1、 第26届北京市高中力学竞赛决赛试题 （景山学校杯） g1078g573g3745g12464g20174g948g25g4677g20174g952g8709g4677g20174g27g2108g952g1959g23g27g2108g949g31. g2375g1244g3416g3424g10803g16024g19858g11444g1405g13726g13526g7263g1100g13567 117g451g2375g13532 37g712g14811g7135g12289g11444g1405g13726g13526g7263g1100g13567 37g451g2375g
2、1353256.g6558g6357g18051g16932g712g1168g17921g5283g1131g5213g16849g2114g14811g7135g12289g7206g19492g1082g242410g9961g3416g14811g7135g12289g3373g19573g1955g13099g4502g19602g1134g15996g6357g2682.g16901g1376g16849g3416g2375g1244g11444g7206g19492g5316g7263 g712g10806g11105g7263 . 2. g4018g33741g6256g121
3、38g712g1913g9473g17816g18051PABCDEg11105g11556g17816g18051g2748g1108g1114g2426g5556g3447g11560g2620g11444g3382g5463g17816g18051g17934g6613g13884g6208. g4671g9473g3463g11105g20744hg11444Pg9961g18426g7022g9473g1083g712g7184g16874hg2566g1413g1644g712g9473g3463g1085g1354g14177g12267g17816g18051g11444g18
4、200g2102g7263 g712g2591g14125g7472g1912g14177g12267g17816g18051g11444g18200g2102g7263 g712g13567g17911g16917g18200g2102g1147g2622g2591g14125g14177g12267g17816g18051g11444g18200g2102g7263 . 3. g4018g33742g6256g12138g712g1072g3463g4598g5334g1130g8804g4598g5334g114441/2g11444g3713g7113g3463g17934g6613g
5、2144g17835g5481g12887g11444g1072g12575g712g5481g12887g2582g1072g12575g3370g4554g3416g7846g5317g712g3713g7113g3463g4540g1944g9128g8913g3416g8804g1117g7206g5481g12887g1384g193755mmg452g4018g7628g8804g7846g1301g2256g17999g5334 ga 21= g2352g2256g17999g1082g2423g712g3713g7113g3463g17902g2144g12387g4554g1
6、0470g5681g2622g5481g12887g1384g19375 mmg712g10806g11105g7263 g452 4. g1411g1842960kgg11444g11805g17409g17920g2264g2696g712g341650mg11444g8708g17291g1117g712g17319g17409g2622g114441.0sg1973g2256g17999g712g2622g7573g2352g17999g712g135678.0sg17409g2144g13560g9961. g6209g1308g2591g1376g12743g2090g17920g
7、2264g2696g3416g17409g2264g1117g11444g7472g3927g2255g10679g7263 W.g708g1549g11145g1108g1405g7481g7032g7072g4487g709 5. g7481g1072g12285g13603g13099g2459g7247g712g8701g7247g3416g11934g4554g11444g17816g18051g1082g17920g2264g712g8701g7247g1082g11096g13558g13603g5852g2618g1072g1114g4480g7247g712g4018g337
8、43g6256g12138. g12387g4554g7206g8701g7247g2748g4480g7247g19492g11444g13558g13603g7145g2625g5316g6455g2625g3424g5619g712g1398g7481g7206g4480g7247g1354g2561g11087g6774g2264g712g4480g7247g1082g7184g2264g2251g16117g13726g712g1130g9144g19604g6774g2264g1455g13558g13603g7145g2625g6455g2625g3424g5619g712g25
9、91g18423g2566g11444g6618g7149g7263 g712 g10806g11105g7263 . 图2 h A B CDE F OOR R R R R 图1 P g33745 A B C D v1 v1 v2 x y 6. g4018g33744g6256g12138g712g1072g21827g17822g7022g3416g12999g13065g3424g19858g1082g712g2595g17897g13143g19856g1913g9473g11444g12550g11556g3785g3825g712g21827g17822g18429g18431g10
10、85g16849g712g1958g1082g11105g13603g13138g5852g2618g1072g18429g10393Gg712g5154g11797r =R/3g712g21827g17822g1086g3424g19858g19492g11444g6809g6934g3344g7072g1130g712g21827g17822g3892g1214g19849g8594g5283g16017g10470g5681. g4018g7628g3790g3927rg712g1958g1286g7569g1318g1085g2568g712g21827g17822g7263g2646
11、g14125g3892g1214g5283g16017g10470g5681g731 g12676g726 g712 g10806g11105g7263 . g1218g573g16855g12749g20174g948g1959g20g19g21g2108g949g37.g70816g2102g709g4018g33745g6256g12138g712g10803g1086g2592g19558g11560g12000g11444g5778g3901g13099g7072g1130e )( g6613g17921g17999g5334g2102g12267g17999g5334 e= g71
12、2g8703g13527g2592g19558g11444g4589g5334g2748g20744g5334g11560g2620g712g3447g12665g1214 lg712g16917g10803g3416g2592g19558g1082g5481g17443g712g8703g8529g3447g5481g17319g2620g7783g20744g5334g1092g3416g8804g5283g18200g2102g11444g2620g1072g1405g13726g712g2467AB=CDg712g8818g10803g11444g8804g5283g17999g533
13、4g2748g8703g8529g5481g17319g11444g20744g5334g712g10803g1086g2592g19558g19492g7184g6809g6934. 8g714g70816g2102g709g10409g16790g6216g3867g17421g3785S0g712g1301g17999g5334 0 g17319g17443g712g4018g33746g6256g12138g712g1981g11096g14154g17564g3785g19858g1072g8529g712g17627g1411g2568g1130g12550g11556g2625g
14、1082g11444g17920g2264g1301g13591g13597g2423g20744g712g3785g1086g19899g5317g1147g19492g11444g19849g6809g6934g3344g7072g1130g714g8818g14125g1455g1258g1411g18429g5619g7481g7472g3927g5739g2423g20744g11444g17319g17443g16386. 图6 S0 g33744 图3 g8701g7247 g4480g7247 g3424g5619 9g714g70820g2102g709g4018g33747
15、g6256g12138g712Ag451Bg451Cg451Dg451Eg1220g1114g7538g6320g9540g2696g3416g17934g13597g19856g17921g7022g13726g11444g17443g7599g1082g16024g9540g7538g6320g714g1286g1308g2612g14362g11444g17240g18431g2102g2139g1130m1g712m2g712m3g712m4g2748m5.Ag9540g2696g1278h1g20744g5334g17443g2144g12636g1072g1114g17443g75
16、99g1082. Bg451Cg451Dg6613g11632g1072g1114g1114g16091g12550g11556g2625g1082g5481g17319g2622g2552g12550g11556g14957g1083g2144g11560g18155g11444g17443g7599g1082g714g17443g7599g11444g17240g18431g2591g1301g5677g11157g712g16901g8818Eg9540g2696g16091g5481g17319g11444g20744g5334h5g7263g3914g4673g731 10. g70
17、825g2102g709g4018g33748g6256g12138g712g1072g7785g17240g18431g2591g1301g5677g11157g11444g13558g7542g712g19375g11302lg712g1108g12575g2748g1117g5619g3892g2102g2139g3370g17934g11632g17240g18431g1130mg11444g4671g10803Bg451Dg2748Cg712g5424g4091g7206g19849g8594g3416g1913g9473g11444g8804g5283g7804g19858g108
18、2. g7804g19858g1082g2582g7481g1072g17240g18431g1130Mg11444g4671g10803Ag712g1301g1072g13577g4554g17999g5334v0g8943g3506g11556g1214g7542DBg11444g7145g2625g1086g2595g12575g4671g10803Bg1420g5481g5719g12000g6862. g8818g2122g12000g2622g4671g10803Ag451Bg451Cg451Dg11444g17999g5334g712g5286g16918g13558g16856
19、g16874g1301g2622g2591g14125g2561g11087g11444g17920g2264g5877g2021. 11.g70825g2102g709g4018g33749g6256g12138g712g1072g3447g2352g3382g11528g712g17240g18431g1130Mg712g2426g5556g1130Rg712g19849g8594g7022g3416g1072g1913g9473g8804g5283g3424g19858g1082g712g1117g5619g1085g3370g4554. g17240g18431g1130mg11444
20、g1258g712g2125g4091g19849g8594g12553g3416g3382g11528g17897g13640g1082g708g1258g2591g11579g1420g17240g9961g709g712g5507g1258g1301g11560g4649g17999g10679ug8943g3382g11528g17897g13640g17312g2264g2622g712g11528g11444g17820g2264g16386g17999g5334g3927g4671g113023m um M R = + g712g8818g11528g5619Og11444g17
21、999g5334g3927g4671. 图7 O R A m 图9 m m m M D B C A V0 g33748 第26届北京市高中力学竞赛决赛试题答案 （景山学校杯） g1078g573g3745g12464g20174g31g714g1083g24243g9961g3914g7082g2102g709g17g3424g10803g11105g16303g2625g1100g14362g17820g71224g4671g7206g17820g1072g2712g712g13567g5334g1130360g1000g712g8703g1965215g1000g51501g4671g72
22、06g712117g1000-37g1000=80g1000g712g135265g1114g3914g4671g7206g7086g2102g709g17 2g714Ag279Bg279C g7082g2102g709 g17 Cg279Dg7083g2102g709 . Eg279F g7083g2102g709. 3g7147.5 g7082g2102g709g17 g8804g2748g3713g7113g3463g18221g17333g18429g712F g5481=F g9118-m g3713g708g+ag709=g708g178g8804-g178g3713g709V g
23、3713g708g+ag709g7086g2102g709g17 4g7142.7 103 g7088g2102g709 a= Pm=mav= W3107.232032060 = 5g714g4480g7247g6774g2264g7472g1406g3892g7022g13603g712g7472g20744g3892g7014g13603 g712g7022g13603g7206g13603g6393g2251g4649g4480g7247g1674g17231g2255g712g7014g13603g7206g1674g8595g2255g712g2426g1114g2712g7503g
24、1973g17231g2255g13581g4649g1644g3927g1214g8595g2255g712g6393g2251g5739g2255g1130g17231g712g4480g7247g7530g7904g14125g2047g4671g17 g7088g2102g709 6. g14125g712 g1085g14125g7082g2102g709 g17 g5283g16017g7145g12347g1130fR=Grg712 g712g5283g16017g7206 g7086g2102g709 g1218g573g16855g12749g20174g37g451g164
25、03g726g10803g8703g8529g5481g17319g11444g17999g5334v1g18221g11560g2620g712g8703g8529g14957g3424g11444g17999g5334v2g1167g11560g2620g712g11105g14125g18431g4536g5762g726 22212121 mvmglmv =+ glvvvvglvv yxyx 2,2 212122222122 =+= g7082g2102g709 g11105g10379g20143g12000g6862g1948g5439g726 yy evv 21 = g7082g
26、2102g709 g3416g8804g5283g7145g2625g2264g18431g4536g5762g726 xxxx vvmvmv 2121 , = g11105g311g312g313g2591g8818g5575g726 )2(12 )2(,12 2221 分分 eglveglev yy = g5283g6347g1948g5439g726 ， 221111 , gttvytvlgtvv yxyy +=+= T2 T1 T1T2 g1300vy=v2yg712g11105g314g2591g8818g5575g10803g1278g5481g17319g2144g14957g3
27、424g11444g7206g19492g726 )1()1(2112212egelgeeglgvvt yy+=+= g7082g2102g709 g1299g1941g315g1117g2467g2591g8818g5575g10803g11444g8804g5283g17999g5334g726 )1(2)1()1(2)1()1()1(2)1()1(2/1 eeglellegegelegelltlvx +=+=+= g7082g2102g709 g1300vy=0g712g11105g314g2591g8818g5575g10803g17902g7472g3927g20744g5334g6
28、256g19760g7206g19492g726 )1(2112221eglegeglegvt y= g1299g1941g316g1117g2467g2591g8818g5575g10803g6256g14125g17902g2144g11444g7472g3927g20744g5334g726 leegeg lgeeg leegley 222222 1)1(221)1(212=+= g7084g2102g709 8g451g2102g7616g2748g16403g726g3416g16403g12676g7516g20168g7206g712g8984g5951g6809g6934g22
29、51g11444g2018g18431g17932g3927g1214g1258g1411g18429g2251g11444g2018g18431g712g6339g1407g1131g16305g3344g13136g5677g11157g8529g16305g3344g13136g712g7263g13567g5224g11096g2144g11444g6267g8677g17 g1258g1301g16386g17319g17443g712g8804g5283g2125g17999g5334g2748g12550g11556g2125g17999g5334g2102g2139g1130
30、0 0 cosx = g712 0 0 siny = g1278g17319g17443g2144g17564g3785g7206g12458g1117g20238g15996g11444g7206g19492g1130 00 cosst = g2121g1258g17564g3785g2173g12550g11556g7145g2625g11444g17999g5334g1130 00 00sin cosy y sgt g = = g1258g18429g5619g2423g20744g726 2 2 20 0 01 0 0 00 0 01 1 1sin ( ) tan ( )2 cos 2
31、 cos 2 cosys s sh t gt g s g = = = g7086g2102g709 g16878g1258g17564g3785g11444g7206g19492g1130g440tg712g3344g440tg5560g4671g712g2121g19849g6809g6934g2251g11444g2018g18431g17932g3927g1214g1258g1411g18429g2251g11444g2018g18431g712g2467 f GI I g712g11105g2264g18431g4554g10806g5575g726 f yI N t m = = g1
32、3884g3416g8804g5283g7145g2625g2620g7783g11105g2264g18431g4554g10806g2591g11797g726 cosx x oN t m m m = = = g7083g2102g709 g1258g17564g3785g2622g14823g5575g12550g11556g2625g1082g11444g17999g5334g726 00 00sin coscosy y y gs = + = + g1258g17564g3785g2622g1981g1082g2423g11444g20744g5334 2002 2 20 20 02
33、0 00(sin cos ) cos (sin cos ) 1tan ( )2 2 2 2 cosygssh s s gg g g + + = = = + g1258g1411g18429g5619g1082g2423g11444g5739g20744g5334g7262 201 2 0(sin cos )2H h h sg += + = g1300tan = g712g2121 g4649 0 g451s0g1072g4554g7206g712g5507 2 + = g7206Hg7472g3927g714 g2467 1arctan = g7206g712g1258g1411g11444g
34、18429g5619g5739g2423g20744g7472g3927g714g7087g2102g709 9g451 g16403g726g20422g1912g6209g1308g8984g5951g1072g1083g3374g1117g11444g13832g7599g712g1117g19492g7263g1072g1114g7184g19584g18429g11444g7007g7713g714Ag9540g2696g17443g2144g13832g7599g11444g1072g12575g712g2620g7206g6330Bg9540g2696g5481g2144g124
35、58g1117g712g6209g1308g2591g1301g11579g1420g7263g9540g2696g19492g256g17994g17911g257g13832g7599g11444g12000g6862g714g1655g4554g12000g6862g11444g6449g13597g7206g19492g5560g11805g712g11105g8596g6209g1308g2591g1301g1085g13875g15489 g18429g2251g4649g12000g6862g7516g17627g11444g5537g2813g712g3344g1130g341
36、6g12000g6862g11444g7206g19492g440t g18428g712g8703g1072g1114g9540g2696g2748g18429g2251g11560g1955g11444g2018g18431g11801g708g4649g13832g7599g1117g5619g16849g12743g709g1086g440tg6208g8595g8708g712g7263g19854g5224g4671g11444g714 g12000g6862g7206g13832g7599g7007g9961g7263g1085g2264g11444g712g6209g1308g
37、2591g1301g18423g11096g16386g2264g18431g4536g5762g4554g5563g7573g11844g12454g714g2552g11105g1214g13832g7599g19854g5224g17835g712g6209g1308g2591g1301g16852g1130g13832g7599g11444g17820g2264g5919g18431g1130g19750g17g7785g6558g20168g1117g2622g19858g11444g16932g7230g2748g1082g19858g11444g1655g16878g714g62
38、09g1308g2591g1301g16852g1130g12000g6862g7206g7530g7904g14125g7263g4536g5762g11444g712g1167g4705g7263g16932g7263g5481g5719g12000g6862g17 g1300 1g16024g12138Ag9540g2696g12000g6862g2622g11444g17999g5334g17 1g1086g3374g1082g11444 1 g6455g2625g2620g1072g1114g7145g2625g17g11105g13099g13583g11444g16386g226
39、4g18431g2748g7530g7904g14125g4536g5762g712g2591g1301g1993g2090 1 1 1 1 2 2m r m r m r = + g7084g2102g709 2 2 21 1 1 1 2 21 1 12 2 2m m m = + g7084g2102g709 2 2 2 2 20 A B C D1 1 1 1 1+2 2 2 2 2M M m m= + +v v mv v vg16403g17929g1114g7145g12347g13556g712g6209g1308g5575g2144g1108g13556g16403 1g709 1 =
40、 g712 2 0 = 2g709 1 211 2m mm m =+ g71212 11 22mm m = + g7082g2102g709 g12636g1072g13556g16403g11560g5507g1214g12000g6862g1147g2173g727g13884g12636g1212g13556g16403g11560g5507g1214g12000g6862g1147g2622g17B g9540g2696g17443g2144g11560g18155g11444g13832g7599g1082g712g3416g12000g6862g11444g11740g19492g
41、17999g5334g7263 2 g17g3g11560g13591g13884g7573g11444g17911g12347g2748g12636g1072g8529g4540g1944g11560g1388g17g3g3344g8596g1301g2622g11444g9540g2696g5481g17319g11444g17999g5334g11560g5316g3424g1130 23 22 32mm m = + g71234 33 42mm m = + g71245 44 52mm m = + g7085g2102g709 g4662g2173g19858g11444g16849g
42、12743g13571g7628g1299g1258g712g2591g5575Eg9540g2696g5481g17319g11444g17999g5334g1130 1 2 3 451 2 2 3 3 4 4 516( )( )( )( )m m m mm m m m m m m m = + + + + g7083g2102g709 g6256g8818g11444g20744g5334h5g2591g1301g2137g11096g1083g5439g16849g12743 1 12gh = g712 5 52gh = g1214g7263g5575g214421 2 3 45 11 2
43、 2 3 3 4 4 516( )( )( )( )m m m mh hm m m m m m m m = + + + + g7082g2102g709 10g451g16403g7616 g311g4671g10803Ag451Bg12000g6862g11740g19492g712g10803Ag6484g2491Bg712g1958g1420g11096g2251g7145g2625g3506g11556g1214g7542g712g1455g10803 B g14823g5575g8943 0v g7145g2625g11444g17999g5334 Bv .g1278g13884g3
44、416g12000g6862g11740g19492g1455g4671g10803 Cg451Dg11444g17999g5334g1167g8943 0v g7145g2625.g4649g17240g9961g13556Bg451Cg451Dg1086Ag13556g6208g11444g13099g13583g712g12000g6862g2173g2622g2264g18431g4536g5762g452g11105g1214g4671g10803Cg1405g1214g11105Bg451Cg451Dg1081g10803g13556g6208g11444g17240g9961g1
45、3556g11444g17240g5619g3892g712g6256g1301g4671g10803 C g11444g17999g5334g1167g4705g7263g17240g9961g13556g11444g17240g5619g17999g5334.g2591g5575g726 0 A C3M M m= +v v v g7081g709 g7084g2102g709 g312g17240g9961g13556Bg451Cg451Dg1086Ag7263g5481g5719g12000g6862g712g12000g6862g2173g2622g17240g9961g13556g1
46、1444g2264g14125g11560g12665g452g12000g6862g2622 Ag451Bg451Cg451Dg11444g17999g5334g2102g2139g1130 Av g451 Bv g451 Cv g451 Dv g712g5575 2 2 2 2 20 A B C D1 1 1 1 12 2 2 2 2Mv Mv mv mv mv= + + + g7082g709 g7084g2102g709 g313g4649g17240g9961g13556 Bg451Cg451Dg3416g12000g6862g11740g19492g712g3416 Bg3892g
47、2567g2144 Ag10803g11444g1420g11096g2251g712g14613g2566 Bg708g1086 Bg10803g18429g2616g11444g12458g19492g3370g4554g9961g709g1130g2546g13875g9961g712g2121g17240g9961g13556 Bg451Cg451D g3416g12000g6862g2173g2622g712g3910g2251g11801g12665g1214g19750g712g6256g1301g17240g9961g13556g16386g2264g18431g4536g57
48、62. g2591g5575 C D0 2ml ml= +v v g7083g709 g7084g2102g709 g314g11105g7542g11444g2122g5719g7569g1318g7481g726 DccB vvvv = g7084g709 g7084g2102g709 m m m M D B C A V0 g11105g7081g709g451g7082g709g451g7083g709g451g7084g709g5439g712g2591g5575 C 045 6MM m= +v v g7085g709 A 05 65 6M mM m=+v v g7086g709 B 0105 6MM m= +v v g7087g709 D 025 6MM m= +v v g7088g709 g7084g2102g709 g315g12000g6862g2622g2612g4671g10803g11444g17920g2264 g12
