2¦Ðm
ºÉÁ¿Îª£«q£¬¼ÓÔÚÏÁ·ì¼äµÄ½»±äµçѹÈçͼÒÒËùʾ£¬µçѹֵµÄ´óСΪU0£¬ÖÜÆÚT£½.Ò»Êø
qBT
¸ÃÁ£×ÓÔÚt£½0¡«Ê±¼äÄÚ´ÓA´¦¾ùÔȵØÆ®ÈëÏÁ·ì£¬Æä³õËÙ¶ÈÊÓΪÁã.ÏÖ¿¼ÂÇÁ£×ÓÔÚÏÁ·ìÖÐ
2µÄÔ˶¯Ê±¼ä£¬¼ÙÉèÄܹ»³öÉäµÄÁ£×Óÿ´Î¾¹ýÏÁ·ì¾ù×ö¼ÓËÙÔ˶¯£¬²»¿¼ÂÇÁ£×Ó¼äµÄÏ໥×÷ÓÃ.Çó£º
ͼ7
(1)³öÉäÁ£×ӵĶ¯ÄÜEk£»
(2)Á£×Ó´ÓÆ®ÈëÏÁ·ìÖÁ¶¯ÄÜ´ïµ½EkËùÐèµÄ×Üʱ¼ät0. q2B2R2¦ÐBR2£«2BRd¦Ðm´ð°¸ (1) (2)£ 2m2U0qB½âÎö (1)Á£×ÓÔ˶¯°ë¾¶ÎªRʱ£¬ÓÐ
qvB£½m£¬
12q2B2R2
ÓÖEk£½mv£¬½âµÃEk£½.
22m
(2)ÉèÁ£×Ó±»¼ÓËÙn´Î´ïµ½¶¯ÄÜEk£¬ÔòEk£½nqU0.
qU0
Á£×ÓÔÚÏÁ·ì¼ä×öÔȼÓËÙÔ˶¯£¬Éèn´Î¾¹ýÏÁ·ìµÄ×Üʱ¼äΪ¦¤t£¬¼ÓËÙ¶Èa£½£¬
md12
Á£×Ó×öÔȼÓËÙÖ±ÏßÔ˶¯£¬ÓÐnd£½a¡¤¦¤t£¬
2T
ÓÉt0£½(n£1)¡¤£«¦¤t£¬
2¦ÐBR2£«2BRd¦Ðm
½âµÃt0£½£.
2U0qB
ÃüÌâµãÈý µç³¡Óë´Å³¡µþ¼ÓµÄÓ¦ÓÃʵÀý·ÖÎö
¹²Í¬Ìص㣺µ±´øµçÁ£×Ó(²»¼ÆÖØÁ¦)ÔÚ¸´ºÏ³¡ÖÐ×öÔÈËÙÖ±ÏßÔ˶¯Ê±£¬qvB£½qE. 1.ËÙ¶ÈÑ¡ÔñÆ÷
v2R
ͼ8
(1)ƽÐаåÖе糡ǿ¶ÈEºÍ´Å¸ÐӦǿ¶ÈB»¥Ïà´¹Ö±.(Èçͼ8)
E
(2)´øµçÁ£×ÓÄܹ»ÑØÖ±ÏßÔÈËÙͨ¹ýËÙ¶ÈÑ¡ÔñÆ÷µÄÌõ¼þÊÇqvB£½qE£¬¼´v£½. B(3)ËÙ¶ÈÑ¡ÔñÆ÷Ö»ÄÜÑ¡ÔñÁ£×ÓµÄËٶȣ¬²»ÄÜÑ¡ÔñÁ£×ӵĵçÐÔ¡¢µçºÉÁ¿¡¢ÖÊÁ¿. (4)ËÙ¶ÈÑ¡ÔñÆ÷¾ßÓе¥ÏòÐÔ.
E
Àý3 Èçͼ9ËùʾÊÇÒ»ËÙ¶ÈÑ¡ÔñÆ÷£¬µ±Á£×ÓËÙ¶ÈÂú×ãv0£½Ê±£¬Á£×ÓÑØͼÖÐÐéÏßˮƽÉä³ö£»
BÈôijһÁ£×ÓÒÔËÙ¶ÈvÉäÈë¸ÃËÙ¶ÈÑ¡ÔñÆ÷ºó£¬Ô˶¯¹ì¼£ÎªÍ¼ÖÐʵÏߣ¬Ôò¹ØÓÚ¸ÃÁ£×ÓµÄ˵·¨ÕýÈ·µÄÊÇ( )
ͼ9
E
A.Á£×ÓÉäÈëµÄËÙ¶ÈÒ»¶¨ÊÇv> BE
B.Á£×ÓÉäÈëµÄËٶȿÉÄÜÊÇv< B
C.Á£×ÓÉä³öʱµÄËÙ¶ÈÒ»¶¨´óÓÚÉäÈëËÙ¶È D.Á£×ÓÉä³öʱµÄËÙ¶ÈÒ»¶¨Ð¡ÓÚÉäÈëËÙ¶È ´ð°¸ B 2.´ÅÁ÷Ìå·¢µç»ú
ͼ10
(1)ÔÀí£ºÈçͼ10Ëùʾ£¬µÈÀë×ÓÆøÌåÅçÈë´Å³¡£¬Õý¡¢¸ºÀë×ÓÔÚÂåÂ××ÈÁ¦µÄ×÷ÓÃÏ·¢Éúƫת¶ø¾Û¼¯ÔÚA¡¢B°åÉÏ£¬²úÉúµçÊƲËü¿ÉÒÔ°ÑÀë×ӵĶ¯ÄÜͨ¹ý´Å³¡×ª»¯ÎªµçÄÜ. (2)µçÔ´Õý¡¢¸º¼«Åжϣº¸ù¾Ý×óÊÖ¶¨Ôò¿ÉÅжϳöͼÖеÄBÊÇ·¢µç»úµÄÕý¼«.
(3)µçÔ´µç¶¯ÊÆU£ºÉèA¡¢BƽÐнðÊô°åµÄÃæ»ýΪS£¬Á½¼«°å¼äµÄ¾àÀëΪl£¬´Å³¡´Å¸ÐӦǿ
¶ÈΪB£¬µÈÀë×ÓÆøÌåµÄµç×èÂÊΪ¦Ñ£¬ÅçÈëÆøÌåµÄËÙ¶ÈΪv£¬°åÍâµç×èΪR.µ±Õý¡¢¸ºÀë×ÓËùU
Êܵ糡Á¦ºÍÂåÂ××ÈÁ¦Æ½ºâʱ£¬Á½¼«°å¼ä´ïµ½µÄ×î´óµçÊƲîΪU(¼´µçÔ´µç¶¯ÊÆ)£¬Ôòq£½
l
qvB£¬¼´U£½Blv.
l
(4)µçÔ´ÄÚ×裺r£½¦Ñ. SU
(5)»Ø·µçÁ÷£ºI£½. r£«R
Àý4 (¶àÑ¡)´ÅÁ÷Ìå·¢µçÊÇÒ»ÏîÐÂÐ˼¼Êõ£¬Í¼11ÊÇËüµÄʾÒâͼ£¬Æ½ÐнðÊô°åA¡¢C¼äÓÐÒ»ºÜÇ¿µÄ´Å³¡£¬½«Ò»ÊøµÈÀë×ÓÌå(¼´¸ßÎÂϵçÀëµÄÆøÌ壬º¬ÓдóÁ¿Õý¡¢¸º´øµçÀë×Ó)ÅçÈë´Å³¡£¬Á½¼«°å¼ä±ã²úÉúµçѹ£¬ÏÖ½«A¡¢CÁ½¼«°åÓëµç×èRÏàÁ¬£¬Á½¼«°å¼ä¾àÀëΪd£¬Õý¶ÔÃæ»ýΪS£¬µÈÀë×ÓÌåµÄµç×èÂÊΪ¦Ñ£¬´Å¸ÐӦǿ¶ÈΪB£¬µÈÀë×ÓÌåÒÔËÙ¶ÈvÑØ´¹Ö±´Å³¡·½ÏòÉäÈëA¡¢CÁ½°åÖ®¼ä£¬ÔòÎȶ¨Ê±ÏÂÁÐ˵·¨ÖÐÕýÈ·µÄÊÇ( )
ͼ11
A.¼«°åAÊǵçÔ´µÄÕý¼« B.µçÔ´µÄµç¶¯ÊÆΪBdv
BdvSRC.¼«°åA¡¢C¼äµçѹ´óСΪ
RS£«¦ÑdBdv
D.»Ø·ÖеçÁ÷Ϊ R´ð°¸ BC
½âÎö µÈÀë×ÓÌåÅçÈë´Å³¡£¬´øÕýµçµÄÀë×ÓÒòÊܵ½ÏòϵÄÂåÂ××ÈÁ¦¶øÏòÏÂƫת£¬´ø¸ºµçµÄÀë×ÓÏòÉÏƫת£¬¼´¼«°åCÊǵçÔ´µÄÕý¼«£¬A´í£»µ±´øµçÀë×ÓÒÔËÙ¶Èv×öÖ±ÏßÔ˶¯Ê±£¬qvB£½
q£¬ËùÒÔµçÔ´µç¶¯ÊÆΪBdv£¬B¶Ô£»¼«°åA¡¢C¼äµçѹU£½IR£¬¶øI£½Ed
BdvS£½£¬ÔòdRS£«¦ÑdR£«¦Ñ
S
Bdv
U£½
BdvSR
£¬ËùÒÔC¶Ô£¬D´í.
RS£«¦Ñd
3.µç´ÅÁ÷Á¿¼Æ
(1)Á÷Á¿(Q)µÄ¶¨Ò壺µ¥Î»Ê±¼äÁ÷¹ýµ¼¹Üijһ½ØÃæµÄµ¼µçÒºÌåµÄÌå»ý. (2)¹«Ê½£ºQ£½Sv£»SΪµ¼¹ÜµÄºá½ØÃæ»ý£¬vÊǵ¼µçÒºÌåµÄÁ÷ËÙ.
(3)µ¼µçÒºÌåµÄÁ÷ËÙ(v)µÄ¼ÆËã
Èçͼ12Ëùʾ£¬Ò»Ô²Ðε¼¹ÜÖ±¾¶Îªd£¬Ó÷ǴÅÐÔ²ÄÁÏÖƳɣ¬ÆäÖÐÓпÉÒÔµ¼µçµÄÒºÌåÏòÓÒÁ÷¶¯.µ¼µçÒºÌåÖеÄ×ÔÓɵçºÉ(Õý¡¢¸ºÀë×Ó)ÔÚÂåÂ××ÈÁ¦×÷ÓÃÏ·¢Éúƫת£¬Ê¹a¡¢b¼ä³öÏÖµçÊÆU
²î£¬µ±×ÔÓɵçºÉËùÊܵ糡Á¦ºÍÂåÂ××ÈÁ¦Æ½ºâʱ£¬a¡¢b¼äµÄµçÊƲî(U)´ïµ½×î´ó£¬ÓÉq£½qvB£¬
dU
¿ÉµÃv£½. Bd
ͼ12
(4)Á÷Á¿µÄ±í´ïʽ£ºQ£½Sv£½
¦Ðd2U¦ÐdU
¡¤£½. 4Bd4B
(5)µçÊƸߵ͵ÄÅжϣº¸ù¾Ý×óÊÖ¶¨Ôò¿ÉµÃ¦Õa>¦Õb.
Àý5 (¶àÑ¡)ΪÁ˲âÁ¿Ä³»¯¹¤³§µÄÎÛË®ÅÅ·ÅÁ¿£¬¼¼ÊõÈËÔ±Ôڸó§µÄÅÅÎÛ¹ÜÄ©¶Ë°²×°ÁËÈçͼ13ËùʾµÄÁ÷Á¿¼Æ£¬¸Ã×°ÖÃÓɾøÔµ²ÄÁÏÖƳɣ¬³¤¡¢¿í¡¢¸ß·Ö±ðΪa£½1 m¡¢b£½0.2 m¡¢c£½0.2 m£¬×ó¡¢ÓÒÁ½¶Ë¿ª¿Ú£¬ÔÚ´¹Ö±ÓÚÇ°¡¢ºóÃæµÄ·½Ïò¼Ó´Å¸ÐӦǿ¶ÈΪB£½1.25 TµÄÔÈÇ¿´Å³¡£¬ÔÚÉÏ¡¢ÏÂÁ½¸öÃæµÄÄÚ²à¹Ì¶¨ÓнðÊô°åM¡¢N×÷Ϊµç¼«£¬ÎÛË®³äÂú×°ÖÃÒÔijһËٶȴÓ×óÏòÓÒÔÈËÙÁ÷¾¸Ã×°ÖÃʱ£¬Óõçѹ±í²âµÃÁ½¸öµç¼«¼äµÄµçѹU£½1 V.ÇÒÎÛË®Á÷¹ý¸Ã×°ÖÃʱÊܵ½×èÁ¦×÷Óã¬×èÁ¦Ff£½kLv£¬ÆäÖбÈÀýϵÊýk£½15 N¡¤s/m£¬LΪÎÛË®ÑØÁ÷ËÙ·½ÏòµÄ³¤¶È£¬vΪÎÛË®µÄÁ÷ËÙ.ÏÂÁÐ˵·¨ÖÐÕýÈ·µÄÊÇ( )
2
ͼ13
A.½ðÊô°åMµçÊƲ»Ò»¶¨¸ßÓÚ½ðÊô°åNµÄµçÊÆ£¬ÒòΪÎÛË®ÖиºÀë×ӽ϶à B.ÎÛË®ÖÐÀë×ÓŨ¶ÈµÄ¸ßµÍ¶Ôµçѹ±íµÄʾÊýÒ²ÓÐÒ»¶¨Ó°Ïì C.ÎÛË®µÄÁ÷Á¿(µ¥Î»Ê±¼äÄÚÁ÷³öµÄÎÛË®Ìå»ý)Q£½0.16 m/s
D.ΪʹÎÛË®ÔÈËÙͨ¹ý¸Ã×°Öã¬×ó¡¢ÓÒÁ½²à¹Ü¿ÚӦʩ¼ÓµÄѹǿ²îΪ¦¤p£½1 500 Pa ´ð°¸ CD
½âÎö ¸ù¾Ý×óÊÖ¶¨Ôò£¬Öª¸ºÀë×ÓËùÊܵÄÂåÂ××ÈÁ¦·½ÏòÏòÏ£¬Ôò¸ºÀë×ÓÏòÏÂƫת£¬N°å´ø¸ºµç£¬M°å´øÕýµç£¬ÔòN°åµÄµçÊƱÈM°åµçÊƵͣ¬¹ÊA´íÎó£»×îÖÕÀë×ÓÔڵ糡Á¦ºÍÂåÂ××ÈÁ¦UU
×÷ÓÃÏÂƽºâ£¬ÓÐqvB£½q£¬½âµÃU£½vBc£¬ÓëÀë×ÓŨ¶ÈÎ޹أ¬¹ÊB´íÎó£»ÎÛË®µÄÁ÷ËÙv£½£¬
cBc
3