڣĩٶȶΪ㣬ݶܶúΪ㣬 F Ϊ㣬 D ȷ 𰸣BD 8.

бˮƽĽΪ CBC Ϊ L1AC ˮƽΪ L2AC ˮƽ нΪ ȣͼʾѩˮƽĦ W1mgL1бĦ L2 W2mgcos mgL2ڻѩ߾ AB ιУĦ WW1W2 cos mg(L1L2)mgL.Իѩ߿˷ĦĹΪ mgL.ѡ C ȷ 𰸣C 90t1 ʱڣ龲ֹF ĹΪ㣬ѡ A t2 ʱ̺ A ļٶѡ B ȷt2 ʱ̺ A ǰ˶ѡ C t1t3 ʱ ڣһֱ˶t3 ʱ̺˶ t3 ʱ A Ķѡ D ȷ 𰸣BD 10ڸתĹʵڿ˷ĹʣPmgLcos60 1 mgLأC ȷ 2 𰸣C 11(1)ж M681044.8105 kg ǣʱٶ Pmfvm f0.1Mg0.16810410 N4.8105 N жijᶼ 7 7 Pm P1P2 210 110 vm m/s62.5 m/s. 5 f f 4.810 (2) t10 s ʱv1at10 m/s.ֻеһڳṩг P11 fMa v1 P119.6106 W<P12107 W. ˵ֻеһڳṩ԰Ҫʻ ʱһ ڳ Ժڳ Fmf2M2a

M258104 kg4.0105 kg. õһڳ Fm8105 N. 𰸣(1)62.5 m/s (2)8105 N 12(1)֪ÿʻ 100 km ĵ 1 kW h 3.6106 J ĵܣʻ 3 x 10010 Ϊ v5 m/sʻ 100 km ʱ tv s2104 s 5 6 W 3.610 綯 P W180 W. t 2104 شĵ EUIt36123 600 J. 36123 600 E x 100 km 100 km43.2 km. 3.6106 3.6106 (2) PFv P FfF v 36 N Ff 36 k 0.03. ?mM?g 1 200 (3)ʱܵ Ff䣽k(mM)g(mM)gsin5 120 N. P v䣽 1.5 m/s. Ff 𰸣(1)180 43.2 (2)0.03 (3)1.5 m/s 13.

ͼʾΪ FTĦΪ Ffľ m Բ˶ FTcosm2R FTsinFf R l2r2 l cos R ϸʽɵã m2?r2l2? m2r r2l2 FT Ff l l ֪ BC m3r?l2r2? FT ľٶȷ򲻴ֱ ֶľ A PFTRsin ã P l D ȷ 𰸣D ٲ(ʮ) ܶӦ

1A ѡٶȵķ仯С䣬䶯ܲ仯 A B ѡ ܺΪ㣬ֻҪٶȴС䣬䶯ܾͲ仯Բ˶У Ϊ㣬ٶȴСʼղ䣬ܲ䣬 B C ѡУ嶯ܱ仯 һ仯˶״̬ı䣬C ѡȷD ѡУٶȱ仯ɷ仯 ʱ䶯ܲ䣬Բ˶Уٶȱ仯ʼղ䣬 D

𰸣C 2E ϣW 裫mghE £mghW 裬 E ϣE £ бǴֲڵģ AB v ϣ v £t ϣt £ 𰸣D 3һС A Ϸɾֹͷţպͨ B ʱǡöԹûѹ ֻṩmgmv2/R v2gRȫöܶɵѡ D ȷ 𰸣D 4̧߹УĦʼո˶ֱ֧ ĴΪ㣬֧Ĺ mgLsin»֧˶ʼմֱ m v2 1 ɶܶɵãmgLsinWf Wf mv2mgLsinBD 2 2 ȷ 𰸣BD v2 v2 1 5ɲУɶ֪ܶmgl mv2 l ֪׳ 2 2g 2a 䶯ĦС(ͼ 1)ҳ䶯Ħ(ͼ 2)ɲʱļٶ a gҳɲܺãͬijٿʼɲҳͣB ȷ 𰸣B 6.

˽ͼʾȱֱ˶ĹУ(2v0)202aL 1 2 v2 1v02aLɽ v1 5v0 A B ȷݶܶУmgLsinFfL 2 2 2 m(2v0) ɽ Ffmgsin2mv0/LC ȷʵֵΪ Pm2mgv0sinD 𰸣BC 7 С˶̣ ֪ڿ˷Ħ Ļеܲϼ٣ mgh h 0.30 ݶܶɵ mghmgx0 BC ֮们е· x m3 m С mg 0.10 ͣ B 㣬ѡ D ȷ 𰸣D P s 8ɶܶɵãPtfs0f t t ڷǰ vm vm 2 vm mv2 f P s mvm m ʱ䣬ٵʱ t2 a t2 , Ttt2 ʱ a m m vm P vm P ѡ B. 𰸣B 9ݶܶС˶ x0 ʱĶΪʱ F Ĺ ڱ£ ֱùĹʽ㣬 øͼķ 1 1 x0?2 x0 F ĹĴСڰԲġСEkW S Բ ? Fmax . 2 2 ?2? 2 2 Ek Fmaxx0 x C ѡȷ 4 8 0 𰸣C 10廬ʱϵһٶȷΪˮƽҵٶ v

ٶ vٶΪ 2vҳ 45 ķôҵ˶켣϶ֱߣ A ȷܻĦ fmgٶͬһֱϣ ȣ45 ҵļٶҲ򣬾 t ߲Ҿֹţٵڶ d 2 1 ɣ mgma ag˶ L 2 d L at2L a t 2 2 2 2 2v d 1 ṿ B C 󣮻֮ǰٶΪ vΪ mv2 gd 2 1 2 ֹͣ󣬾ٶҲ vҲ mv ĻֻĦ˹ 2 û仯ҶԹĦΪ㣬 D ȷ 𰸣AD 11(1)һ׶ηɻٶΪ a2ƽΪ f20.2mg F ƣf2ma2 a24.0 m/s2. 1 (2)ɶܶF ǣ l1F lf1l1f2(ll1) mv2 2 F ǣ6.8105 N. 𰸣(1)4.0 m/s2 (2)6.8105 N 12(1)ԲߵӦţٵڶɵ 2 v1 mgm R A 㵽ߵӦöܶ 1 1 mg(2R)mgL1 mv2 mv2 2 1 2 0 A ٶ v03 m/s. (2)Сǡͣ C ȫ̽о 1 mg(L1L2)0 mv2 2 v䣽4 m/s. Ե 3 m/svA4 m/s ʱСͣ BC 䣮 1 СǡԽʱУh gt2svCt 2 1 2 1 A C Уmg(L1L2) mvC mv2 2 2 ãv壽5 m/sԵ vA5 m/sСԽ ϣ A ٶȷΧ 3 m/svA4 m/s vA5 m/s. 𰸣(1)vA3 m/s (2)Χǣ3 m/svA4 m/s vA5m/s 13(1)С C A ˶ƽ˶ С C ٶΪ vC C A xvCt 1 2R gt2 2 gx2 ʽ v2 C 4R 1 2 С A C W2mgR mvC 2 x2 2 Wmg(2R )(0.5x 0.5) J. 8R mv2 C (2) W Сʱպܹͨ C 㣬ʱ mg R

gx2 2 C A ƽ˶ vC Գ 4R ʽx2R 빫ʽúСֵΪ Wmin(0.50.540.252)J0.625 J WF (3)ɹĹʽ F x 0.5 ? W(0.5x20.5) Jʽ F? ? x 0.5x? N 0.5 ѧ֪ʶ֪ 0.5x x1 ʱ F С x Fmin1 N. 2 𰸣(1)W(0.5x 0.5)J (2)0.625 J (3)1 N 14ɶܶз̼ɵͣˮƽɳ BC ͬһ㣬׻ е·һһе·̣ ȫеˮƽλһȫеˮƽλ ƣѡ A ȷD 󣻼 B Ķһ BĶܣ B һ Bʣѡ BC 𰸣A ٲ(ʮ) еغ㶨ɼӦ

1 1 1 1ܻеΪ E mv2ɻеغã mv2mgh mv2 2 2 2 2 v 1 ֪ mgh2 mv2 h ѡ C. 2 3g 𰸣C 2С˶͵ʱȣ0T1abT1mgmv2 1/LС 1 ˶ߵʱȣ180 СT2abT2mgmv2 2L mv2 2/L mg 2 1 1 2 b mv ãg ѡ D ȷ 2 2 3m 𰸣D 1 1 3ٶĵӦ͵ʱݻеغ㶨ɣ mv2 mv2 2mgR 2 2 C v2 24gR 1 C ã v 6vC A ȷ C УmgNCm NC mg B 5 R 5 2R 5R T v ٶСʱɵ T ֮СٶڱT g 5R ҪСT< C ȷлеغ㣬һֱ˵ϵĵ㣬 g ǵĸ߶֮Ͷ 2RǵܵĺȣܵĻеغ㣬ǵĶ ֮Ҳȣ D ȷ 𰸣ACD 4ڻУֻ͵ɵԻ͵ɵϵͳ еغ㣬D ȷ c ˮƽΪοƽ棬򻬿 a ĻеΪ 6 J c ʱٶΪ 0ҲΪ 0ԵֵܵΪ 6 J c b ɵĵԻ ĹڵܵļСΪ 6 Jѡ BCD. 𰸣BCD 1 1 5С A δǰ AB ɵϵͳеغ㣬mgh mv2 (3m)v2 2 2

v

gh .A غB ڹٶ v ˶ B 뿪ߵٶȼΪ v 2

gh . 2 𰸣A 6С A бϡС B ƽʱ˷ֱ AB » A еܲغ㣬ɵϵͳеغ㣬A B ȷӿʼ» 1 ڹ⻬ˮƽ˶ûеغ㶨ɿɵãmAg(Lsin30 h)mBgh (mA 2 2 6 1 mB)v2 v m/sC » B еܵΪ E mBv2 3 2 2 mBgh JD ȷ 3 𰸣BD 7𰸣A 1 8(1)mg(H2R) mv2 2 D 2 mvD Fmg R 2mg?H2R? ãF mg R ȡ(0.50 m,0)(1.00 m,5.0 N)ʽã m0.1 kgR0.2 m. (2)軬龭ߵ D ֱ䵽ֱ AB Բĵȸߵ E (ͼʾ)

R OE sin30 xOEvDt 1 R gt2 2 õvD2 m/s. D ٽٶ vmin gR 2 m/s. vD>vminԴһ H ֵʹû龭ߵ D ֱ䵽ֱ AB Բĵȸߵĵϣ 1 mg(H2R) mv2 2 D õH0.6 m. 𰸣(1)0.1 kg 0.2 m (2) 0.6 m 9(1)ڶͷ AB AB ˶B ŵغA ͵໥ A ɻָԭУɶ A ܹΪ㣮 1 2 A ӿʼɻָԭ̣ɶܶ mgH mv1 2 v1 2gHϣ (2)赯ɵľϵΪ k һͷ A B ǰ ϲĵ A ƽ⣮ mg 赯ɵα(ѹ)Ϊ x1 x1 k һͷ AB B Ҫʱɲϵĵ B ƽ

mg 赯ɵα(쳤)Ϊ x2 x2 k ڶͷ AB B Ҫʱɲϵĵ B ƽ mg 赯ɵα(쳤)Ϊ x3 x3 k ɢڢۢܵ x1x2x3 ״̬ɵĵܶΪ Ep ڵһͷ AB B ŵǰ̣ AB ͵ɵϵͳɻеغ 1 2mgh 2mv2 2 B ŵغ B ҪصḶ́ A ͵ɵϵͳɻеغ 1 2 mv Epmg(x1x2)Ep 2 ڶͷź󣬶 A ͵ɵϵͳ A ɻָԭ B Ҫع̣ ɻеغ 1 2 1 mv mgx3Ep mv2 2 1 2 2 2Ep ɢ٢ޢߢ v2 gH m 2Ep 𰸣(1) 2gH (2) gH m 10(1)Բǡ½ h3 mɻеغ㶨ɵ mghMghA h2l2(lhA)2 Ӧϵ M3m. (2)Բ½ h3 m ʱٶ v5 m/sɻеغ㶨ɵ 1 1 2 mghMghA mv2 MvA 2 2 ͼʾAB ٶȹϵΪ h vAvcosȣv 2 2. h l M 35 ϵΪ . m 29

(3)B A ĴԽ࣬Բ½ h3 m ʱٶԽ󣬵 m?M ʱΪ B ̻еغ㣬 1 mgh mv2 . 2 m Բٶ vm 60 m/s7.8 m/s. Բ½ h3 m ʱٶȲܳ 7.8 m/s. 𰸣(1)M3m M 35 (2) m 29 (3)7.8 m/s

1 11ɶܶ mv2mgh A ȷͨԲͰߵ㣬߶ȵ 2 v2 2R D ԣ ڵߵǰԲб˶߶С ʱжܣ B 2g C ԣ 𰸣ACD ٲ(ʮ) ܹϵ غ㶨

1γĩλZͬ͵ɵĵĹͬģлĦ ʼСΪĦ·̣·йأĦͬ 𰸣ABD 2.

ľͼʾɶܶ WFmghWFfEk C ԣ ʽãWFWFfEkmgh WFWFfEkEpE A D ԣ ܱ仯ϵ֪ B ԣ BCD ԣ 𰸣BCD 3һµɵĵȫתΪܣ QFfLE ڶ пͣ B (ȫתΪ)ʱ xLҲͣλZĩ ̬ĵܲΪ㣬תΪܵҲСһЩСͨ·С L. 𰸣BC 4ܵļС 3 J3 J A 󣮵糡ڵܵļС糡 1 JܼС 1 J B 󣮳 ĸܹڻеܵ糡 1 Jе 0.5 JԿ 0.5 J C ȷڶܵڸ ܹΪ2.5 JԶܼС 2.5 J D ȷ 𰸣CD 5пĻеܼССĻеܵ˷ ĹEFf hΪһκϵԭ׳ʱеܲΪ㣬 A ȷ 𰸣A 6 AB ͵ɿһϵͳϵͳеغ㣬 B ֱ B ȹУA Ķ󣬵ɵ B ĻеһֱСѡ A ȷɶܶB ĶܵĹ֮ͣѡ B ȷ B еܵļڵɵĵܵ A ֮ͣѡ C A ͵ɵϵͳɹܹϵϸ A Ĺ A 뵯ɵϵ ͳеܵѡ D ȷ 𰸣ABD 7ܵתغ㶨ɿ֪ A B Ĺܼ mgh1ȫ ڿ˷Ħ WfABmgh1ͬWfBCmgh2С߶ȵĽ ͣ˶еͬλZԹѹС WfABWfBC mgh1mgh2 ãh1h2C ȷ 𰸣C

8 v2v1ҪĦ½еܶǼٵģ ѡ B ȷģ軬߶Ϊ hп˷ĦΪ W Ħɶ 1 2 mghW Ħ mv1 .̶ܺȵĸ߶Ϊ h䣬ʱٶΪ v 2 1 1 1 ĦΪ W Ħ䣬ɶܶ mgh䣫W Ħ䣽 mv2 mv2֪mgh䣽 2 1 2 2 1 h mv2 2mgh䣫W Ħ䣽 mv2 W Ħ䣼W Ħɵ h䣾 ȵλZ 2 1 2 A ϷC ȷ 𰸣BC 9ݶܶ鵽ҶʱеĶΪ Ek1Ek1F(Ll)Ff(L l)(FFf) (Ll)A ȷ鵽ҶʱСеĶܿɸݶܶʽEk2 Ek2FflB ȷɹĹʽ˷ĦĹΪ WfFf(Ll)C ȷ ӵĻе Ekm(FFf)(Ll)СӵĻе EkMFflСӵĻе Ϊ EkmEkMF (Ll)FfL.ֱɹܹϵýۣD 𰸣ABC 1 10鱻ɵõĶ Ek mv2Epж A б BC 2 Ep ϵ߶Ϊ hɶܶ Epmghmghcotȣ0 h mg(1cot) Ep ͬĸ߶ȲͬB 󣻿˷ mgh C ȷе 1cot Epcot ʧڿ˷ĦĹ Emghcotȣ D ȷ 1cot 𰸣CD 11Ҫͣбײ軬龭·Ϊ xԻ˶ȫӦ 1 ùܹϵȫΪ Q mv2 mgx0sinȣ 2 0 ȫ̲ڿ˷ĦĹ Qmgxcosȣ 2 1 v0 ʽɵ x ?2gcosȣx0tan?. ? ? 2 1? v0 𰸣 2gcosȣx0tan? ? ? v0 12(1)˶ķֽɵС鵽 C ʱٶȴС vC 4 m/s cos60 (2)С C D ĹУɻеغ㶨ɵã 1 1 mgR(1cos60 ) mv2 mv2 2 D 2 C ݽ vD2 5 m/s. 2 vD С D ʱţٵڶɵãFNmgm R ݽ FN60 N ţٵɵ FNFN60 Nֱ (3)Сջľʱǡľﵽͬٶ vСľϻеĹ УС볤ľļٶȴСֱΪ mg mg a1 g3 m/s2, a2 1 m/s2 m M ٶ㣺vD a1ta2tv ľϵͳغ㶨ɵ 1 1 mgL mv2 (mM)v2 2 D 2

ãL2.5 mľij 2.5 m. 𰸣(1)4 m/s (2)60 N (3)2.5 m 13(1)С E Cɻеغ㶨ɵ 1 mg(hR) mv2 2 C v2 C C 㣬ţٵڶɵãFNmgm R ٢ڽ FN12.4 N. (2) EDCBA ̣ɶܶ WGW 製0 WGmg[(hRcos37 )LABsin37 ] W 製mgcos37 LAB ۢܢݽ LAB2.4 m. (3)Ϊ mgsin37 >mgcos37 ( <tan37 ) ԣС岻ͣбϣС C ΪģB ΪһߵԲ ˶ E 㿪ʼֱȶϵͳĦ QE Emg(hRcos37 ) ޢ߽ Q4.8 J. 𰸣(1)12.4 N (2)2.4 m (3)4.8 J 14Ϊ SСֵΪ kУܷ ֵ 1/2ǡÿԾֹƯƣkS/2mg վƴ A 䣬mgkS/8ma1 a13g/4. ʱkSmgma2 a2g. ˶еٶ gѡ A B ʱٶΪ vB ĸ߶ hȱֱ˶ɣ2a2h2a2(Hh) h3H/7ѡ B ߴ A B ˷Ĺ W2kS/8 (Hh)kSH/14.B C ˷Ĺ W2kS h3kSH/7 ߴ A B ˷ĹǴ B C ̵ 1/6 ѡ C ȷ ɶܶߴ A B ܵ mg(Hh)W23kSH/14С B C ˷ ĹΪ W23kSH/7ѡ D 𰸣C

ٲ(ʮ) ʵ飺̽ܶ ֤еغ㶨

1ԭСȼټ٣˵ʼʱƤĵĦ СĦûȫƽĦ 𰸣CD 2֤еغش˶ʵ֣ 0.02 s ڵλ Ϊ xgT29.7910.022 m3.9 mm. 𰸣C 3(1)ɻб˶֪Ӱ컬鶯ܱ仯ǺĹ Ħ(2)ͼ֪бֱ˶Уmgsinȣmgcos( h x2 x2 Ϊб)ɵ ̣tanȣ 2 2.(3)˶ѧʽ A ˲ʱٶ vA f 2T 2 L h x3x1 x3x1 B ˲ʱٶ vB f. 2T 2

𰸣(1)Ħ (2)

h L h2
2

x2 x3x1 (3) f f 2 2 4𰸣(1)ƽ ̶ȳ (2)m?M ƽĦ 1 1 2 2 (3)mgL M(v2 (4)mgL (mM)(v2 v2 2v1) 1) 2 2

5. 1 (1)ڹĩ˵ٶΪ vɻеغ㶨ɵ mv2mghƽ˶ 2 1 2 ɵ H gt svt s24Hh. 2 210 1 m2 2 (2) s h ϵͼֱߵб k 4H H0.5 m. 110 1 m 𰸣(1)4Hh (2)0.5 m (3)ͼ (4)С (5)СĦ 1 6AB ˶УϵͳĻеغ㣬 m1ghm2gh (m1m2)(v2 2 2 2 v1)Գ˼¼ B ͨʱٶ v1v2 ⣬ҪУm1 m2֮ľ h. 𰸣(1)AB m1 m2֮ľ h 1 2 (2)(m1m2)gh (m1m2)(v2 2v1) 2 ѡ 31 ٲ(ʮһ) ض 糡

1ŤװZ÷Ŵ˼ЧҸ׹۲˿Ťת 1 q1q2 ȣҿƱо F 2о Fq1q2Ӷó F 2 ȷѡΪ A r r C. 𰸣AC 2Ҫ鳡ǿʸԣͬһֱɲǿĵ ļӻɴֵҵȣ E1E2 ĵ һϳǿΪ㣬һϳǿΪ 2E1Ӧѡ C. 𰸣C 3𰸣AC 4⿼ǵ糡ǿȵĸ˶ڿѧ֪ʶ ⣮ʵǸɣ糡Ӧ븺ܵĵ糡෴Ϊ ٶǵݼģķӦٶȷнǴ 90 ѡ D ȷ 𰸣D qQ 3 6mgL2 53k 2 cosȣmgsinȣ q . L 3 6kQ 𰸣C

6СС֮Ŀɿضɵ F

kq2 ѡ l2

B ȷ 𰸣B 7ɶԳԺ͵糡ĵӿ֪ED0 B ȷɴ O C 糡ָ O 㣬糡 C ȷ֮ɴ O C 糡ܼС 𰸣BC 8AB дϵ糡ߵķֲǴ C д࣬糡ǿȴС 󣬺С C Ϊ㣬ԶΪ㣬е C Ǹɣָ C 㣬ѡ Aе C ɣ C д⣬ѡ D. 𰸣AD 9Ӧ巨 AB OA Ϊ 2mg OA ֱѡ C ȷAB Ȼٲø뷨 B Ϊо AB ƫڵ糡ĺȲӵ糡ʱҪѡ D ȷ 𰸣CD

10. t0 ʱ֮ǰֱ˶ܺһΪ㣬ܵĻ ĦֻҲΪ㣬ֱֻ˶AB t0 ʱE0qcos (E0qsinȣmg)0 t0 ʱ֮EE0ktţٵڶ Eqcosȣ(Eqsin mg mg)ma ktq ( )ma֪糡ǿ󣬻Ħ󣬺󣬼ٶ E0q ˶ֹC D ԣ 𰸣D 11ȷ B ijʼٶǡõ㣬óʼʱ A B Ŀس Fm2gsin m1gsinF Ϊ LʱA ļٶ a1 m1 ʼʱ B ƽ⣬໥ų˶һξ󣬿һ СС m2gsin m2gsinF Լٶ a2 б£a2 m2 a1a232 F䣽0.25m2gsin ɿʽ LL21. 𰸣ȷ21 12(1)B ˶ֻ A Ŀã˶ O ʱٶȸ 1 1 A ͬΪ v0.ĹΪ B W mv2 mv2. 2 0 2 1 (2)Ϊ A ˶t0 ʱ˶λ xv0t0 q1q2 kq1q2 ʱĿ Fk 2 2 2 x v0t0 Ϊ A ʼ˶Էǿ糡 B Ŀƽ ⣮ B 򵽴 O ʱСľСˣ糡 A Ҳ󣬵糡ǿҲ F kq2 E 2 2. q1 v0t0

(3)ͬѧĽⷨǴģ Ϊ B A 򿿽Ḷ́ȻǵСȣ˶λƲȣ ໥Ĺ W1W2 ĴСȣ W2W1 Ǵģ 1 1 kq2 𰸣(1) mv2 mv2 (2) 2 2 (3) 2 0 2 1 v0t0 13ֲɵ AB ĵ糡ЧΪֲɵ k 2q ĵ糡ʹɵҰĵ糡ĺϵ糡 E E䣬ɵҰ ?2R?2 k 2q M ĵ糡ɵ AB N ĵ糡Сȣ E䣽 E ?2R?2 kq E A ȷ 2R2 𰸣A ٲ(ʮ) 糡ܵ

1֪ Q 磬 AB0|UA||UB|ƶ̽ ɿ˷糡ȣ q1|UA|q2|UB| q1q2ѡ A C ȷΪ E Q k 2A B Q EAEBѡ B 󣮸ݵ糡ܱ仯Ĺ r ϵq1 A ĵܵ q2 B ĵܣѡ D 𰸣C 2ݵֵɵ糡ص㣬AB 糡ǿͬAB Ʋ ȣѡ A ȷB 󣻽һɴ A Ƶ B 㣬糡ѡ C A ĵС B ĵܣѡ D 𰸣A 3ݵ糡ߴֱãһ糡 PQ غϣP Ϊ ɣʸõ糡߱ش P ֱָ Q糡ָ򸺵ɣ PQ Ϊ ֵɣA ѡ󣻵糡ǿʸab 糡ǿȷͬB ѡ ԽɣԽߣ c Ƹ d ƣC ѡ󣻸ݵߵķֲ PQ ĵԣc ڵĵߵƸ a ڵߵĵƣɴ a c糡 ܼ٣D ѡȷ 𰸣D 4糡ܼ٣糡ӣ֪糡 Q Q ܼ٣ݳ()е( ֮)֪ D ѡȷ 𰸣D 5 vt ͼ֪ q ٶļ˶ܵ糡󣬵糡 ǿȱEBEAA ԣ糡ķ(a)ͼ󣬹ʵ糡ߵķΪ AB ABB ȷ EpqUԸ qEpAEpBC ݵ糡ߵķ͵糡ǿ ص֪˵糡һǸγɵĵ糡D ԣ 𰸣ABD 6 AB0 ֪ AB ΪһߣUCAգ糡ֱ AB ת B 㵽 D 㣬ͼʾ

UCA 2 3 α߳Ϊ aǿ糡ijǿΪ E asin60 3a

ת UADEasin30

3 3 UADADɵãD գ C ȷ 3 3

𰸣C 7ڵ糡Уɲô˶ܵ糡ѡ A DA ǵ 棬ѡ B ȷص糡߷ƽͣڵƸߴܴѡ C ȷ ܴ糡ǿȴ󣬸ܵĵ糡Ҳѡ D 𰸣BC 8A λZĵ糡߷ֲ B ϡ裬˵ A ĵ糡ǿС B ĵ ǿȣѡ A ˵ȷΪŵ糡߷򣬵𽥽ͣе糡ߴ A ڵָ B ڵ棬 A ĵƸ B ĵƣѡ B ˵ȷ ɴӵƽϸߵ A Ƶƽϵ͵ B 㣬øɵĵ󣬵糡ѡ C ˵A C ĵȣԽɴ A Ƶ C 㣬糡Ϊ㣬 ѡ D ˵ȷΪ C. 𰸣C 9 0 x1 ΣԽԽ˵糡ǿȼССܵ糡 СA 󣻴 x1 x2 ԽԽͣСɣСĵԽԽСB 󣻴 0 x1ٶСʱ x1 ٶǡõ㣬ݶܶ0q0 1 2q mv2 ֪ٶ v0 ֻҪԽ x1 λZһܵ x4 C 󣻵 2 0 m 1 1 x3 ڴ 0 x4 ˶Уݶܶ0q mv2 mv2 ٶ 2 2 0 0q 60q v02 v D ȷ m m 𰸣D 10糡ԽΪ Wݶܶ W24 J8 J12 Jɵ W 4 J˷糡 4 J 4 Jѡ BC 󣻵糡 ϶磬ѡ A 󣻻еܵļڿ˷ĦĹͿ˷糡 ֮ͣԽĻеܼ 12 Jѡ D ȷ 𰸣D 11ڵ糡Ҽ٣˶λΪ x1ɶܶã 1 (qEmg)x10 mv2 2 0 2 mv0 x1 2?qEmg? ݵ x10.4 m ֪˶ 0.4 m ʱٶȼΪ㣬ܵĵ糡 FqE0.03 NFf mg0.02 N齫 x Ḻ٣ O ֮Ħ¼٣ ֹͣ O ijõ O Ϊ x2ȫɶܶãmg(2x1x2) 1 2 0 mv0 . 2 ֮ x20.2 m. 𰸣 O O 0.2 m 12.

糡ǿΪ EСΪ qΪСֱ˶ܵĵ糡 qE mg ĺشֱͼʾ mgqEtan

g ɴ˿֪Сȼ˶ļٶȴСΪ a sin O 㵽ߵλΪ x ˶ѧʽ v2 02ax ˶ˮƽλΪ x䣽xcos O 㵽ߵĹУ糡ӣСߵ O ĵ ֮ΪEpqEx 1 ʽãEp mv2 cos2. 2 0 1 𰸣 mv2 cos2 2 0 13(1)嵽 C ʱٶΪ vɶܶãqE(sABR)mgsAB 1 mgR mv2 2 v10 m/s. 1 (2)ֱ CD ߶Ϊ hɶܶãmghqEh0 2 mv2 5 h m. 3 ߵ㣬ܵĦ FfmaxqE4 N Gmg2 N Ϊ G<Ffmax 5 Դվֹ C ֱΪ m 3 5 𰸣(1)10 m/s (2) C ֱΪ m 3 14ٶȴﵽһֵʱСڵ糡˶ һĿ꼫Ͻij˵ܻûмٵٶȾѾ򵽼ϣ A 󣻶ַѹȣľ벻ȣԻҳ糡ǿ СȣB ȷַ糡ԵֵΪ qUC ȷ ˶ʱqEkvʽ qk ͬ E ͬ v ȣ D 𰸣BC ٲ(ʮ) ڵ糡е˶

Q S 1ݵغ֪A C C ֪֮ľ d ʱ U d ¼ĵƲB Ϊֵɣãʵ ֮ľʱ糡ɵĵC ԣɣ Űʱ Ӧ ֮ĵѹʹʱ ŵ ˸о΢ĵD Ҳȷ 𰸣CD 2΢δ磬糡£΢ܵĵ糡ϣ΢ƫ תA ƫתе糡ݵ糡ܱ仯ϵܼС B ΢ڴֱڵ糡ֱ˶λ xvtص糡ٶΪ 1qU 2 1qU?x?2 ȼֱ˶λ y t Ϊ߷̣C ȷʽпԿ 2dm 2dm?v? ˶켣 q йأD 𰸣C 3⿼ڵ糡˶ڵ糡ƫתˮƽ s 1 ֱ˶tvǵ˶ʱȣA ֱh at2hQ2hPaQ2aP 2

EqQ EqP U 2 qPqQ12B C ȷ EkqUEkPqP EkQ m m 2 qQUEkPæEkQ14D 𰸣C 4뿪ƫת糡ʱٶȵķӳһƫת糡ˮƽλƵ 㣬Ե뿪ƫת糡ʱƫתǶԽ(ƫתԽ)ľԽԶ 1 2 Ӿ U1 ٺٶΪ v0 eU1 mv0 2 eU2 L AB ƽ˶뿪ƫת糡ʱٶΪ vyat md v0 vy U2L Ϣ٢ʽٶȵƫת tanȣ . v0 2dU1 Ȼʹ Ӧ U2L߼С U1d.ȷѡ B. 𰸣B 5⿼糡糡Ļ鿼Ծԭ⼰ 糡֪ʶգԴ磬ŵ缫磬ڵ糡 Ǩƣ˵ɣA 󣻵糡ɼָŵ缫B ȷ 糾磬ܵ糡糡෴C ͬһλZ糡ǿһ FqE ֪Խijܵ糡ԽD ȷ 𰸣BD U 6΢ P ֹʱ Eqmg qmg. AB ֮ d ʱĵ C С QCU ãQ ҲСڵ·һ ܣе򵼵ԣܷŵ磬ʵ AB ϵĵ䣬ǿ䣬 糡Ե΢ʴ΢Ա־ֹ״̬C ѡȷ 𰸣C 7 y ֵ 1 2qU1 qU1 mv2 v0 . 2 0 m 2 2 1 U2qL U2L y at2 . 2 2dmv2 4dU1 0 ɴ˿ȷ ACD ȷ 𰸣ACD 8ָſǶ AB ĵѹȣֿ S պϣ ǽ AB 忿Щǽ AB СЩAB ĵѹ ڵԴ綯ƣָſǶȽ䣬ѡ A B ȷϿ S Q AB 忿Щ Q ֲ䣬 C U C СָſǶȽСѡ C ͬϿ S 󣬽 AB СЩ Q 䣬C С UQ/C ָſǶȽѡ D 𰸣B 9 AC ֱļнΪ ȣԴС A C糡С 磬ɶܶmg AC cosȣqE BC cosȣ0õ糡Ϊ qE3mgѡ A ȷB Сˮƽֱ˶ A B ˶ʱǴ B C ˶ʱ 2 ѡ C Сֱȼٺ٣С A B B C ֱٶȱ ĴСȣˮƽٶȲ䣬С A B B C ٶȱ仯ĴСȣѡ D ȷ 𰸣AD 10⿼ʾܵԭڿ鿼ʾԭգ 02t1 ʱ ڣɨѹɨһΣźŵѹһڣ UY ΪֵʱӴӫ λƣ UY ΪֵʱӴӫиλƣһ

ӫϵͼΪ B. 𰸣B 11(1)΢ A ˶ B ĹУɶܶ |q|E1d1|q|E2d20 E1 d2 d10.50 cm. E2 (2)΢ MN ļٶȴСֱΪ a1a2ţٵڶ|q|E1ma1 |q|E2ma2 ΢ MN ˶ʱֱΪ t1t2˶ѧʽ 1 2 d1 a1t1 2 1 2 d2 a2t2 2 tt1t2 ϸʽ t1.510 8 s. 𰸣(1)0.50 cm (2)1.510 8 s 12(1)б滬µĹУɴ磬糡ֱ£ܵ Ħ f(mgqE)cos37 赽б׶ʱٶΪ vݶܶ h ? 1 2 (mgqE)hf? sin37 ? ?2mv v2.4 m/s. (2)һ뵲ײб淵ĸ߶Ϊ Hݶܶ H ? 1 2 (mgqE)Hf? ?sin37 ?2mv H0.10 m. (3)վֹб׶ˣܺ͵ܵļڿ˷ĦĹ ڲ QmghEqh0.96 J. 𰸣(1)2.4 m/s (2)0.10 m (3)0.96 J L2 L 13(1)⣬B yBL˫߷ y õ xB 4x 4 L 1 2 Ӵ B ˶ C ̣ݶܶãeE mv 4 2 1 eE MNPQ ƽ˶ˮƽsvtֱL at2a 2 m ãsLӴ P 1 1 eE s2 (2)ͷλZΪ(xy) eEx mv2svty at2 t2ãy 2 2 2m 4x 2 2 L L y õEkeE(x ) 4x 4x L ѧ֪֪ xy ʱ Ek Сֵ EkeEL. 2 𰸣(1)Ӵ P (2)eEL 14УmgE1qУmgE2qϣȼ˶ ٶȼΪ 0 ٷ٣ٴλص˶ 𰸣C 㶨 ٲ(ʮ) 繦͵繦

1ǷӳϵԺû뵼Ĵϸ޹أ ¶ȵӰԣϵĵ¶ȵ߶󣬹 AC D е ʱȶ࣬ԽĵʵIJϴ D B ȷ 𰸣B 2ûеʱеɵɣеĵӣΧԭ ӺתDzƶŷķڽ͵Һ磬 嵼Ͱ뵼嵼粻ã һɰ뵼Ƴɵģ Щ뵼ϵ ص¶ߣֵС 𰸣AC q ne L L 10L IT 3ɵ I ڹʽɵ Tv n t t c/10 c e 10IL 11 510 ѡ A ȷ ce 𰸣A 4ÿֻ׳ƺͷܵĹʷֱΪ 60 W 10 W 4 ڻͥÿ ͥÿ 6 Сʱ㣬ȫһʡĵӽ 41082(60 10)10 3 10 kW3656 h8.7610 kW hѡ B ȷACD 𰸣B 5ȼ AB CD ıֵŷķ µĵȣ AB ĺΪ S1 CD ĺΪ S2 lab S1 4 S1 1 R1 AB ·ʱΪ R1CD ·ʱΪ R2 . S2 2 R2 lbc 1 S2 I1 R2 1 µ֮Ϊ I24I14 Aѡ A ȷ I2 R1 4 𰸣A 6ʱĵΪ I׵·ܵΪ I ף3Iҵ· Ϊ I ңI PUI P ף3P ңӦѡ B. 𰸣B 7ͼ֪ߵѹֱΪ UA6 VUB4 VǴ 3RB RA LASB SA 1 2RAɵ趨ɿ֪ ѡ B ȷ RB LBSA SB 3 𰸣B 8貢ӵѹΪ U ĵԴʱĵĹʶ P˵ʱ U2 ֵȣֵ R1R2 P .ӳͼʾ R1 1 ·ȻڸõԴˣ R2 D ֵСڵ R1 R1 ˵ѹ U1 2 1 UD R2 ˵ѹ U2 U D IU ͼ֪ѹԽСD ĵԽԴ 2 1 ʱ RDR2.ͼܵΪ I R2 ĵ I2 I PI2R P14P2ѡ A 2 U2 ѡ C ȷ P ãPDP2ѡ D ѡ B ȷ R 𰸣BC 9綯δʱ˵ѹ ULEI1r12.5 V100.05 V12 V UL ݵ RL 1.2 ݹ P1ULI1120 W綯ʱI258 A˵ I1 U2 9.62 L ѹ ULEI2r9.6 Vݹ P2 W76.8 WƵĹʽ P RL 1.2 P1P243.2 W.

𰸣B 10(1)ĵ R U2 /P 10 0.9 Ķ I P /U A0.3 A. 3 (2)Ҫ·ְȫҪ· II 0.3 A ʱԴѹֵ UmU U0 U ΪĶѹU0 Ϊ R0 ֵ R0m10 ʱ R0 ˵ĵѹU0I R 0m0.310 V3 V ԵԴѹֵ UmU U06 V. (3)ʵʼʱ ab ĵѹΪ UʵʵΪ R䴫ݵһʵ ¼ݴ UR䴫 I1U1U0.16R䴫1.48 ݵڶʵ¼ݴ룺 UR䴫 I2U2 U0.22R䴫0.91 ãR䴫9.5 U3 V. ĵ仯Ϊ RR R䴫10 9.5 0.5 ˴Ȼʹã 𰸣(1)10 0.3 A (2)6 V (3)ʹ U3 V l 11ɵ趨 R ֪ڵʺ͵һ£ S ȣ C 㵽 A ĵ͵ B ĵıֵ AC BC.

ڲеĵЧ·ͼԴ A A ʱΪڻ· ACCA ʱ UB72 V © R ϵĵѹ AC BC ÿߵĵ UB R Ϊ RAC RBC E 2RACR UA R ͬԴ BBʱ E 2RBCR RACRBC/4. l ɵ趨 R lɵ AC Ϊ lACl/50.4 km. S 𰸣0.4 km 12ԴʣPI(EIr) Ե綯غ㣺PP PR ֣P mgvPRI2R I(EIr)mgvI2R I?EIr?mgv R I2 5?11051?50100.85 52 4 𰸣4 13ͼͷĵָͬƫͬ A1A2 ̲ͬ ʾͬ A B ԣͼ A1A2 еĵͬʾͬ߱ ͷеĵȣָƫDzͬ CD 𰸣B

ٲ(ʮ) ·ĻɼӦ

1·ĵ𽥼Сʱ·еĵڵѹ·˵ѹ СA ѡȷԴڵʱĿûȷ ڵ֮ĹϵԲжı仯B ѡ󣻵ԴڲĵĹʺ͵ йأԽڵ·ĵĹԽC ѡȷԴĹЧʵ·˵ѹ Դ綯Ƶıֵ·˵ѹСD ѡȷ 𰸣ACD 2 P 1.410010 3 W0.14 Wĵȹ 3 2 P ȣ(10010 ) 2 W0.02 WĻѧܹ P P P ȣ0.12 W. 𰸣AC 3⿼鴫պϵ·ŷķɣ·Ϊ 3 A 12 ݱպϵ·ŷķɣѹСӦ R2 R СֵΪ 2 R 3 300.02F F ֵ Fm1 400 NA ȷB 󣻵 F0 ʱR30 12 ʱ·еĵ I A0.375 AC ȷD 302 𰸣AC 4С L ϱС6 V 6 Wõݵĵ RLU2/P62/6 6 · ǰڵ··ܵΪ RRLr6 2 8 ܵΪ IE/R1 A Զ·ǰͨ R1 ĵΪ I11 Aѡ A 󣻵 L ͻȻ·󣬵·еΪ IE/r 4 AIc1.2 A̬תΪ̬ʱ·ܵΪ R䣽2 2 4 8 4 I䣽E/R䣽 A2 A·ͨ R1 ĵΪ I1䣽 Aѡ BC ȷѡ 4 3 D 𰸣BC 5ͼʾλZʱ󣬴 m 㵽ͼʾλZԲܵ󣬴 ͼʾλZ q λZԲܵС R ˵ĵƲȼ Q ĵѹȼ C C ĵȼСC ԣ U 𰸣C 6ӹǿʱRt ֵС·ܵСܵ󣬵Դڵ ѹ·˵ѹС A Ʊ䰵A ƵĵСR0 ϵĵ R0 ϵĵ ѹ B ƵĵѹСB Ʊ䰵ѡ B ȷ 𰸣B 7Ҫѧŷķ÷Χ繦͵ȵҪѧ ŷķɡ 繦ʼɵӦã ڵ綯ǷǴԪ ŷķɲã 綯빦 P1UIȹ P2I2R P3mgvP1P2P3ɽãU mgv E mgv IR ɱպϵ·ŷķɵãEUIr r 2 R綯ס I I I E ʱ綯ɴԪܵ I ܣ 󣬹ʵԴĵĹ P Rr ѡ BC ȷ 𰸣BC 8ԴͼСݵķߵĽ㣬ΪԴСʱ r1 E1/I1 I2 Ĺ״̬Ϊʱĵѹ͵Դ֮ A ȷ r2 E2/I2 I1 Դ綯ƾΪ 10 VֵΪ 11B ԣ״̬£СĵĹ֮

P1 I1U1 35 1 R1 U1/I1 36 C ȷ״̬£Сݵĵ֮ P2 I2U2 56 2 R2 U2/I2 55 18 D ѡ D  25 𰸣D 9 ab ƶʱ R1 Ϊ·ܵСݱ ϵ·ŷķɿ֪ȼСA ·˵ѹ UEIrΪȼ С·˵ѹСB ȷԴʱԴ 󣬻ʱǡõڵ裬ʱ˵Դ ȼСC 󣻵Ƭ a ˻ b ˵ʱ R1 ·ʱ R1 ĵĹ Ϊ㣬 R1 СD 𰸣B 10(1)ͼ AB ӳ U 20 V I 1.0 A ԵԴ E ĵ綯Ϊ E20 V r 20 . I (2) P R3 Ҷʱ·Ӧͼе B 㣬 U24 VI20.8 A R2 U2 5 . I2 (3) P R3 ʱͼ֪ʱ U ⣽16 VI ܣ0.2 A U R ⣽ 80 I R 1R 3 Ϊ R ⣽ R2 R3300 . R1R3 𰸣(1)20 V 20 (2)5 (3)300 11(1)ȫ·ŷķɣEUIr ͼ׿֪ I0 ʱEU12 V E12 VR2 ʱU6 Vȫ·ŷķɿɵãr2 . (2)ʱƬ¶ʱѹ UAB0 E Ƭ϶ʱ EUABIrI R0r ɵʱѹ UAB11 V ԣʱѹΧΪ 011 V. (3)ӸصСֵΪ R䣬 ʱƬӦ϶ˣ Դ I2 A У R 0R EI(R ⣫r) R ⣽ ݿɵãR䣽4.9 . R0R 𰸣(1)12 V 2 (2)011 V (3)4.9 R3 12(1)S Ͽʱ R3 ˵ѹΪ U3 E16 V R2R3r R1?R2R3? S պϺΪ R 6 R1R2R3 R ·˵ѹΪ U E21 V Rr R3 ʱ R3 ˵ѹΪ U3 U14V R2R3 R4 ܵΪ QCU3CU36.010 12C. qU3 (2)΢Ϊ mΪ q S ϿʱУ mg d qU3 S պϺ΢ٶΪ a mg ma d ΢ܴ C ĵ糡ˮƽ˶ʱΪ

t

L v0 d 2

1 ֱλΪy at2 2 ϸʽãy6.2510 3m


΢ܴ C ĵ糡 𰸣(1)6.010 12C (2) 13·ṹR1R2 R3 A1 ͨ R1 ĵ I1A2 ͨ R2 ĵ I2V ·˵ѹ U.R2 ĻƬ a bR2 ֵС·ܵС I 󣻸ݱպϵ·ŷķ֪·˵ѹ UEIrԵѹʾ U СR1 ˵ѹ U1UU3 U3IR3U3 U1 С I1 С II1I2 I2 𰸣B ٲ(ʮ) ʵ(һ)

1𰸣1.554 0.98 1.114 2ͼ֪ƶƬʱʾб仯ʺ͵Ļ·в ڶϵ㣬 A ƬӴ·ве B A ˽ӴƬƶʱ͵ѹ仯 D ڶ· ˵ѹΪ㣬ѹָ벻ƶƬʱֻеָ仯ѡ C  𰸣C 3𰸣(1)ͼʾ (2)R1 (3)A

4(1)΢Ĺ̶̶ϿԿ׿̶Ѿ¶ Ӧ 0.5 mmɶ̶Ͻӽ 18 ̶ߣԹ 0.180 mm( 0.179 mm) Ըý˿ֱӦΪ 0.5 mm0.180 mm( 0.179 mm)0.680 mm( 0.679 mm) (2)ɵ·ͼ֪Դڸɵأ綯 3 V 3 V ̵ĵѹ AΪ ˿ĵԼΪ 5 3 V ĵѹȫڵ˿ϣ 0.6 A 0.6 A ĵ Cн˿ĵԼΪ 5 Ϊ˼СʵӦѡ 10 Ļ E. L Rd2 (3) R ɵãѣ . S 4L 𰸣(1)0.680( 0.679) (2)A C E ڵڻĻƬ ˵ڽӷ Rd2 (3) 4L 5𰸣(1)A D E (2)ͼ

(3)0.7 6𰸣(1)ACDEFH (2)·ͼ

(3)25 7(1)α꿨ߵľΪ 0.1 mm L(5010.1) mm5.01 cm ΢ĶΪ d(531.60.01) mm5.316 mm. (2)Ϊ˱ڽͨ·֮ǰҪʹ·еܵ辡ܴȻС ·еĵ裮 𰸣(1)5.01 5.316(5.3105.320) (2)ٴ ڴ (3)1 280 ٲ(ʮ) ʵ()

1ѹӦѡֵģԵûرҪB 𰸣B 2ڵѹзãԵԽԽСȷһЩ ѡ AB ȷ 𰸣AB 3𰸣(1)ֱѹ 1.18 V (2)ֱ 48 mA (3) 1.7 k (4)á1 kʣµ 졢ڱʷֱӴ ̶ָָȣٳԱʣòֵ (5)OFF ѹ 500 V λ (6) 4(1)·ʵͼͼʾ

(2)ʵֵ UI ͼͼʾͼԵóͼ U ϵĽؾΪ 2.962.0 1 2.96 V ÿڵصĵ綯Ϊ E 2.96 V1.48 V ͼбʵľֵΪ k 2 1.32 1 0.727ԴΪr 磽0.727 ÿڵصΪr r 磽0.364 . 2

𰸣(1)ͼ (2)UI ͼ߼ͼ 1.48 0.364 5졢ڱʶ̽ӵʱ E Ig RrgR0 E 1.5 RrgR0 5 000 . Ig 300106 ָָм(ֵ)ʱ豻ֵΪ Rx Ig E 2 RrgR0Rx Rx5 000 . ʹŷķʱֵ 5 k ҶΪ׼ȷ׼ȷֵΧ 3 k8 k. B ȷ 𰸣B 6𰸣(1)110 (2)ͼʾ

IaI0 R2 (3) IaI0 RR0 E 1 7 EI(Rr) R r R ͼбʼΪ綯ƵĴС I I E2.4 V( 2.5 V)ͼؾľֵΪ r1 . 𰸣2.4( 2.5) 1 8(1)ʵе𵽸ı·ܵͷѹãΪȷİȫ һ㽫ĵȵֵ (2)ڶֵ R010 ѡ÷ 1ѹʾСʾ仯ΧҲ Сѡ÷ 2. R0r U 1 1 1 (3)ɵ E (R0Rr)Ϊ R б k ؾ R0 U ER0 ER0 ER0 R0r 1 b b E r R0. ER0 kR0 k 𰸣(1)ֵ (2)2 1 b (3) R0 kR0 k 9(1)Ϊ綯ƱֵΪ 3 Vֻѡѹ V2 ·ܵѹV1 ֵĵѹ·еĵֵѡ C. (2)UI ںϵĽؾŦ﮵صĶ· 2.60 mAؾǵ綯 2.90 VбʼΪ 1.11 k. (3)·˵ѹΪ 1.5 V ʱصԴ UI ߶СΪ 1.26 mAĵĵ Ϊ 1.89 mW. 𰸣(1)ͼʾ

(2)2.60(2.582.62 ) 2.90(2.882.92 ) 1.11(1.091.13 ) (3)1.89(1.861.91 ) ڰ ٲ(ʮ) ų ųԵ

1ڵųֱ FBIL ab ߵ L ͬB ͬ F Iѡ D ȷ 𰸣D 2a ʵʴŸӦǿΪ 0ֱߵ a ĴŸӦǿǿųڸ ĴŸӦǿȵʸΪ 0ֱߵ a Ba1 Tɰඨ ֱеĵֱֽ Բϸ㵽ֱߵľͬ ֱߵ ԲϸĴŸӦǿȴСΪ 1 Tͬ b ϣ c ң d £bcd ʵʴŸӦǿȷֱΪ 2 TбϷ B 45 нǣ2 T ң 2 Tб· B 45 нǣѡ AB ȷ 𰸣AB 3תת෴Ļεɰඨ֪ڴ 봦ųķ OOڴ N ָΪųӦѡ C. 𰸣C 4ܵĴųĺΪ㣬Уܵ ұܵdzԽߣŸӦǿԽܵұܵ 𰸣A 5ȦĴͨͨ絼ɵģͨ絼ߴԲϷ ԴȦĴͨΪ㣬ͨ絼ֱƶҲӰܴͨı仯 𰸣C 6ֶ֪ͨ絼ܰб·ţٵɣ ܵбϷĴų BC ȷ 𰸣BC 7⿼ǰͶ֪ܶʶڿѧӦ֪ʶʵ ֪ŸӦǿ BkI FBIdkI2dɶܶɵãFL mv2 2kdL vI ɴʽж BD ѡȷ 2 m 𰸣BD 8ac ˽ӵԴbd ˽ӵԴʱ MNڴųϣ MN ˶A ѡȷbd ˽ʱMN е NMų£ ⣬B ѡȷC ѡa ˽b c ̽ӣd ˽Ӹʱͬ A ѡ  D ѡҲȷ 𰸣ABD 9ðඨжڴĴųҪעǺϴųķȻ ֶжߵ򣬿ȷ B ȷģ 𰸣B 10軬·ֵΪ RܵİСΪ F BIL E BL ˮƽ󣬶Եƽɵ MgfF 0 R r

E 1 Nmgfܦmg1 N ɵ 2 NF 4 N 2 NBL 4 N 2 R5 Rr ѡ D 𰸣D 11 S պϺ󣬵Һе C Dֶ֪Һ Ҫܵҵİ F ãҺвѹǿ p ab Һ潫ָ߶ F BLI BI Һвѹǿ pp gh S Ld d ghd ԴŸӦǿ B I ghd 𰸣 I 12(1)赱ʾΪʱɵ쳤Ϊ x mgkx mg ɢʽãx . k (2)ΪʹͨеĽ MN İ£ M Ӧ (3)ƫʱͨ MN ǿΪ Im BIm ab mgk( cb x) ڢ۲ݵ Im2.5 A (4)󣬴ŸӦǿȱΪ B䣬 2BIm ab mgk( cb x) ɢ٢ʽã k cb B䣽 2Im ab ݵãB䣽0.10 T. mg 𰸣(1) (2)M (3)2.5 A (4)0.10 T k 13 fBILBLkt<mg ʱص¼٣ fBLkt>mg ʱص ¼٣ڰֹͣ˶ǰĦΪĦСΪ fBLktֹͣ˶ ʱĦΪĦСΪ fmgѡ C ȷ 𰸣C ٲ(ʮ) ų˶ɵ

mv 1 r ֪B Сr ԽԽ󣬹ʵӵľ a. Bq 𰸣B 2𰸣C 3ɵ֪õͨԲijһλZ(ijһ)ĵ ʱıֵ ʱΪڴųԲ˶ T ʽ Iq/T еĵ 2m q2B q Ϊôӵĵ T I .ѡ D ȷ qB 2m 𰸣D 4ӶϿСٶȴС䣬Բ䣮СܴҲܴ 磬磬ӶϿСʱ뷽Բ˶С򲻱(ԭ Ϊ)˶뾶򲻱䣮磬ӶϿС˳ʱ뷽Բ

˶ ǰСܵĴСȷ 仯Ʋȷ ˶뾶󣬿ܼСҲܲ䣮 𰸣A 5⿼ڴųе˶ڿ鿼Ӧѧ֪ʶ ͷֶӵƫתжӴ磬ѡ A mv2 qBr ṩ qvB ɵ v r Խ v Խͼ֪ r ֵΪ rmax r m 3dL L ѡ B ȷ r СֵΪ rmin r ֵСֵ v ıʽ 2 2 3qBd ٶ֮Ϊ v ɼѡ C ȷD 2m 𰸣BC 6Ȼ䷽ֱб£ʹбѹ 󣬹ĦʧĻеӣ 𰸣B 7.

L?2 2 ? ͼܴұߴ˶뾶ٽֵΪ r1 r2 1L r12 ? ? mv1 5 5BqL 5BqL r1 L.Ϊ r1 v1 v ʱܴұߴܴ 4 qB 4m 4m L qBL BqL ˶뾶ٽֵΪ r2 r2 v2 v ʱܴߴ 4 4m 4m 𰸣AB 8.

2m ڴųе˶켣ͼʾڹʽ T ֪Ӵ O qB 2m m 2m һͨ O ʱ t B ѡȷ qB1 qB2 qB2 𰸣B 9켣ͼͼʾ׵óԲδųеĹ켣(켣Ӧ ԲĽ)δųеģ ABD ȷ

𰸣ABD

10. ٶ뾶ֱԲһ a · e ʱԲĽǡ mv Ϊ 90 ͼʾ r ٶΪԭ 2 뾶ҲΪԭ 2 qB ԲĽDz䣬ӦҲΪԭ 2 ǡô d A ȷӵٶ Ϊԭ 3 뾶ҲΪԭ 3 ͼп f 㿿£B mv ӵٶȲ䣬ųĴŸӦǿȱΪԭĶ r ã뾶ԭ qB 2m һ룬 ae еC 󣻸˶ T ֪˶ٶ qB T ޹أ e d ӣתԲĽǶ 90 ˶ʱ䶼 ˶ʱͬD 4 𰸣A 11(1)ڴų˶ṩӵٶȴСΪ v ʱ ڴųе˶뾶Ϊ R FqBv mv2 ţ˶ F R Сٶȵ P ʱ켣һ AP ΪֱԲ(ͼԲ O1 ʾ) ɼιϵ֪ sAP 2l sAP 2 R l. 2 2 2qBl ӵСٶ v . 2m 2m (2)ڴųе˶ T qB ڴų˶ʱ켣ӦԲĽΪ ȣڴųе˶ʱΪ m t T . 2 qB ͼ֪ڴų˶ʱӵ˶켣ͼԲ O2 ʾʱӵij ٶȷֱϣ

3 ɼιϵ ȣ . 2 3m ڴų˶ʱ t . 2qB 2qBl 𰸣(1) 2m 3m (2) 2qB 12A ƽ˶ʱ t ߽磬Lv0t

1 ֱλƣy at2 2 Eqma



v2 C ڴųԲ˶ qvBm R ɼιϵ2Rsinȣy ڴų˶ʱڵ糡˶ʱȣ 2 t T 2 2m T qB EqL Ϲϵãv0 6m Em B 3 6qL 3L C y EqL Em 3L 𰸣(1) (2) (3) 6m 3 6qL 13Сʼ»ʱУmgsinȣ(mgcosȣqvB)ma v a 󣬵 mgcos v ʱֵ gsinȣ˺»Уmgsinȣ(qvBmgcos)ma v qB mg?sinȣcos? a С vm ʱa0.Уv һֱ󲻱䣻a qB С B ѡȷ 𰸣B ٲ(ʮ) ڸϳе˶

1 OaObdΪڴųԲ˶Բ˶İ mv0 mv0 õ d r dõ B .ǿ糡ˮƽ v0 ֱ qB qd d 2mv2 1 qE E 0 ˶ֱ y Ḻȼ˶ d ?v ?2õ E 2 m ? 0? qd B 2v0ѡ C ȷ 𰸣C 2a Ҫڵ糡ųĸϳֱ˶һֱ ˶ʶ a УBqvEqֻҪ EBvӴ绹Ǹ磬Ӷ ֱߴϳȥųֻ糡ʱ b ڵԲȷ޷ж b

Ӵ OϷ· AB b ڴ糡ĹбȻܵ 糡öƽ˶糡ܼС󣬹 C ȷD 𰸣C 2R 3ӱٺٶܵ D κа뾶 R Լ v 2RfA T 1 1 ȷ뿪 Ekm mv2 m42R2f22m2R2f2ٵѹ U 2 2 mv 1 2 1 2 ޹أB 󣻸 R Uq mv12Uq mv2ӵ 2 κ͵ 1 ξ D Bq 2 2 м뾶֮Ϊ 21C ȷ Ekm2m2R2f2 m Rf йأD 𰸣AC 4ܵ qv0BmgܵûеҲ Ħʴ˷ĦĹΪ 0A ȷ qv0BmgĦ 1 ֹͣʿ˷ĦĹΪ mv2 C ȷ qv0Bmg忪 2 0 mg ʼʱĦö٣ٶȴﵽ v ʱ岻ĦãԿ qB 1 ? 2 ?mg?2? ĦĹΪ m?v0? qB ? ?D ȷ 2 𰸣ACD 5С˶糡ãעСֱ˶һ Ϊֱ˶ AB ſֱ˶ֱ˶ʱ糡е ӣBC ȷ 𰸣BC 6 PQ ѹΪ Uа뾶Ϊ R Բϵ糡ǿΪ E. PQ m v2 1 1 ٹ qU mv2 mv 2 ھ qE ʽ v 2 2 0 R ER 1 v v ͬ v ͬA 󣻽϶ܱʽ Ek mv2 ֪ B 2 ER2U 0 0 2 mv mv ER ڴų˶Ĺ뾶 r qE ɵ r r ͬ v ͬC ȷ qB R vB 1 ERm q ʽƵ r r Խ ԽСD B q m 𰸣C U 7ȶʱֱ˶ qvBqEq U d U d S?Bdv R? A ȷ Bdv I r ѣ S d? I ? Rr 𰸣A 8Сб˶ʱܵĴųķֱб棬б⻬ʱ бµķṩٶȣٶȴСбйأԽ󣬼ٶԽ б淽ٶȱʽΪ mgcos/(qB)ٶȴСʽΪ gsinȣʱ ıʽΪ tmcot/(qB)ǵгȣԽʱԽС v2 max2asmax v2 1?mg?2cos2 m2gcos2 max smax £ sasbACD ѡȷ 2a 2? qB ? gsin 2q2B2sin 𰸣ACD 9糡ʱ糡ĺպṩ ѡ A ȷ糡ѡ C ȷ糡Сѡ B ȷڵ糡ķ仯ѡ D 𰸣ABC

10(1) P ֹʱбѹ mgqE P ˮƽٶȺԲ˶ ɶԳԿɵ P 䵽бʱٶȷб ļнΪ 45

v2 0 qv0Bm R 2R 2m T v0 qB P A C ʱ䣺 T E t 4 2gB m v0 (2)ɢʽ֪P Բ˶ R qB ɼιϵ֪ x 2R 2Ev0 ɢ٢ݢ޿ɽλ x gB 2Ev0 E 𰸣(1)45 (2) 2gB gB v2 mv 11(1) qvBm r r qB

B0.20 Tv2.0106 m/sm1.610 27 kgq1.610 19 C r0.1 m. (2)ãԲ D λ y ij㣬ɼιϵɵãC ԭ 2 3 ľ m. 20 5 5 2m 5 (3)ڴų˶ʱ t1 T 10 7 s1.310 7 s 12 12 qB 12 19 5 qE 1.610 10 ڵ糡 a 1013 m/s2. m 1.610 27 v 2106 ӽ糡ʼٶȵһΪʱ t2 210 7 s a 1013 A ٶȵһΪõʱ tt1t23.310 7 s 2 3 𰸣(1) 0.1 m (2) m (3) 3.310 7 s 20 mg 12(1)΢ qEmg0 E q v2 mv (2)΢ڴų qvBm R R qB


ͼʾ PQ ΪԲδųֱʱԲδųС

rRsin

m2v2sin2 Sr2 q2B2 2R 2m T v ( T ) qB ݼιϵ֪ƫתΪ 2 2 2m ڴų˶ʱ t2 T 2 qB L2Rsin MPQN 2cos MP t1t3 v L2Rsin 2m ˶ʱ t t1 t2 t3 vcos qB 2m qB mg 𰸣(1) q m2v2sin2 qBL2mvsin 2m (2) q2B2 qBvcos qB 13ֶжϣԲֱܵµֱ˵ ĦʼʱСʱֱϣԲҼ ˶ٶȼССԽԽĦԽԽ󣬹ٶ ˶ֱٶΪھֹ״̬ѡûжӦͼ󣻵ʼʱ̵ ʱΪ㣬ĦΪ㣬Բֱ˶A ȷʼʱ ʱֱ£Բ˶ٶȼССС ڵСĹУĦ𽥼С㣬ٶ𽥼Сļ˶Ħ Ϊʱʼֱ˶D ȷ 𰸣AD ѡ 32 ھ ŸӦ ٲ(ʮһ) ŸӦ ζ mv L2 sin qB 2m qBL2mvsin vcos qB qBvcos

1ҪŸӦ󣬲ǴȦĴͨ仯 ޸Ӧֻ D ȷ 𰸣D 2⣬߿иӦ˳ʱ뷽߿ܵ ߿ϴ󣬹߿Ϊֱֶ֪ߵʱ߿ܵ İֱߵʱ߿ܵҵİ A ԣ 𰸣A 3ab 뱻ָԲɵĻ· ab ˶Уͨ

ֲ䣬޸Ӧ 𰸣D 4֪y ԽСBy ԽУͨӣA ζжϣе˳ʱ뷽򣬵 Uab0B ֱ ab ܰϣԲ ab ܰ£ֱ ab ڴųǿλZܰϴ󣬰Բ ab ĵЧ ˮƽֱȣڴųλZܰСܰ ϣ C ȷD 𰸣C 5ab ܴųֱϣֶ֪ͨ ab ĵ a ָ b ֶ֪ȦƳųʱbc иŸ߿ɲ˳ʱ뷽ĵȻ ҲζжϵȦƳųʱͨС˳ʱĸӦ B ȷ ab cd ΪתʱͼʾλZ߲иŸߣ޵ CD 𰸣B 6⿼ζɵӦüжϣԲ˶ʱ Ĵͨζɿ֪Ӧʱ˳ʱ룻 Ҳ˶ʱĴͨζɿ֪Ӧ˳ʱʱ 룬A ԣκλZԲඨĺϰʼˮƽ C D ԣ 𰸣AD 7ͷ M ͻȻ˶߹ܻų⣬ζɣ S ɶϿպϵ˲䣬ѡ A ȷ 𰸣A 8պϵĽʱ򴩹պϵĽܵĴͨ仯 Ӧ ζɿ֪Ӧ谭ӦĴͨı仯 Ӷ谭 ͨ򲻱պϵĽܣ޸ӦҲû谭ãӶ ֪ѡ A ȷ 𰸣A 9Բ˶ʱԲĴųͬҶӵģ ԲвĸӦͬԲдͨԲԶų ڸӦķͬӦ໥£ B ȷ 𰸣B 10Ҫʹ·вĸӦӦʹ·еĸӦ綯Ӧʹ ȦƽڵĴͨ仯죬 дŸӦǿȵĴС䣬 ݹʽ֪Ȧƽ ͨı仯ʱĸӦC ѡ D ѡԣ 𰸣CD 11岻ᱻŻδΧڵĴųûʱһģ ƽʱĴͨ󣬴ӶӦʹĻеܼ٣ ҲС˶ڴųֱƽ棬ֶж ˮƽ˶򲻻ᷢƫת AD ȷ 𰸣AD 12 A ͼдŸӦǿʱӣ е ba߹ܡdc ųı仯ʲϼС߹еСˣ߹ܲĴųԲĴŸ ٣ ζɣ Ϊ谭ֱ仯 Բ߹ܣ ܵϵĴųã B ͼų仯ʱ߹ܲĵ󣬴ԲĴŸ߱࣬ҪųԲCD ͼųǾȱ仯ģ߹иӦȺģĴųDzģԲĴ ͨ䣬޸Ӧ߹ܴų໥ã˱ȷѡ A. 𰸣A 13𰸣(1)ûõʱab ֮ûеѹΪ˫ƳɵijȦ еĵǴСȶ෴ģоĴͨΪ 0ȦвиӦ

Ʋ (2)վڵ󴥻ߣͨߺأͨߣ ѹооͻдͨı仯ӶӦ綯ƣѿۿؾͻϿ T 14 T ʱڣζɿ֪߿иӦķΪ˳ʱ룬 2 ֶж߿ܰĺңѡ B ȷ 𰸣B ٲ(ʮ) ڵŸӦ Ը

1ȦʽͲȦĴų񶯣ӦŴ¼¼ ʱʹͲв仯ĸӦʱŴϱ仯Ĵųʹͷ ȦвӦչڽͨʱ˲ʱߵѹֶ˵ Ӧԭ׳ûõŸӦԭѡ ACD ȷ 𰸣ACD 2ƽ˶иŸߵٶȵˮƽٶȣֲ䣬ʸӦ ƴС䣮 𰸣C T ? a ?2ƽӦ 3֪߿ת ʱͨ BS2B? ? 8 ?2 2? 2 8?32 2?a B 綯 E A ԣB t T ζ֪۵߿ôתǴ߿ĴͨС EHGFEC D ԣѡ AD. 𰸣AD 4رպϵ·еȶʱڣA 𽥱䰵 ȶB 𽥱ȶѡ A ȷB 󣮿ɱպϵϿ˲䣬 ͨ A ƣһ A һϨѡ CD 𰸣A B B 5ݷڵŸӦɵ E Sͼ ֵΪ 0.1 T/s t t t Em Em0.01 VIm 0.01 AA 󣻸ζжϵ 4 s ĩΪB R 󣻵 3 s Ȧ޸ӦȦȣC 35 s ڴȦĴͨ٣ Ϊ谭ͨ٣ȦƣD ȷ 𰸣D 6ųĴŸӦǿȴСȣ෴һ·ʱ OOԳƣ ʱ·ĴͨΪ㣬A ȷabcd иŸߣ൱Դ ֶ֪·иӦΪʱ룬ԴӦ綯Ϊ 2Blv0B ȷ C ֶ֪ abcd ܰD ȷ 𰸣ABD E 2BS qR 7qIt tn tn n B . R tR R R 2nS 𰸣C 8ƽɵãСܵµĵ糡 mgΪС磬 U Ϊ壬ζɿ֪ųڼ q mgݷڵŸӦ U d n ɵ B ȷ t 𰸣B

9(1)ĵ綯 EBlv0.2 V R1R2 2 R R1R2 3 E ͨĸӦ I 0.1 A. Rr 1 (2)ĵѹ UIR V 15 QCU210 8 C. 𰸣(1)0.1 A (2)210 8 C 10(1)ԽΪо E Blv vat EBlv I FIBlma R R 2 2 Bl ãFma at R ͼȡ(0,0.1 N)(10 s,0.2 N)뷽̣ ãa1 m/s2m0.1 kg 1 (2)Ӿֹʼ˶ t ʱڸ˵λΪx at2 2 ·Ĵͨı仯BSBlx ͨ R ĵΪq I t 𰸣(1)0.1 kg 1 m/s2 Balt2 (2) 2R E Balt2 t R R 2R

Blv0 Bv0 11(1) ab ڵ֮ijΪ lŷķɵ I . 3lr 3r 2 3 (2) O 㵽 ab ľΪ x ab Ч l䣽2xtan30 xΪ ab 3 B v0 2 3 B x 3r 3 BIl 2 3B2v0 ˶ kxBIl䣬k . x x 9r 1 Q (3)ֹֻܾ O 㣬䶯ȫתΪȣ Q mv2 Qab 2 0 3 2 mv0 6 Bv0 2 3B2v0 mv2 0 𰸣(1) (2) (3) 3r 9r 6 12 AB ٻʱ·в㶨ĸӦ綯ƣ· I10I2 0AB 󣻵 AB ٻʱݷڵŸӦɣ·вĸ Ӧ綯ڳʱ·еĵ I10I20C D ȷ 𰸣D ٲ(ʮ) ŸӦɵۺӦ

E Blv 1ͼҿ֪ǾӣȼС i lԽ R R ߿иŸߵЧӦǾӣȼСA ϣBC ߿м䲿 ֽųиŸߵЧȲ䣻D ЧȲǾȵӺͼС 𰸣A 2պͭɸߴֹ䣬ϴͭĴͨ󣬸ζ ֪ͭв˳ʱ뷽ĸӦ(¿) N O ĹУͭ

ĺϴͨӦΪ˳ʱ뷽򣻴 O 㵽 S ĹУͭ ĺϴͨҼСӦΪʱ뷽뿪 N ϴͭĴͨ СӦΪʱ뷽ͭٶԽԽʱ뷽Ӧֵ ˳ʱ뷽Ӧֵ󣬹ѡ B ȷ 𰸣B B2L2v 3һ˶ʱص췽mgsinȣ ڶ R 2 2 2B L v ﵽٶʱص췽 Fmgsinȣ Fmgsinȣʱ F Ĺ P R F2v2mgvsinȣѡ A ȷB 󣻵ٶȴﵽ v/2 ʱص췽mgsin B2L2v 1 ma a gsinȣѡ C ȷٶȴﵽ 2v Ժĺ 2R 2 ȫתΪ R ϲĽȣѡ D 𰸣AC 4ĸӦ綯Ϊ EBlvΪ IBlv/RΪ FBIlB2l2v/R lv ڼСţٵڶ֪ٶҲڼС A ùУȫת 1 ΪӴΪ mv2 B ùУ ͨܵΪ QBS/R ã 2 0 QR ʼ˶ʱ뵼ɻ· S C ԣɲĸӦ綯 EBlv ͵ B IBlv/R֪ D 𰸣C 5 x5 cm ʼȦųȦиӦڰС ˶ٶ v λ x С x15 cm ʱȦȫųС˶ Сˮƽ l10 cm A x30 cm ʱ Ȧʼ뿪ų d30 cm5 cm E nBhv2 25 cm.B x10 cm ʱͼ֪Ȧٶ v27 m/sӦ I R R 1 7 AC ȷȦ뿪ųʱСٶ v32 m/sȦϲĵ Q (M 2 2 2 m)(v1v3)5.76 JD 𰸣C 6Сÿ滬롢ųУڴųЧӦе ͨųתΪȣС黬ųĸ߶ԽԽСԣС Ϊǡò뿪ų ϱֱ߽ڴΪߵ˶ 1 2 㣬ɵãQmg(ba) mv ȷѡΪ D. 2 𰸣D 7 abc 壬ƽ֪ʶã2mgsinȣmcg mc2msinȣb ϵǰ c ٵܵ ac ӵĶ a ֮ͣb ϵ c ٵܵ ac ӵ·ĵĵ֮ͣ b mgsin ˵BILmgsinȣ I ѡ AD ȷ BL 㣺⿼غϵԼƽ֪ʶ 𰸣AD 8(1) ֶжϽеĸӦΪ a b. (2)»ٶȴﵽ 5 m/s ʱ Ӧ綯 EBLv0.415 V2 V E 2 Ӧ I A1 A R 2 ܵİ FBIL0.411 N0.4 N ţٵڶɵãmgsinȣmgcosȣFma a2 m/s2.

(3)˶ﵽȶʱܰΪ F䣬ص췽ƽ mgsinȣmgcosȣF F䣽0.8 N F 0.8 ʱӦ I䣽 A2 A BL 0.41 ·е R ĵĵ繦 PI2R222 W8 W. B2L2v (⣺ F䣽 ȶʱٶȴﵽֵ vm10 m/s˷ R ʵڵ R ĵĵ繦ʣ PFv0.810 W8 W) 𰸣(1) a b (2) 2 m/s2 (3)8 W BLvt1 9(1) 0.30.6 s ͨĵ q1I1t1 Rr BLx2 00.3 s ͨĵ q2 Rr Rr 2 ֪ q1 q2 x20.3 m. 3 (2) 00.6 s ͨλΪ xx1x2vt1x2 x0.75 m 1 غ㶨 MgxmgxsinȣQ (Mm)v2 2 Q2.85 J ڽ R ȣݽ QI2RtõDz r ȣԽ 00.6 s ڲ Qr Q1.9 J. Rr 𰸣(1)0.3 m (2)1.9 J 10 B2B1 B2 ܰС򲻱䣬Խ B2B1 B2 Сȼٺ» B2 B1 B2 ȼٺ» 𰸣BCD ʮ ٲ(ʮ) IJ

1⿼ŸӦ󣬻⣮߿ǿųתʱ ߿Ÿߴֱʱͨ󣬸Ӧ綯СͼʾλZ߿Ÿƽ nBS ʱͨСӦ綯AB C ԣЧֵ I ɱʽ 2R ֪ٶһ󣬵ҲһD ȷ 𰸣CD 2t0 ʱȦͨ󣬴ͨı仯СԸӦ綯ơӦ С ζɿжϣ t0 ʱ̿ʼȦдͨС ĸӦ i Ϊ CD ȷ 1/4 ںdc иŸߣΪ·г ĵB ȷӦѡ A. 𰸣A 3 2/Tأ314 rad/s֪˽Ϊ T0.02 sСݵĶ ѹָǽѹЧֵѹֵָǽѹֵ 𰸣D 2 U U2 2 4Чֵ t 2t U У U R R 2 2 U 壽 2U У 2 UU 2

U100 V ʱB ԣACD 𰸣B 5⿼ҽͼڿ鿼ҽͼȡ Ϣt0.005 s ʱӦ綯߿Ĵͨ仯ҲA t 0.01 s ʱӦ綯Ϊ㣬߿ͨ߿ƽغϣB ȷӦ 311 綯ƵֵΪ 311 VЧֵΪ VC 綯ƵΪ 0.02 sƵ 2 ڵĵΪ 50 HzD 𰸣B 6t0 ʱ̴ȦĴͨ󣬴ͨı仯Ϊ㣬ʵѹΪ㣬A 2 ͼ֮Ϊ 23 ɽٶ أ ýٶڳɷȣ B ȷ T ͼ a ֵΪ 10 Vأ5УɽӦ綯˲ʱֵʽ eEmsint(V)( 濪ʼʱ)ãu10sin5t(V) C ȷֵ EmnBS.Ըν 2 20 ٶ ıֵɵã b ֵΪ 10 V V D 3 3 𰸣BC 1 1 7 A ͼ֪ٶȼСļ˶ T ʱٶ T 4 4 1 1 1 3 T ٶļ˶ T ʱٶΪ㣮 T T ӷٶȼСļ 2 2 2 4 3 3 ˶ T ʱٶ T T ٶļ˶T ʱٶΪ㣬صԭ 4 4 λZ˶ͬķɵ BC Ҳԣ 𰸣ABC 8ѹʾʾЧֵΪ 220 Vѡ A 󣻵·ʱ 440 220 · I A A3 AȻѡ B ȷůȫתΪܣ 220 220 ̻ҪתΪеܣȻůȹԶڳ̻ȹʵ 2 ѡ C 1 min ̻ĵĵΪ WPt220 W60 s1.32104 Jѡ D ȷ 𰸣BD 9ijĴͨȦ޹أȦ£ͨı T BSѡ A Ȧת 90 ʱ t ƽ綯 E N 4 2 t BS 2NBS Emax NBS N ѡ B ȷȦĸӦ綯ƵЧֵΪ E . 2 2 2 E NBS ·еЧֵΪ I . Rr 2?Rr? ԣ R ϲΪ E T N2B2S2R QI2Rt?Rr?2R ? ? 4 4?Rr?2 . ѡ D ȷΪ BD. 𰸣BD P U2 10 õĵΪ R ҽԴѹЧֵΪ U 2 R ?10 V?2 ֱʱP ֵ Um 2Uɽ Um10 Vѡ C ȷ R 𰸣C

11. (1)Ȧ abcd תУֻ ab cd иŸߣ ab cd ת Ϊ v L2 vء 2 t ʱ̣ ab cd иŸ߶ĸӦ綯ƾΪ E1BL1v ͼ֪ vͣvsint ȦĸӦ綯Ϊ e12E1BL1L2sint (2)Ȧͼ(c)λZʼ˶ʱ t ʱȦĸӦ綯Ϊ e2BL1L2sin(t0) (3)ɱպϵ·ŷķɿ֪ E I Rr E ΪȦĵ綯ƵЧֵ Em BL1L2 E 2 2 Ȧתһ R ϲĽΪ QRI2RT 2 T BL1L2 QRR? Rr ?2. ? ? 𰸣(1)e1BL1L2sint (2)e2BL1L2sin(t0) BL1L2 (3)R? Rr ?2 ? ? 12ͼʾһڽ ut ͼӰֶӦʱ t1 ʾ޺Ʋܷʱ䣬ݶԳԣһ޺ƲܷʱΪ 4t1.

uu060 2 V ʱ u120 2 sint V ã 1 t1 sɶԳԵһܷʱ 600 1 1 ? 1 tT4t1? ?504600? s75 s. ɱϵ 1 h ޺Ʒʱ 3 600 1 ? t䣽? ? 0.02 75? s2 400 s.

1 s(ͼ t2 ʱ 300 1 1 t3 ʱ)˵۾Ӿ󣬶ӾʱԼΪ s Զ s 10 300 ˾ƹ̼۲ԶݵϨо 𰸣2 400 s 13 (1)ٶͼɵã ijʱ̵г˶ٶȱʽ vt10sin10t m/s. ĸӦ綯Ƶ˲ʱֵʽ eBLvt1.6sin10t V. (2)Ӧ綯ƵֵΪ Emax10BL1.6 V Ӧ綯ƵЧֵΪ EEmax/ 2 ·еܵΪ R䣽rR/20.8 Emax ·еĵ IE/R䣽 2 A. 2?rR/2? · 1 min ڲΪ QI2Rt96 J. 𰸣(1)e1.6sin10t V (2)96 J 102 T 202 T U2 14Чֵ壬 T U5 10Vѡ D. R2 2 R2 2 R2 𰸣D ޺ڹǺģ Ϩʱֻ ٲ(ʮ) ѹ ܵ

1 A ͼ uab 䣬A ޵ B ͼ uab ɰඨ֪M ǿĴųP ӵĴͨζɺͰඨ֪A е d c AB ͬ CD ȷ 𰸣CD l 2ԭ·еĹ PI2R ߣ R ߣ ߵĺ S ߵĵСܹСϵĹģA ȷ PUI ͹һ£͵ѹ U ԽԽСԽСB ȷ ѹһ͹Խ I Խ󣬵·ĵĵ繦ԽC УѹԽߣڰȫͼҪԽߣ˲ѹԽԽãD ȷ 𰸣ABD Um 5 3ѹʾΪѹЧֵͼҿɵ U Vѡ A B 2 2 n2 Um2 ȷȦѹֵΪ 5 000 V ʱ 1 000𻨵ǸȦ n1 Um1 n2 ѹֵ 5 000 V 1 000ѡ C ȷD n1 𰸣BC 4 MN ˶ʱ㶨ȦĴͨ䣬 Ӧ綯ƣ C ᱻ磮 MN Ҽ٣ĵֶ ֪Ϊ MNɰඨ֪ұȦ·ĴųȦ ϵĴͨҼζ֪ȦвӦ綯ƣʹ C ϼ磬 C ȷͬ B D ԣ 𰸣CD 5̨ƵĹָݺܹʣ ABCD ѡ֪C ѡѹΪ㣬Դܹ(̨Ĺ)ֻ ݵĹ 20 WѡУۻǷѹӷӷ

йģ̨ƵĹʶ 20 W C ѡȷ 𰸣C 6 R2 ڴֻʱֵСѹ R1 ˵ѹ󣬵 R1 Ĺʱ󣬵ѹ V2 ʾСѡ AB 빦ʵʿ֪ R2 ڴֻʱ A ʾ ѡ C ɱѹѹʽѹѹΪ 22 Vѹ V1 ʾΪ 22 Vѡ D ȷ 𰸣D I n2 7ڵʾΪЧֵ ֪ I210I P100I2Rѡ A I2 n1 n1 ȷѹԭȦ˵ѹΪ U1 10IR100IRѡ B 󣻴͵㿪ʼʱ n2 иӦ˲ʱֵıʽΪ i 2Icos tѡ C 󣻵еֵΪ 2I F 2BIlѡ D ȷ 𰸣AD 8ˮƽͭԲ˶뾶иŸ߲㶨ĸӦ綯൱ڵ Դ R1 ʱѹԭȦӵǺ㶨ѹȦеĴͨһͨı仯 Ϊ㣬ѹΪ㣬֪ AC B ԣ R1 仯ʱԭȦӵIJ ѹԭȦĵϵȷ D 𰸣B B 0.4 9U1 SB0cost ͼж B0 أ U120cost V t U2 I1 n2 Ȧ U2 ЧֵΪ 100 2 VI2 0.1 2 A I1 2 A. R I2 n1 𰸣C 10ɱѹʽȦѹΪ 10 Vڽͨڵ R ˵ĵԲӦŷķɼʾѡ AB 󣻵 R ĵĵ Ϊ P100/10 W10 Wѡ C ȷȦѹֵΪ 10 2 V ѹֵ 10 2 Vѡ D ȷ 𰸣CD 11(1)·ͼͼʾ

(2)ѹѹȦѹΪ n2 10 U2 U1 220 V2 200 V. n1 1 n1 ѹѹȦΪ I2 I1 n2 ѹѹԭȦ PI1U1 3 P 4410 I1 A200 A U1 220 n1 I2 I120 A. n2 ·ϵĵѹʧ͹ʧֱΪ URI2R200.2 V4 V 2 PRI2 2R20 0.2 W80 W0.08 kW. ӵѹѹԭȦϵ͵ѹΪ I3I220 AU3U2UR2 200 V4 V2 196 V. ѹѹȦѹ͵ֱΪ

n4U3 1 U4 2 196 V219.6 V n3 10 n3 I4 I31020 A200 A n4 ûõĹ P4U4I443.92 kW. (3)øѹ磬·ʧѹΪ UR䣽I1R2000.2 V40 V. ûõĵѹ U䣽U1UR䣽220 V40 V180 V. ûõĹΪ P䣽I1U䣽200180 W36 kW. 𰸣(1)ͼʾ (2)219.6 V 43.92 kW (3)36 kW 180 V E W귢 W 12 (1)վˮתΪܵЧ ıʽ ǣ E MgH QgH ݣ ǣ 8.4010101033 600 100%67.1 %. 1.01034.51101110100 W (2)ݹʽ P t 10 8.40 10 W t 192.3 죮 P 1.8210724 n1 U0 18 9 (3)ѹѹıѹ n2 U 500 250 6 P1 4.510 еĵ I A9.0103A U 500 ĵĵ繦 P 50%P1I2R ·ܵ 6 3 0.05 P1 0.054.510 10 R ߣ 2 2.78 . 3 2 I ?9.010 ? W 𰸣(1)ǣ 67.1% QgH (2)192.3 (3)9250 2.78 13պ S ʱ·СȦеV1 ʾ䣬A2 ʾ A1 ʾҲ V1 ʾ䣬A2 ʾ V2 ʾСA3 ʾС 𰸣B ٲ(ʮ) Ӧ

1𰸣A 2ͷ P ƣʹСܵĵ󣬴Ӷǿʹ R СմﵽݵĵЧ 𰸣A 3𰸣ABD 4ֱ·н·лϺ󣬵ʧ 붨ֵ裬˲ȶȦڶԱ仯ĵ谭ã˲ ﵽȶ 𰸣ABD

5¶Ϊ 20 ʱ Rt ϵͼԿʱֵΪ 4 k I EIR 9.0210 34 000 E E ֪ Rg 500 Ϊ 3.6 mA ʱ I I RRg 210 3 RRg EIRg 9.03.610 3500 R 2 kȻ Rt ϵͼԿʱӦ¶ I 3.610 3 Ϊ 120 . 𰸣D 6⿼鴫Ԫʣĸ ԪֵǿȵǿСɰѹѧΪһѧ ؿأ¶ȷӦУ 𰸣С ¶ 7ͼ߿֪¶ȵ߶СӶʹ·еĵ Ҫ¶ȹʱ죬 c Ӧ a ʱ·ŻͨƬ P ƶʱ ʹ¶ߣ ·ҸԪڹ״̬·ֲ ܹ˵·еСĴ̫²ܿҲĵ·ͨԭж ǵԴ˵ѹСȦ٣򵯻ɵľϵȣ 𰸣(1)a (2) (3)ͼߵԴ˵ѹ̫СȦ̫٣ߵɵľϵ̫ȣ 8·ͼͼʾ

̣պ S¶ȵֵʱֵͨż̵ĵ ʹK ͨ¯˿ȣ¶ȴﵽֵʱСijֵͨż ĵﵽK Ͽ¯˿ϵ磬ֹͣȣ¶ȵֵظǰ ̣ 𰸣 9𰸣йʱֵС·еȦĴ ʹܷڸɻɹڵʻƬŻ Ƭԭķ״̬ɱպ״̬ ·֮ͨûйպʱֵܴ󣬵· ĵСɻɹڵʻƬڷ״̬ӷĵ·Ͽ 10תֵĽٶȡתٷֱΪ ءnת ʱΪ tͨ ȦĴͨı仯Ϊ ȦвĸӦ綯ƵƽֵΪ E. BS ݷڵŸӦ EN N t t E ɱպϵ·ŷķɵãӦƽֵ I R t n 2 IR ϸʽ n 2NBS ɴ˿ɼͬѧĽȷģ 𰸣ȷ U2 11̬ʱ PTC ϵС P ֪䷢ȹʴ¿죬A ԣ R ͼ֪¶ȽϵʱPTC ϵСȹʴȴɢȣ¶ߣѸ

󣬷ȹʻСȹСɢȹʱ¶ȽͣСȹ 󣬹ʷȹʵɢȹʱ¶Ȼȶͼ T6T7 ֮䣬ʵԶ ȣ C ԣBD 𰸣AC ѡ 33 ʮһ ѧ ٲ(ʮ) Ӷ ѧ

1һӼƽ d ıʽӵģͣ 3 3 d V0 M 4 ѡɹʽɿѡ B ȷ NA 4 ѡһÿѡӸ ܷӼƽ d.磺 A ѡֻӵܸ ÷ӵƽռ V0 A ѡȷͬʱɶѡ CD зжϣC ֻܶȣD ʵ 𰸣B 2ˮѹʱˮӼСƽλZ֮룬ˮ֮ ҲгΪѡ D ȷ 𰸣D 3˶ָҺеĹС޹˶Ƿӵ˶ A 󣻼Ȼ޹΢ûй̶˶켣 B 󣻶ij΢ ԣڲͬʱ̵ٶȴСͷDzȷģ޷ȷijһʱ̵ٶȣ Ҳ޷ٶȣʱͼߣ C ֻ D ȷ 𰸣D 4ͬ 0 ˮ 0 ˮǵʵͬǵķ ͬģ¶ͬ壬ƽͬ 0 ˮ 0 ˮķƽ ͬ 0 ˮΪ 0 ˮҪӼ󣬶Ƿ ƽͬ˷ܲͬҲͬ 𰸣C 5ˮˮʱӼľСͳ D ȷ 𰸣D 6δȫɢȾͿǷֱijǧ򱶣A ȷ еľƾˮܿӷӰֱĴСB 󣻼Ĥʱ ȥвһķ񣬻ʹĤIJֵСC ȷD лʹһҺ ֵС D 𰸣AC 7ѧڶɿ֪Էشӵ崫壬 Ӱ ӵµڲµⲿ Ҫѹİ ܣ BC. 𰸣BC 8ѹʱӣ¶ߣСѹǿ ֻ B ȷ 𰸣B 9⿼ܡѧһɣ 800 Jͬʱų 200 Jѧһɵ UWQ800 J200 J600 J¶ߣ 600 J A ȷ 𰸣A

10ԶסӵΪ㣬Ϊ㣮 ac ΪҷܼСӣ cd ηΪ 󣬶ܼ٣ 𰸣CD 11Ŀ֪ܶ ѣ8102 kg/m3 M0.810 3 kg ͵ 3 M 0.810 V m310 6 m3. 8102 ͵εˮʱ γɵĤΪӲ㣬 ɵĤ V ֱķɵĤS d ʽ d ΪֱĤȣ ΪһֱΪ 10 10 md10 10 m 10 6 S 10 m2104 m2. 10 𰸣B 12(1)˶ˮӶҺС޹˶ B AB ƿˮܶȲͬ(ˮܶȽС) AB ƿˮͬˮ ĸͬˮӼƽҲȣֻ A ȷ 3 000 500 (3)⣬ ˮĦΪ 18 g/mol B ƿˮĦΪ n mol mol 18 3 B ƿˮӸԼΪ NnNA1.01026 𰸣(1)A (2)ȴ A B Ȼнейصĺ۹̶з (3)1.01026 13(1)շӶۺѧɲ׼ȷ⣮ݵ̣ ڵѹǿС¶Ȳ䣬ƽܲ䣬ɲ֪ ΢ΪӼ󣬷ӼС¶Ȳ䣬ӵƽܡƽ ʲ䣬˹ΪԷ̣D ȷ (2)ѧһ֣ץסֻ¶йصصд ¹ܲ䣬ѧһ UQW 0.6 Jһ ͬʱ 0.6 Jܱ֤ܲ䣮¶Ḷ́ 0.2 J. (3)΢㣬 עӵλƼۣ սֻҪ֤ȷɣ Ϊ V0ҺΪ V1 V0 d3 n NAV1n ( V1nd3) m 6 V1 3 V1 3 d NA ( d NA) V0 6m V0 m V1 110 4.(910 5210 4 ) V0 𰸣(1)D (2) 0.6 0.2 (3)110 4(910 5210 4 ) 14⿼ѧһɣ ѹǿ΢۽ͣ ֪ܵʶ㣮b Ϊգ a Ͷⲻѧһ UWQ ֪ھʱ ܲ䣬A B ԣϡ壬ֻжܣ¶Ȳ䣬 pV C ֪ѹǿСC D ԣ T 𰸣BD ٲ(ʮ) 塢Һ

1𰸣B 2ݷʷֲ߿֪¶ T1 T2ӵʶ ijֵֵԽԶԽ٣Ҳ˵㡰ͷмࡱֲ̬ ɣͼ¶ T1 ӦķƽҪС¶ T2 Ӧķƽܣ¶ T1<T2. Ϊ C. 𰸣C 3⿼ѹǿ¶ȵĹϵϸзΪо ϴ¸ˮλʱϸзѹǿ󣬶¶Ȳ䣬ɲ֪ С B ȷ 𰸣B 4ƿ±仯ʼ״̬ѹǿΪ pΪ Vƿ С 2V ʱѹǿСΪ xp pV1.2p(VV)xp(V2V)ãx1.5 ԣѹǿ 50%.Ϊ D. 𰸣D 5䣬λڵķ䣬¶ߣӵƽ ÿӶڵײ ͬʱÿײλڵķҲ࣬ ѹǿ ˱ѡ BD. 𰸣BD 6У¶ߣѹǿ𽥼С״̬ pV c()֪ѡ A ȷ T 𰸣A mgsin 7Իб淽ɵãpSmgsinp0S pp0 S p0 p 󣬸 pV֪ V С׺ͻԣϸߵ T(Mm)gsin б׵֧ F(Mm)gcos ѹǿ޹أ ѡ C ȷ 𰸣C 8(1)׺Ϊ Sʼʱ׶ V12SLѹ ǿ p11.0105 Pa¶Ϊ T127273 (K)300 K. ˶ײ L ߴʱ V2SL¶Ϊ T257273 (K)330 K. p2V2 p1V1 ʱѹǿΪ p2 T2 T1 5 ݵ p22.210 Pa. (2)ѹǿ pp2p12.2105 Pa1.0105 Pa1.2105 Pa. pS S0.001 m2 ѹǿʽ pmg/s ɵû m g 1.21050.001 kg12 kg. 10 𰸣(1)2.2105 Pa (2)12 kg 9(1)ȫװϣȻܷ¼ʼ¶ t1Ȼ ܷ©ʱ¼ڿ¶ t2ȷ˳Ϊ deacb. (2)֪ T1300 KT2360 Kp01.0105 Paܷ䣬ɲ 5 p0 p p0T2 1.010 360 ɿɵã p Pa1.2105 Pa. T1 T2 T1 300 𰸣(1)deacb (2)1.2105 Pa 10(1)ѹװмƿͣλڵķ٣¶Ȳ䣬 ӵƽܲ䣬λʱײڵλϵķ٣ѹǿС (2)Һ x L ƿƿװҺǰѹǿΪ p ң1 atm Ϊ V14 LװСΪ V ҡ䣽(4x)LʱƿѹǿƿѹǿȣΪ

p ɵ±仯 p V ңpV ҡ ƿ忪ʼѹΪ p ף6 atmΪ V ף1 LѹǿΪ pΪ V ס (1x)L ɵ±仯 p V ףpV ס ٢ڴ x2 L 𰸣(1)ѹװмƿͣλڵķ٣¶Ȳ䣬ӵ ƽܲ䣬λʱײڵλ

:
״Ԫ֮·2015-2016ѧ¿α2ϰ:ģ...
״Ԫ֮·2015-2016ѧ¿α2ϰ:ģ.doc__...ʵ MN ˶ȱ˶ :ͼ֪,ʵں...
״Ԫ֮·2014-2015¿αѡ3-2:Ԫ...
״Ԫ֮·2014-2015¿αѡ3-2:Ԫ...:A 2. պȦǿųתʱ, ...:ѹ U1,빦ʲ, I1 ...
״Ԫ֮·һܸϰаӢ
״Ԫ֮· ߿ʱ һܸϰ Ӣ(а) 뵼 ٲ(ʮ...: ѧijѧ, Ѿش֡ a newcomerһ...
״Ԫ֮·һܸϰ¿αʷ뵼
״Ԫ֮·һܸϰ¿αʷ뵼_ʷ_ʷ_н_ר...:B 1-2 :ѧʷڷ]...
״Ԫ֮·2016һָϰ 2໥ ...
״Ԫ֮·2016һָϰ 2໥ ׶ο2__...C ȷ. :C 2 ͼ 2-4 4.(2014 ¿αȫ)ͼ 2-4 ʾ,...
״Ԫ֮·һܸϰ¿αӢュ뵼
״Ԫ֮·һܸϰ¿αӢュ뵼_Ӣ_н_רĿ ¼ ...:B 2. : refuse Ϊܾ; ignore Ϊӡ; miss Ϊ...
״Ԫ֮·2014-2015¿αѡ3-2:Ԫ...
״Ԫ֮·2014-2015¿αѡ3-2:Ԫ(1)__н_...ܵľĦ.ѡ D ȷ,ABC . :D ) 12....
״Ԫ֮·һܸϰ¿αӢ뵼
״Ԫ֮·һܸϰ¿αӢ뵼_Ӣ_н_רĿ ¼ ...:B 2. : refuse Ϊܾ; ignore Ϊӡ; miss Ϊ...
״Ԫ֮·2014-2015¿αѡ3-3:Ԫ...
״Ԫ֮·2014-2015¿αѡ3-3:Ԫ...B.2 D.0.7 :һѹ൱ 10...D ȷ. :AD ) 9.ͼʾһ...
״Ԫ֮·2015-2016ѧ ģۺϲ ...
״Ԫ֮·2015-2016ѧ ģۺϲ ˽̰2__...ʵ MN ˶ȱ˶ :ͼ֪,ʵں...
رǩ: