´óѧÎïÀíѧ¿ÎºóϰÌâ´ð°¸ ÕÔ½ü·¼ È«

Ìâ2-2ͼ

X·½Ïò£º Fx?0 x?v0t ¢Ù

Y·½Ïò£º Fy?mgsin??may ¢Ú

t?0ʱ y?0 vy?0

1y?gsin?t22

ÓÉ¢Ù¡¢¢ÚʽÏûÈ¥t£¬µÃ

1y?2gsin??x22v0

2-3 ÖÊÁ¿Îª16 kg µÄÖʵãÔÚxOyÆ½ÃæÄÚÔ˶¯£¬ÊÜÒ»ºãÁ¦×÷Óã¬Á¦µÄ·ÖÁ¿Îª-7 N£¬µ±t£½0ʱ£¬x?y?0£¬x£½-2 m¡¤s£¬µ±t£½2 sª«Ê±ÖʵãµÄ (1)λʸ£»(2)ËÙ¶È£®ª¥

-1

ffx£½6

N£¬y£½

vvy£½0£®Çó

½â£º

ax?(1)

fx63??m?s?2m168 fy?7ay??m?s?2m16

ÓÚÊÇÖʵãÔÚ2sʱµÄËÙ¶È

35vx?vx0??axdt??2??2??m?s?10842?77vy?vy0??aydt??2??m?s?10168

25?7??v??i?j48(2)

m?s?1

?1?1?22r?(v0t?axt)i?aytj22?1?7?13?(?2?2???4)i?()?4j2821613?7???i?jm48

2-4 ÖʵãÔÚÁ÷ÌåÖÐ×÷Ö±ÏßÔ˶¯£¬ÊÜÓëËٶȳÉÕý±ÈµÄ×èÁ¦kv(kΪ³£Êý)×÷Óã¬t=0ʱÖʵãµÄ

ËÙ¶ÈΪ

v0£¬Ö¤Ã÷(1) tʱ¿ÌµÄËÙ¶ÈΪv£½v0ek?()tm£»(2) ÓÉ0µ½tµÄʱ¼äÄÚ¾­¹ýµÄ¾àÀëΪ

mv0mk?()tv()0x£½(k)£Û1-em£Ý£»(3)Í£Ö¹Ô˶¯Ç°¾­¹ýµÄ¾àÀëΪk£»(4)Ö¤Ã÷µ±t?mkʱËÙ

1v¶È¼õÖÁ0µÄe£¬Ê½ÖÐmΪÖʵãµÄÖÊÁ¿£®

?kvdva??mdt ´ð: (1)¡ß

·ÖÀë±äÁ¿£¬µÃ

dv?kdt?vm vdvt?kdt???0m

¼´ v0vv?ktln?lnemv0 v?v0e¡à

0(2)

(3)ÖʵãÍ£Ö¹Ô˶¯Ê±ËÙ¶ÈΪÁ㣬¼´t¡ú¡Þ£¬

k?mt

x??vdt??v0e?tk?mtdt?mv0?kt(1?em)k mv0k

¹ÊÓÐ

x???v0e0k?mtdt?m (4)µ±t=kʱ£¬ÆäËÙ¶ÈΪ

v?v0e1v¼´ËٶȼõÖÁ0µÄe.

km?m?k?v0e?1?v0e

2-5 Éý½µ»úÄÚÓÐÁ½ÎïÌ壬ÖÊÁ¿·Ö±ðΪm1£¬m2£¬ÇÒm2£½2m1£®ÓÃϸÉþÁ¬½Ó£¬¿ç¹ý»¬ÂÖ,Éþ×Ó

1²»¿ÉÉ쳤£¬»¬ÂÖÖÊÁ¿¼°Ò»ÇÐĦ²Á¶¼ºöÂÔ²»¼Æ£¬µ±Éý½µ»úÒÔÔȼÓËÙa£½2gÉÏÉýʱ£¬Çó£º(1) m1ºÍm2Ïà¶ÔÉý½µ»úµÄ¼ÓËÙ¶È£®(2)ÔÚµØÃæÉϹ۲ìm1£¬m2µÄ¼ÓËٶȸ÷Ϊ¶àÉÙ?ª¥

½â: ·Ö±ðÒÔm1,m2ΪÑо¿¶ÔÏ󣬯äÊÜÁ¦Í¼Èçͼ(b)Ëùʾ£®

?(1)Éèm2Ïà¶Ô»¬ÂÖ(¼´Éý½µ»ú)µÄ¼ÓËÙ¶ÈΪa?£¬Ôòm2¶ÔµØ¼ÓËÙ¶Èa2?a?a£»ÒòÉþ²»¿ÉÉ쳤£¬

¹Êm1¶Ô»¬ÂֵļÓËÙ¶ÈÒàΪa?£¬ÓÖm1ÔÚˮƽ·½ÏòÉÏûÓÐÊÜÇ£Á¬Ô˶¯µÄÓ°Ï죬ËùÒÔm1ÔÚˮƽ·½Ïò¶ÔµØ¼ÓËÙ¶ÈÒàΪa?£¬ÓÉÅ£¶Ù¶¨ÂÉ£¬ÓÐ

m2g?T?m2(a??a)

T?m1a?

Ìâ2-5ͼ

ÁªÁ¢£¬½âµÃa??g·½ÏòÏòÏ (2) m2¶ÔµØ¼ÓËÙ¶ÈΪ

a2?a??a?g2 ·½ÏòÏòÉÏ

??'?m1ÔÚË®Ãæ·½ÏòÓÐÏà¶Ô¼ÓËÙ¶È£¬ÊúÖ±·½ÏòÓÐÇ£Á¬¼ÓËÙ¶È£¬¼´a¾ø?aÏà?aÇ£

g25a1?a??a?g??g42 ¡à

a1??arctan?arctan?26.6oa?2£¬×óÆ«ÉÏ£®

?v?m2-6Ò»ÖÊÁ¿ÎªµÄÖʵãÒÔÓëµØµÄÑö½Ç=30¡ãµÄ³õËÙ0´ÓµØÃæÅ׳ö£¬ÈôºöÂÔ¿ÕÆø×èÁ¦£¬ÇóÖÊ

222µãÂäµØÊ±Ïà¶ÔÅ×ÉäʱµÄ¶¯Á¿µÄÔöÁ¿£®

½â: ÒÀÌâÒâ×÷³öʾÒâͼÈçÌâ2-6ͼ

Ìâ2-6ͼ

ÔÚºöÂÔ¿ÕÆø×èÁ¦Çé¿öÏ£¬Å×ÌåÂäµØË²Ê±µÄÄ©ËÙ¶È´óСÓë³õËÙ¶È´óСÏàͬ£¬Óë¹ìµÀÏàÇÐбÏòÏÂ, ¶øÅ×ÎïÏß¾ßÓжÔyÖá¶Ô³ÆÐÔ£¬¹ÊÄ©ËÙ¶ÈÓëxÖá¼Ð½ÇÒàΪ30£¬Ôò¶¯Á¿µÄÔöÁ¿Îª

oÓÉʸÁ¿Í¼Öª£¬¶¯Á¿ÔöÁ¿´óСΪ£¬·½ÏòÊúÖ±ÏòÏ£®

2-7 Ò»ÖÊÁ¿ÎªmµÄСÇò´Óijһ¸ß¶È´¦Ë®Æ½Å׳ö£¬ÂäÔÚˮƽ×ÀÃæÉÏ·¢Éúµ¯ÐÔÅöײ£®²¢ÔÚÅ׳ö1 s£¬Ìø»Øµ½Ô­¸ß¶È£¬ËÙ¶ÈÈÔÊÇˮƽ·½Ïò£¬ËÙ¶È´óСҲÓëÅ׳öʱÏàµÈ£®ÇóСÇòÓë×ÀÃæÅöײ¹ý³ÌÖУ¬×ÀÃæ¸øÓèСÇòµÄ³åÁ¿µÄ´óСºÍ·½Ïò£®²¢»Ø´ðÔÚÅöײ¹ý³ÌÖУ¬Ð¡ÇòµÄ¶¯Á¿ÊÇ·ñÊØºã? ½â: ÓÉÌâÖª£¬Ð¡ÇòÂäµØÊ±¼äΪ0.5s£®ÒòСÇòΪƽÅ×Ô˶¯£¬¹ÊСÇòÂ䵨µÄ˲ʱÏòϵÄËÙ¶È´óСΪv1?gt?0.5g£¬Ð¡ÇòÉÏÌøËٶȵĴóСÒàΪv2?0.5g£®ÉèÏòÉÏΪyÖáÕýÏò£¬Ôò¶¯Á¿µÄÔöÁ¿

?mv0????p?mv?mv0

????p?mv2?mv1·½ÏòÊúÖ±ÏòÉÏ£¬

´óС

Åöײ¹ý³ÌÖж¯Á¿²»Êغ㣮ÕâÊÇÒòΪÔÚÅöײ¹ý³ÌÖУ¬Ð¡ÇòÊܵ½µØÃæ¸øÓèµÄ³åÁ¦×÷Óã®ÁíÍ⣬Åöײǰ³õ¶¯Á¿·½ÏòбÏòÏ£¬ÅöºóÄ©¶¯Á¿·½ÏòбÏòÉÏ£¬ÕâҲ˵Ã÷¶¯Á¿²»Êغ㣮

??p?mv2?(?mv1)?mg?F?(10?2t)i2-8 ×÷ÓÃÔÚÖÊÁ¿Îª10 kgµÄÎïÌåÉϵÄÁ¦ÎªN£¬Ê½ÖÐtµÄµ¥Î»ÊÇs£¬(1)Çó4sºó£¬

ÕâÎïÌåµÄ¶¯Á¿ºÍËٶȵı仯£¬ÒÔ¼°Á¦¸øÓèÎïÌåµÄ³åÁ¿£®(2)ΪÁËʹÕâÁ¦µÄ³åÁ¿Îª200 N¡¤s£¬

?-1

¸ÃÁ¦Ó¦ÔÚÕâÎïÌåÉÏ×÷Óöà¾Ã£¬ÊÔ¾ÍÒ»Ô­À´¾²Ö¹µÄÎïÌåºÍÒ»¸ö¾ßÓгõËÙ¶È?6jm¡¤sµÄÎïÌå,

»Ø´ðÕâÁ½¸öÎÊÌ⣮

½â: (1)ÈôÎïÌåÔ­À´¾²Ö¹£¬Ôò

??t?4??1?p1??Fdt??(10?2t)idt?56kg?m?si00,ÑØxÖáÕýÏò£¬

????p1?1?v1??5.6m?sim???I1??p1?56kg?m?s?1i ?1ÈôÎïÌåÔ­À´¾ßÓÐ?6m?s³õËÙ£¬Ôò

?tt?F?????p0??mv0,p?m(?v0??dt)??mv0??Fdt0m0ÓÚÊÇ

t??????p2?p?p0??Fdt??p10, ?????v??v1,I2?I1 ͬÀí£¬ 2Õâ˵Ã÷£¬Ö»ÒªÁ¦º¯Êý²»±ä£¬×÷ÓÃʱ¼äÏàͬ£¬Ôò²»¹ÜÎïÌåÓÐÎÞ³õ¶¯Á¿£¬Ò²²»¹Ü³õ¶¯Á¿Óжà´ó£¬

ÄÇôÎïÌå»ñµÃµÄ¶¯Á¿µÄÔöÁ¿(Ò༴³åÁ¿)¾ÍÒ»¶¨Ïàͬ£¬Õâ¾ÍÊǶ¯Á¿¶¨Àí£® (2)ͬÉÏÀí£¬Á½ÖÖÇé¿öÖеÄ×÷ÓÃʱ¼äÏàͬ£¬¼´

I??(10?2t)dt?10t?t2Ò༴ t?10t?200?0 ½âµÃt?10s£¬(t??20sÉáÈ¥)

02t

2-9 Ò»ÖÊÁ¿ÎªmµÄÖʵãÔÚxOyÆ½ÃæÉÏÔ˶¯£¬ÆäλÖÃʸÁ¿Îªª¥

ÇóÖʵãµÄ¶¯Á¿¼°t£½0 µ½½â: ÖʵãµÄ¶¯Á¿Îª

t??2?ª«Ê±¼äÄÚÖʵãËùÊܵĺÏÁ¦µÄ³åÁ¿ºÍÖʵ㶯Á¿µÄ¸Ä±äÁ¿£®

???r?acos?ti?bsin?tj

½«t?0ºÍ

t??2?·Ö±ð´úÈëÉÏʽ£¬µÃ

????p1?m?bj,p2??m?ai,

????p?mv?m?(?asin?ti?bcos?tj)

Ôò¶¯Á¿µÄÔöÁ¿Ò༴ÖʵãËùÊÜÍâÁ¦µÄ³åÁ¿Îª

??????I??p?p2?p1??m?(ai?bj)

?1vm?s02-10 Ò»¿Å×Óµ¯ÓÉǹ¿ÚÉä³öʱËÙÂÊΪ£¬µ±×Óµ¯ÔÚǹͲÄÚ±»¼ÓËÙʱ£¬ËüËùÊܵĺÏÁ¦Îª

F =(a?bt)N(a,bΪ³£Êý)£¬ÆäÖÐtÒÔÃëΪµ¥Î»£º(1)¼ÙÉè×Óµ¯ÔËÐе½Ç¹¿Ú´¦ºÏÁ¦¸ÕºÃΪÁ㣬

ÊÔ¼ÆËã×Óµ¯×ßÍêǹͲȫ³¤ËùÐèʱ¼ä£»(2)Çó×Óµ¯ËùÊܵijåÁ¿£®(3)Çó×Óµ¯µÄÖÊÁ¿£®

½â: (1)ÓÉÌâÒ⣬×Óµ¯µ½Ç¹¿Úʱ£¬ÓÐ

F?(a?bt)?0,µÃ

(2)×Óµ¯ËùÊܵijåÁ¿

t?ab

t1I??(a?bt)dt?at?bt202

t?½«

ab´úÈ룬µÃ

a2I?2b

(3)Óɶ¯Á¿¶¨Àí¿ÉÇóµÃ×Óµ¯µÄÖÊÁ¿

2-11 Ò»ÅÚµ¯ÖÊÁ¿Îªm£¬ÒÔËÙÂÊv·ÉÐУ¬ÆäÄÚ²¿Õ¨Ò©Ê¹´ËÅÚµ¯·ÖÁÑΪÁ½¿é£¬±¬Õ¨ºóÓÉÓÚըҩʹµ¯Æ¬Ôö¼ÓµÄ¶¯ÄÜΪT£¬ÇÒÒ»¿éµÄÖÊÁ¿ÎªÁíÒ»¿éÖÊÁ¿µÄk±¶£¬ÈçÁ½ÕßÈÔÑØÔ­·½Ïò·ÉÐУ¬ÊÔÖ¤ÆäËÙÂÊ·Ö±ðΪª¥

Ia2m??v02bv0

2kT2Tv+m, v-km

ÁªÏµ¿Í·þ£º779662525#qq.com(#Ìæ»»Îª@)