ÌâÄ¿ÄÚÈÝ
I¹ØÓÚ¶àÓõç±íµÄʹÓã¬ÏÂÁÐ×ö·¨ÕýÈ·µÄÊÇ
A£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÖ±Á÷µçѹµ²£¬ÓÃͼ1¼×Ëùʾµç·£®ºÏÉÏ¿ª¹ØS£¬Ôò¿É²âСµÆÅÝÁ½¶ËµÄµçѹ
B£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÖ±Á÷µçÁ÷îõ£®ÓÃͼ1ÒÒËùʾµç·£¬ºÏÉÏ¿ª¹ØS£¬Ôò¿É²âͨ¹ýСµÆÅݵĵçÁ÷
C£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÅ·Ä·µ²£¬½øÐе÷Áãºó£¬ÓÃͼ1±ûËùʾµç·£¬¿ª¹ØS±£³Ö¶Ï¿ª£¬Ôò¿É²âСµÆÅݵĵç×è
D£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÅ·Ä·µ²£¬½øÐе÷Áãºó£¬ÓÃͼ1¶¡Ëùʾµç·£¬»á¹Û²ìµ½´Ëʱŷķ±íʾÊýºÜС
IIÏÖÒªÑéÖ¤¡°µ±ºÏÍâÁ¦Ò»¶¨Ê±£¬ÎïÌåÔ˶¯µÄ¼ÓËÙÓëÆäÖÊÁ¿³É·´±È¡±ÕâÒ»ÎïÀí¹æÂÉ£®¸ø¶¨µÄÆ÷²ÄÈçÏ£ºÒ»Çã½Ç¿ÉÒÔµ÷½ÚµÄ³¤Ð±Ã棨Èçͼ2Ëùʾ£©¡¢Ð¡³µ¡¢¼ÆʱÆ÷¡¢Ã׳ߡ¢µ¯»É³Ó£¬»¹Óй³ÂëÈô¸ÉʵÑé²½ÖèÈçÏ£¨²»¿¼ÂÇĦ²ÁÁ¦µÄÓ°Ï죩£¬ÔÚ¿Õ¸ñÖÐÌîÈëÊʵ±µÄ¹«Ê½»òÎÄ×Ö£®
£¨1£©Óõ¯»É³Ó²â³öС³µµÄÖØÁ¦£¬³ýÒÔÖØÁ¦¼ÓËٶȵõ½Ð¡³µµÄÖÊÁ¿M
£¨2£©Óõ¯»É³ÓÑØбÃæÏòÉÏÀС³µ±£³Ö¾²Ö¹£¬²â³ö´ËʱµÄÀÁ¦F£®
£¨3£©ÈÃС³µ×ÔбÃæÉÏ·½Ò»¹Ì¶¨µãA1´Ó¾²Ö¹¿ªÊ¼Ï»¬µ½Ð±Ãæµ×¶ËA2£¬¼ÇÏÂËùÓõÄʱ¼ät£®ÓÃÃ׳߲âÁ¿AÓëA2Ö®¼äµÄ¾àÀës£¬´ÓÔ˶¯Ñ§½Ç¶ÈµÃС³µµÄ¼ÓËÙ¶Èa=
£®
£¨4£©ÔÚС³µÖмӹ³Â룬Ëù¼Ó¹³Âë×ÜÖÊÁ¿Îªm£¬Òª±£³ÖС³µÓë¹³ÂëµÄºÏÍâÁ¦²»±ä£¬Ä㽫ÈçºÎµ÷½ÚA1Ïà¶ÔÓÚA2µÄ¸ß¶Èh£¿
£¨5£©¶à´ÎÔö¼Ó¹³Â룬ÔÚС³µÓë¹³ÂëµÄºÏÍâÁ¦±£³Ö²»±äÇé¿öÏ£¬¿ÉµÃ¹³Âë×ÜÖÊÁ¿mÓëС³µ´ÓA1µ½A2ʱ¼ätµÄ¹ØϵʽΪ£ºm=
-M
-M£®
CD
CD
£®A£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÖ±Á÷µçѹµ²£¬ÓÃͼ1¼×Ëùʾµç·£®ºÏÉÏ¿ª¹ØS£¬Ôò¿É²âСµÆÅÝÁ½¶ËµÄµçѹ
B£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÖ±Á÷µçÁ÷îõ£®ÓÃͼ1ÒÒËùʾµç·£¬ºÏÉÏ¿ª¹ØS£¬Ôò¿É²âͨ¹ýСµÆÅݵĵçÁ÷
C£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÅ·Ä·µ²£¬½øÐе÷Áãºó£¬ÓÃͼ1±ûËùʾµç·£¬¿ª¹ØS±£³Ö¶Ï¿ª£¬Ôò¿É²âСµÆÅݵĵç×è
D£®°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÅ·Ä·µ²£¬½øÐе÷Áãºó£¬ÓÃͼ1¶¡Ëùʾµç·£¬»á¹Û²ìµ½´Ëʱŷķ±íʾÊýºÜС
IIÏÖÒªÑéÖ¤¡°µ±ºÏÍâÁ¦Ò»¶¨Ê±£¬ÎïÌåÔ˶¯µÄ¼ÓËÙÓëÆäÖÊÁ¿³É·´±È¡±ÕâÒ»ÎïÀí¹æÂÉ£®¸ø¶¨µÄÆ÷²ÄÈçÏ£ºÒ»Çã½Ç¿ÉÒÔµ÷½ÚµÄ³¤Ð±Ã棨Èçͼ2Ëùʾ£©¡¢Ð¡³µ¡¢¼ÆʱÆ÷¡¢Ã׳ߡ¢µ¯»É³Ó£¬»¹Óй³ÂëÈô¸ÉʵÑé²½ÖèÈçÏ£¨²»¿¼ÂÇĦ²ÁÁ¦µÄÓ°Ï죩£¬ÔÚ¿Õ¸ñÖÐÌîÈëÊʵ±µÄ¹«Ê½»òÎÄ×Ö£®
£¨1£©Óõ¯»É³Ó²â³öС³µµÄÖØÁ¦£¬³ýÒÔÖØÁ¦¼ÓËٶȵõ½Ð¡³µµÄÖÊÁ¿M
£¨2£©Óõ¯»É³ÓÑØбÃæÏòÉÏÀС³µ±£³Ö¾²Ö¹£¬²â³ö´ËʱµÄÀÁ¦F£®
£¨3£©ÈÃС³µ×ÔбÃæÉÏ·½Ò»¹Ì¶¨µãA1´Ó¾²Ö¹¿ªÊ¼Ï»¬µ½Ð±Ãæµ×¶ËA2£¬¼ÇÏÂËùÓõÄʱ¼ät£®ÓÃÃ׳߲âÁ¿AÓëA2Ö®¼äµÄ¾àÀës£¬´ÓÔ˶¯Ñ§½Ç¶ÈµÃС³µµÄ¼ÓËÙ¶Èa=
2s |
t2 |
2s |
t2 |
£¨4£©ÔÚС³µÖмӹ³Â룬Ëù¼Ó¹³Âë×ÜÖÊÁ¿Îªm£¬Òª±£³ÖС³µÓë¹³ÂëµÄºÏÍâÁ¦²»±ä£¬Ä㽫ÈçºÎµ÷½ÚA1Ïà¶ÔÓÚA2µÄ¸ß¶Èh£¿
¼õС¸ß¶Èh£¬±£³Ö£¨M+m£©h²»±ä
¼õС¸ß¶Èh£¬±£³Ö£¨M+m£©h²»±ä
£¨5£©¶à´ÎÔö¼Ó¹³Â룬ÔÚС³µÓë¹³ÂëµÄºÏÍâÁ¦±£³Ö²»±äÇé¿öÏ£¬¿ÉµÃ¹³Âë×ÜÖÊÁ¿mÓëС³µ´ÓA1µ½A2ʱ¼ätµÄ¹ØϵʽΪ£ºm=
Ft2 |
2s |
Ft2 |
2s |
·ÖÎö£ºIµ±ÓöàÓõç±í²âµçѹºÍµçÁ÷ʱºì±í±ÊÓ¦¸Ã½ÓÁ¬½ÓµçÔ´µÄÕý¼«£¬ºÚ±í±ÊÁ¬½ÓµçÔ´µÄ¸º¼«£¬²âµç×èʱ£¬Ó¦¸Ã°Ñµç×èÓëµç·¶Ï¿ª£¬¶ÁÊýÊDZíÅÌʾÊýÓ뱶Âʵij˻ý£®
IIС³µ×öµÄÊdzõËÙ¶ÈΪÁãµÄÔȼÓËÙÖ±ÏßÔ˶¯£¬¸ù¾ÝÔ˶¯¹æÂÉ£ºs=
at2¿ÉÇó³ö¼ÓËÙ¶Èa£®
IIС³µ×öµÄÊdzõËÙ¶ÈΪÁãµÄÔȼÓËÙÖ±ÏßÔ˶¯£¬¸ù¾ÝÔ˶¯¹æÂÉ£ºs=
1 |
2 |
½â´ð£º½â£»I¡¢A¡¢¶àÓõç±í²âÖ±Á÷µçѹºÍµçÁ÷ʱ£¬ºì±í±ÊÓ¦¸Ã½ÓÁ¬½ÓµçÔ´µÄÕý¼«£¬ºÚ±í±ÊÁ¬½ÓµçÔ´µÄ¸º¼«£¬¹ÊA¡¢B´íÎó£®
C¡¢²âµç×èʱ£¬Ó¦¸Ã°Ñµç×èÓëµç·¶Ï¿ª£¬¶ÁÊýÊDZíÅÌʾÊýÓ뱶Âʵij˻ý£®¹ÊCÕýÈ·£®
D¡¢ÔÚµç±íÄÚ²¿£¬¶àÓõç±íµÄºÚ±í±ÊÓëÄÚ²¿µçÔ´µÄÕý¼«ÏàÁ¬£¬°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÅ·Ä·µ²£¬½øÐе÷Áãºó£¬ÓÃͼ1¶¡Ëùʾµç·£¬ÓÉÓÚ¶þ¼«¹ÜµÄµ¥Ïòµ¼µçÐÔ£¬ËùÒÔ¶àÓõç±í²âÁ¿µÄÊÇ·´Ïòµç×裬¼´¹Û²ìµ½´Ëʱŷķ±íʾÊýºÜС£®¹ÊDÕýÈ·£®
¹ÊÑ¡CD£®
II¡¢£¨3£©Ð¡³µ×ö³õËÙ¶ÈΪÁãµÄÔȼÓËÙÖ±ÏßÔ˶¯£¬¸ù¾ÝÔȱäËÙÖ±ÏßÔ˶¯¹æÂÉÓÐs=
at2£¬
ËùÒÔÓУºa=
£¨4£©Ð¡³µÔÚбÃæÉÏÊܵ½ÊúÖ±ÏòϵÄÖØÁ¦¡¢´¹Ö±½Ó´¥ÃæµÄÖ§³ÖÁ¦£¬ÕâÁ½¸öÁ¦ÔÚ´¹Ö±Ð±Ãæ·½ÏòµÄºÏÁ¦ÎªÁ㣬ËùÒÔÑØбÃæ·½ÏòµÄÁ¦ÎªMgsin¦Á£¬¶øбÃæ¸ß¶ÈΪh£¬
¸ù¾Ý¼¸ºÎ¹ØϵÓÐsin¦Á=
£¬ËùÒÔÓÐС³µÊܵ½µÄºÏÍâÁ¦ÎªF=Mg
£®
ÔÚС³µÖмӹ³Â룬Ëù¼Ó¹³Âë×ÜÖÊÁ¿Îªm£¬Òª±£³ÖС³µÓë¹³ÂëµÄºÏÍâÁ¦²»±ä£¬¼´±£³Ö£¨M+m£©h²»±ä£¬ËùÒÔ¼õС¸ß¶Èh£¬±£³Ö£¨M+m£©h²»±ä£®
£¨5£©¸ù¾ÝÔ˶¯Ñ§¹«Ê½µÃa=
ËùÒÔF=£¨M+m£©a=£¨M+m£©
m=
-M
¹Ê´ð°¸Îª£ºI£®CD
II£®£¨3£©
£¨4£©¼õС¸ß¶Èh£¬±£³Ö£¨M+m£©h²»±ä
£¨5£©
-M
C¡¢²âµç×èʱ£¬Ó¦¸Ã°Ñµç×èÓëµç·¶Ï¿ª£¬¶ÁÊýÊDZíÅÌʾÊýÓ뱶Âʵij˻ý£®¹ÊCÕýÈ·£®
D¡¢ÔÚµç±íÄÚ²¿£¬¶àÓõç±íµÄºÚ±í±ÊÓëÄÚ²¿µçÔ´µÄÕý¼«ÏàÁ¬£¬°Ñ¶àÓõç±íµÄÑ¡Ôñ¿ª¹ØÐýÖÁÊʵ±µÄÅ·Ä·µ²£¬½øÐе÷Áãºó£¬ÓÃͼ1¶¡Ëùʾµç·£¬ÓÉÓÚ¶þ¼«¹ÜµÄµ¥Ïòµ¼µçÐÔ£¬ËùÒÔ¶àÓõç±í²âÁ¿µÄÊÇ·´Ïòµç×裬¼´¹Û²ìµ½´Ëʱŷķ±íʾÊýºÜС£®¹ÊDÕýÈ·£®
¹ÊÑ¡CD£®
II¡¢£¨3£©Ð¡³µ×ö³õËÙ¶ÈΪÁãµÄÔȼÓËÙÖ±ÏßÔ˶¯£¬¸ù¾ÝÔȱäËÙÖ±ÏßÔ˶¯¹æÂÉÓÐs=
1 |
2 |
ËùÒÔÓУºa=
2s |
t2 |
£¨4£©Ð¡³µÔÚбÃæÉÏÊܵ½ÊúÖ±ÏòϵÄÖØÁ¦¡¢´¹Ö±½Ó´¥ÃæµÄÖ§³ÖÁ¦£¬ÕâÁ½¸öÁ¦ÔÚ´¹Ö±Ð±Ãæ·½ÏòµÄºÏÁ¦ÎªÁ㣬ËùÒÔÑØбÃæ·½ÏòµÄÁ¦ÎªMgsin¦Á£¬¶øбÃæ¸ß¶ÈΪh£¬
¸ù¾Ý¼¸ºÎ¹ØϵÓÐsin¦Á=
h |
s |
h |
s |
ÔÚС³µÖмӹ³Â룬Ëù¼Ó¹³Âë×ÜÖÊÁ¿Îªm£¬Òª±£³ÖС³µÓë¹³ÂëµÄºÏÍâÁ¦²»±ä£¬¼´±£³Ö£¨M+m£©h²»±ä£¬ËùÒÔ¼õС¸ß¶Èh£¬±£³Ö£¨M+m£©h²»±ä£®
£¨5£©¸ù¾ÝÔ˶¯Ñ§¹«Ê½µÃa=
2s |
t2 |
ËùÒÔF=£¨M+m£©a=£¨M+m£©
2s |
t2 |
m=
Ft2 |
2s |
¹Ê´ð°¸Îª£ºI£®CD
II£®£¨3£©
2s |
t2 |
£¨4£©¼õС¸ß¶Èh£¬±£³Ö£¨M+m£©h²»±ä
£¨5£©
Ft2 |
2s |
µãÆÀ£ºI±¾Ì⿼²éÁ˵ç±íµÄʹÓ÷½·¨¼°×¢ÒâÊÂÏÊÇÒ»µÀ»ù´¡Ì⣬ѧÉúÒ»¶¨ÒªÊìÁ·ÕÆÎÕ£®
IIÒªÇå³þʵÑéµÄÔÀí£¬ÊµÑéÖÐÐèÒª²âÁ¿µÄÎïÀíÁ¿ÊÇÖ±½Ó²âÁ¿»¹ÊǼä½Ó²âÁ¿£®
ͨ¹ýÎïÀí¹æÂÉ¿ÉÒ԰ѱäÁ¿½øÐÐת»»£¬ÒÔ±ã¸üºÃÑо¿ºÍ²âÁ¿£®
IIÒªÇå³þʵÑéµÄÔÀí£¬ÊµÑéÖÐÐèÒª²âÁ¿µÄÎïÀíÁ¿ÊÇÖ±½Ó²âÁ¿»¹ÊǼä½Ó²âÁ¿£®
ͨ¹ýÎïÀí¹æÂÉ¿ÉÒ԰ѱäÁ¿½øÐÐת»»£¬ÒÔ±ã¸üºÃÑо¿ºÍ²âÁ¿£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿