ÌâÄ¿ÄÚÈÝ
11£®ÈçͼaͼΪ¡°Ñé֤ţ¶ÙµÚ¶þ¶¨ÂÉ¡±µÄʵÑé×°ÖÃʾ¶Èͼ£®É°ºÍɰͰµÄ×ÜÖÊ×îΪm£¬Ð¡³µºÍíÀÂëµÄ×ÜÖÊÀïΪM£®ÊµÑéÖÐÓÃɰºÍɰͱ×ÜÖØÁ¦µÄ´óС×÷ΪϸÏß¶ÔС³µÀÁ¦µÄ´óС£®¢ÙΪÁËʹϸÏß¶ÔС³µµÄÀÁ¦£®ÓÚС³µËùÊܵĺÏÍâÁ¦£¬Ïȵ÷½Ú³¤Ä¾°åÉÏ»¬Âֵĸ߶ȣ¬Ê¹Ï¸ÏßÓ볤ľ°åƽÐУ®½ÓÏÂÀ´»¹ÐèÒª½øÐеÄÒ»Ïî²Ù×÷ÊÇC
A£®½«³¤Ä¾°åˮƽ·ÅÖã¬ÈÃС³µÁ¬×żº¾´©¹ý´òµã¼ÆÊ±Æ÷µÄÖ½´ø£¬¸ø´òµã¼ÆÊ±Æ÷ͨµç£¬µ÷½ÚmµÄ´óС£¬Ê¹Ð¡³µÔÚɰºÍɰͰµÄÇ£ÒýÏÂÔ˶¯£¬´Ó´ò³öµÄÖ½´øÅжÏС³µÊÇ·ñ×öÔÈËÙÖ±ÏßÔ˶¯£®
B£®½«³¤Ä¾°åµÄÒ»¶ËµæÆðÊʵ±µÄ¸ß¶È£¬ÈÃС³µÁ¬×żº¾´©¹ý´òµã¼ÆÊ±Æ÷µÄÖ½´ø£¬¸ø´òµã¼ÆÊ±Æ÷ͨµç£¬µ÷½ÚmµÄ´óС£¬Ê¹Ð¡³µÔÚɰºÍɰͰµÄÇ£ÒýÏÂÔ˶¯£¬´Ó´ò³öµÄÖ½´øÅжÏС³µÊÇ·ñ×öÔÈËÙÖ±ÏßÔ˶¯£®
C£®½«³¤Ä¾°åµÄÒ»¶ËµæÆðÊʵ±µÄ¸ß¶È£¬ÈÃС³µÁ¬×ÅÒѾ´©¹ý´òµã¼ÆÊ±Æ÷µÄÖ½´ø£¬³·È¥É°ºÍɰͰ£¬¸ø´òµã¼ÆÊ±Æ÷ͨµç£¬ÇáÍÆÐ¡³µ£¬´Ó´ò³öµÄÖ½´øÅжÏС³µÊÇ·ñ×öÔÈËÙÖ±ÏßÔ˶¯£®
D£®½«³¤Ä¾°åµÄÒ»¶ËµæÆðÊʵ±µÄ¸ß¶È£®³·È¥Ö½´øÒÔ¼°É°ºÍɰͰ£¬ÇáÍÆÐ¡³µ£¬ÓÃÑÛ×Ðϸ¹Û²ì²¢ÅжÏС³µÊÇ·ñ×öÔÈËÙÖ±ÏßÔ˶¯£®
¢ÚʵÑéÖÐÒª½øÐÐÖÊÁ¿mºÍMµÄѡȡ£¬ÒÔÏÂ×îºÏÀíµÄÒ»×éÊÇC
A£®M=200g£¬m=10g¡¢15g¡¢20g¡¢25g¡¢30g¡¢40g
R£®M=200g£¬m=20g¡¢40g¡¢60g¡¢80g¡¢100g¡¢120g
C£®M=400g£¬m=10g¡¢15g¡¢20g¡¢25g¡¢30g¡¢40g
D£®M=400g£¬m=20g¡¢40g¡¢60g¡¢80g¡¢100g¡¢120g
¢ÛÔÚÑо¿¼ÓËÙ¶ÈaÓëС³µµÄÖÊÁ¿MµÄ¹ØÏµÊ±Ëæ×ÅС³µÄÚíÀÂëÖð½¥¼õÉÙ£¬¸ù¾ÝʵÑéÊý¾Ý×ö³öµÄa-$\frac{1}{M}$ͼÏó×î½Ó½übͼÖеÄD
·ÖÎö 1¡¢Ð¡³µÏ»¬Ê±Êܵ½ÖØÁ¦¡¢Ï¸ÏßµÄÀÁ¦¡¢Ö§³ÖÁ¦ºÍĦ²ÁÁ¦£¬ÒªÊ¹ÀÁ¦µÈÓÚºÏÁ¦£¬ÔòӦƽºâĦ²ÁÁ¦£»
2¡¢µ±É³ºÍɳͰ×ÜÖÊÁ¿Ô¶Ô¶Ð¡ÓÚС³µºÍíÀÂëµÄ×ÜÖÊÁ¿£¬¼´m£¼£¼Mʱ²Å¿ÉÒÔÈÏΪÉþ¶ÔС³µµÄÀÁ¦´óСµÈÓÚɳºÍɳͰµÄÖØÁ¦£»
3¡¢ÉèÉþ×ÓÉÏÀÁ¦ÎªF£¬¶ÔС³µ¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÓУºF=Ma£¬¶ÔɰͰºÍɰÓУºmg-F=ma£¬Óɴ˽âµÃ£ºF=$\frac{mg}{1+\frac{m}{M}}$£¬ÓÉ´Ë¿ÉÖªµ±M£¾£¾Ê±£¬É°ºÍɰͰµÄÖØÁ¦µÈÓÚÉþ×ÓµÄÀÁ¦£¬¾Ý´Ë¸ù¾Ý¸ÃʵÑéʵÑéÎó²î²úÉúµÄÔÒò¼´¿ÉÕýÈ·½â´ð£®
½â´ð ½â£º£¨1£©ÎªÁËʹϸÏß¶ÔС³µµÄÀÁ¦µÈÓÚС³µËùÊܵĺÏÍâÁ¦£¬Ïȵ÷½Ú³¤Ä¾°åÒ»¶Ë»¬Âֵĸ߶ȣ¬Ê¹Ï¸ÏßÓ볤ľ°åƽÐУ®½ÓÏÂÀ´»¹ÐèÒª½øÐеÄÒ»Ïî²Ù×÷Êǽ«³¤Ä¾°åµÄÒ»¶ËµæÆðÊʵ±µÄ¸ß¶È£¬ÈÃС³µÁ¬×ÅÒѾ´©¹ý´òµã¼ÆÊ±Æ÷µÄÖ½´ø£¬³·È¥É°ºÍɰͰ£¬¸ø´òµã¼ÆÊ±Æ÷ͨµç£¬ÇáÍÆÐ¡³µ£¬´Ó´ò³öµÄÖ½´øÅжÏС³µÊÇ·ñ×öÔÈËÙÔ˶¯£¬¼´Æ½ºâĦ²ÁÁ¦£®
¹ÊÑ¡£ºC
£¨2£©µ±m£¼£¼Mʱ£¬¼´µ±É³ºÍɳͰ×ÜÖÊÁ¿Ô¶Ô¶Ð¡ÓÚС³µºÍíÀÂëµÄ×ÜÖÊÁ¿£¬Éþ×ÓµÄÀÁ¦½üËÆµÈÓÚɳºÍɳͰµÄ×ÜÖØÁ¦£®Òò´Ë×îºÏÀíµÄÒ»×éÊÇC£®
¹ÊÑ¡£ºC£®
£¨3£©Ëæ×Å$\frac{1}{M}$Ôö´ó£¬Ð¡³µÖÊÁ¿ÔÚ¼õС£¬Òò´ËС³µÖÊÁ¿²»ÔÙÂú×ãÔ¶´óÓÚɰºÍСɰͰµÄÖÊÁ¿£¬¼ÓËٶȲ»¿ÉÄÜÒ»Ö±¾ùÔÈÔö´ó£¬¼ÓËٶȵÄÔö´ó·ù¶È½«Öð½¥¼õС£¬¹ÊABC´íÎó£¬DÕýÈ·£®
¹ÊÑ¡D£®
¹Ê´ð°¸Îª£º£¨1£©C £¨2£©C £¨3£©D
µãÆÀ ÒªÌá¸ßÓ¦ÓÃÔȱäËÙÖ±ÏߵĹæÂÉÒÔ¼°ÍÆÂÛ½â´ðʵÑéÎÊÌâµÄÄÜÁ¦£¬Ö»ÒªÕæÕýÕÆÎÕÁËʵÑéÔÀí¾ÍÄÜ˳Àû½â¾ö´ËÀàʵÑéÌâÄ¿£¬¶øÊµÑé²½Ö裬ʵÑéÊý¾ÝµÄ´¦Àí¶¼ÓëʵÑéÔÀíÓйأ¬¹ÊÒª¼ÓÇ¿¶ÔʵÑéÔÀíµÄѧϰºÍÕÆÎÕ£®
| A£® | ÎïÌåÀ뿪ÊÖµÄ˲¼ä£¬ÎïÌåµÄ¼ÓËÙ¶È´óÓÚÖØÁ¦¼ÓËÙ¶È | |
| B£® | ÎïÌåÀ뿪ÊÖµÄ˲¼ä£¬ÊֵļÓËÙ¶È´óÓÚÖØÁ¦¼ÓËÙ¶È | |
| C£® | ÊÖÍÐÎïÌåÏòÉÏÔ˶¯µÄ¹ý³ÌÖУ¬ÊÖ¶ÔÎïÌåµÄ×÷ÓÃÁ¦´óÓÚÎïÌå¶ÔÊÖµÄ×÷ÓÃÁ¦ | |
| D£® | ÊÖÍÐÎïÌåÏòÉÏÔ˶¯µÄ¹ý³ÌÖУ¬ÎïÌ彫ÏȺó¾Àú³¬ÖØ×´Ì¬ºÍÊ§ÖØ×´Ì¬ |
| A£® | R3¶Ï· | B£® | R2¶Ì· | C£® | R2¶Ï· | D£® | R1¶Ì· |
| A£® | æÏ¶ðÈýºÅ½øÈëÔ²¹ìµÀºó£¬ÔÂÇòÒýÁ¦²»×ö¹¦ | |
| B£® | æÏ¶ðÈýºÅÔÚ·ÉÏòB´¦µÄ¹ý³ÌÖÐËÙ¶È»áÔ½À´Ô½Ð¡ | |
| C£® | æÏ¶ðÈýºÅÔÚB´¦ÓÉÍÖÔ²¹ìµÀ½øÈëÔ²¹ìµÀʱ±ØÐëµã»ð¼ÓËÙ | |
| D£® | ÓÉÌâÉèÌõ¼þ¿ÉÒÔËã³öæÏ¶ðÈýºÅÈÆÔ·ÉÐÐʱÊܵ½ÔÂÇòÒýÁ¦µÄ´óС |
| A£® | Ëæ×ŵÍμ¼ÊõµÄ²»¶Ï·¢Õ¹£¬ÎÒÃÇ¿ÉÒÔʹζÈÖð½¥½µµÍ£¬²¢×îÖÕ´ïµ½¾ø¶ÔÁã¶È | |
| B£® | ³£Î³£Ñ¹Ï£¬Ò»¶¨ÖÊÁ¿µÄÆøÌå±»¾øÈÈѹËõºó£¬ÆøÌå·Ö×ӵį½¾ù¶¯ÄÜÒ»¶¨Ôö¼Ó | |
| C£® | 1kg0¡æµÄ±ù±È1kg0¡æµÄË®¾ßÓиü¶àµÄ·Ö×ÓÊÆÄÜ | |
| D£® | ÓÃÓÍĤ·¨²â³öÓÍ·Ö×ÓµÄÖ±¾¶ºó£¬Ö»ÒªÔÙÖªµÀÓ͵ÄĦ¶ûÖÊÁ¿£¬¾ÍÄܼÆËã³ö°¢·üÙ¤µÂÂÞ³£Êý |
| A£® | ´ÅͨÁ¿ | B£® | ´ÅͨÁ¿µÄ±ä»¯Á¿ | ||
| C£® | ´ÅͨÁ¿±ä»¯µÄ¿ìÂý | D£® | Ôڴų¡ÖÐÔ˶¯¿ìÂý |