ÌâÄ¿ÄÚÈÝ
ÔÚ¡°Ì½¾¿Í¹Í¸¾µ³ÉÏñµÄ¹æÂÉ¡±µÄʵÑéÖУ®

£¨1£©Èçͼ1£¬ÒªÊ¹ÏñÄܹ»³ÉÔÚ¹âÆÁµÄÖÐÑ룬Ӧ½«¹âÆÁÏò
£¨2£©ÊµÑé¹ý³ÌÖУ¬µ±ÖòÑæ¾à͹͸¾µ20cmʱ£¬Òƶ¯¹âÆÁÖÁijһλÖã¬ÔÚ¹âÆÁÉϵõ½Ò»µÈ´óÇåÎúµÄÏñ£¬Ôò¸Ã͹͸¾µµÄ½¹¾àÊÇ
£¨3£©½Ó×ÅʹÖòÑæÏò×óÒƶ¯5cm£¬´ËʱӦ¸Ã½«¹âÆÁÏò
£¨4£©Èç¹û½«Í¸¾µµÄÏ°벿·ÖÕÚס£¬¹âÆÁÉϵÄÏñ½«»á
£¨5£©´ÓÀ¯Öòµ½Í¹Í¸¾µ¾àÀëµÈÓÚ2±¶½¹¾à´¦¿ªÊ¼£¬Ïò½¹µã·½ÏòÒƶ¯À¯Öò£¬ÔÚÕâ¹ý³ÌÖУ¬Ïñµ½Í¸¾µµÄ¾àÀë
£¨6£©Èç¹ûËûÔÚʵÑéʱ£¬ÎÞÂÛÔõÑùÒƶ¯¹âÆÁ¶¼ÕÒ²»µ½ÇåÎúµÄÏñ£¬¿ÉÄܵÄÔÒòÊÇ
£¨7£©Ð¡»ª¿´µ½×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±ºÜÏñÒ»¸ö͹͸¾µ£¨Èçͼ2£©£¬¾ÍÏë̽¾¿ËüÊÇ·ñ¾ßÓÐ͹͸¾µµÄÌص㣮ÇëÄã°ïËûÏë³öÒ»¸öÑéÖ¤µÄ·½·¨£®

£¨1£©Èçͼ1£¬ÒªÊ¹ÏñÄܹ»³ÉÔÚ¹âÆÁµÄÖÐÑ룬Ӧ½«¹âÆÁÏò
ÏÂ
ÏÂ
µ÷£¬Ê¹ËüµÄÖÐÐĺÍÖòÑ桢͹͸¾µ
͹͸¾µ
µÄÖÐÐÄÔÚͬһ¸ß¶È
ͬһ¸ß¶È
ÉÏ£»£¨2£©ÊµÑé¹ý³ÌÖУ¬µ±ÖòÑæ¾à͹͸¾µ20cmʱ£¬Òƶ¯¹âÆÁÖÁijһλÖã¬ÔÚ¹âÆÁÉϵõ½Ò»µÈ´óÇåÎúµÄÏñ£¬Ôò¸Ã͹͸¾µµÄ½¹¾àÊÇ
10
10
cm£»£¨3£©½Ó×ÅʹÖòÑæÏò×óÒƶ¯5cm£¬´ËʱӦ¸Ã½«¹âÆÁÏò
×ó
×ó
ÒƵ½Ä³Ò»Î»Öã¨Ñ¡Ìî¡°×ó¡±»ò¡°ÓÒ¡±£©£¬²ÅÄÜÔÚÆÁÉϵõ½µ¹Á¢
µ¹Á¢
¡¢ËõС
ËõС
¡¢Êµ
ʵ
Ïñ£®£¨4£©Èç¹û½«Í¸¾µµÄÏ°벿·ÖÕÚס£¬¹âÆÁÉϵÄÏñ½«»á
±ä°µ
±ä°µ
£®£¨5£©´ÓÀ¯Öòµ½Í¹Í¸¾µ¾àÀëµÈÓÚ2±¶½¹¾à´¦¿ªÊ¼£¬Ïò½¹µã·½ÏòÒƶ¯À¯Öò£¬ÔÚÕâ¹ý³ÌÖУ¬Ïñµ½Í¸¾µµÄ¾àÀë
Ôö´ó
Ôö´ó
£¨Ìî¡°Ôö´ó¡±¡°¼õС¡±¡°²»±ä¡±£©£®£¨6£©Èç¹ûËûÔÚʵÑéʱ£¬ÎÞÂÛÔõÑùÒƶ¯¹âÆÁ¶¼ÕÒ²»µ½ÇåÎúµÄÏñ£¬¿ÉÄܵÄÔÒòÊÇ
ÎïÌå¾à͸¾µµÄ¾àÀëСÓÚÒ»±¶½¹¾à
ÎïÌå¾à͸¾µµÄ¾àÀëСÓÚÒ»±¶½¹¾à
£®£¨7£©Ð¡»ª¿´µ½×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±ºÜÏñÒ»¸ö͹͸¾µ£¨Èçͼ2£©£¬¾ÍÏë̽¾¿ËüÊÇ·ñ¾ßÓÐ͹͸¾µµÄÌص㣮ÇëÄã°ïËûÏë³öÒ»¸öÑéÖ¤µÄ·½·¨£®
·ÖÎö£º£¨1£©ÎªÊ¹ÏñÄÜÍêÕû³ÉÔÚ¹âÆÁµÄÖÐÐÄ£¬±ØÐëʹÖòÑ桢͹͸¾µºÍ¹âÆÁÈýÕßµÄÖÐÐÄÔÚͬһ¸ß¶ÈÉÏ£®
£¨2£©u=2f£¬³Éµ¹Á¢¡¢µÈ´óµÄʵÏñ£»
£¨3£©u£¾2f£¬³Éµ¹Á¢¡¢ËõСµÄʵÏñ£»
£¨4£©Í¹Í¸¾µ³ÉÏñÊôÓÚ¹âµÄÕÛÉäÏÖÏó£¬ÎïÌå·¢³öµÄ¹âÏ߾͹͸¾µÕÛÉäºó£¬»á¾ÛÔÚ͹͸¾µÁíÒ»²àµÄ¹âÆÁÉÏ£¬ÐγÉÎïÌåµÄʵÏñ£»
Èç¹û͹͸¾µµÄ¿Ú¾¶´ó£¬Í¸¹ýµÄ¹â¶à£¬Ïñ¾ÍÁÁ£»¿Ú¾¶Ð¡£¬Í¸¹ýµÄ¹âÉÙ£¬Ïñ¾Í°µ£®
£¨5£©Í¹Í¸¾µ³ÉʵÏñʱ£¬Îï¾à¼õС£¬Ïñ¾àÔö´ó£¬ÏñÔö´ó£®
£¨6£©¹âÆÁÉϵò»µ½ÖòÑæÏñµÄÇé¿öÓÐÈýÖÖ£º¢Ù³ÉµÄÏñÊÇÐéÏñ£¬ÐéÏñÊDz»»á³ÉÔÚ¹âÆÁÉϵģ»¢Ú³ÉʵÏñ£¬µ«ÓÉÓÚÖòÑ桢͹͸¾µ¡¢¹âÆÁÈýÕßµÄÖÐÐIJ»ÔÚͬһ¸ß¶ÈÉÏ£¬ËäÈ»³ÉµÄÊÇʵÏñ£¬µ«¹âÆÁÉÏÏÔʾ²»³öÀ´£»¢Û²»³ÉÏñ£¬µ±ÎïÌåλÓÚ½¹µãÉÏ£¬¼´u=fʱ£¬´Ëʱ²»³ÉÏñ£¬ËùÒÔ¹âÆÁÉÏÒ²µÃ²»µ½ÖòÑæµÄÏñ£®
£¨7£©Èç¹û×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±ÄÜ×ö·Å´ó¾µÊ¹Óã¬×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£®
£¨2£©u=2f£¬³Éµ¹Á¢¡¢µÈ´óµÄʵÏñ£»
£¨3£©u£¾2f£¬³Éµ¹Á¢¡¢ËõСµÄʵÏñ£»
£¨4£©Í¹Í¸¾µ³ÉÏñÊôÓÚ¹âµÄÕÛÉäÏÖÏó£¬ÎïÌå·¢³öµÄ¹âÏ߾͹͸¾µÕÛÉäºó£¬»á¾ÛÔÚ͹͸¾µÁíÒ»²àµÄ¹âÆÁÉÏ£¬ÐγÉÎïÌåµÄʵÏñ£»
Èç¹û͹͸¾µµÄ¿Ú¾¶´ó£¬Í¸¹ýµÄ¹â¶à£¬Ïñ¾ÍÁÁ£»¿Ú¾¶Ð¡£¬Í¸¹ýµÄ¹âÉÙ£¬Ïñ¾Í°µ£®
£¨5£©Í¹Í¸¾µ³ÉʵÏñʱ£¬Îï¾à¼õС£¬Ïñ¾àÔö´ó£¬ÏñÔö´ó£®
£¨6£©¹âÆÁÉϵò»µ½ÖòÑæÏñµÄÇé¿öÓÐÈýÖÖ£º¢Ù³ÉµÄÏñÊÇÐéÏñ£¬ÐéÏñÊDz»»á³ÉÔÚ¹âÆÁÉϵģ»¢Ú³ÉʵÏñ£¬µ«ÓÉÓÚÖòÑ桢͹͸¾µ¡¢¹âÆÁÈýÕßµÄÖÐÐIJ»ÔÚͬһ¸ß¶ÈÉÏ£¬ËäÈ»³ÉµÄÊÇʵÏñ£¬µ«¹âÆÁÉÏÏÔʾ²»³öÀ´£»¢Û²»³ÉÏñ£¬µ±ÎïÌåλÓÚ½¹µãÉÏ£¬¼´u=fʱ£¬´Ëʱ²»³ÉÏñ£¬ËùÒÔ¹âÆÁÉÏÒ²µÃ²»µ½ÖòÑæµÄÏñ£®
£¨7£©Èç¹û×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±ÄÜ×ö·Å´ó¾µÊ¹Óã¬×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£®
½â´ð£º½â£º£¨1£©Èçͼ¹âÆÁλÖÃÆ«ÉÏ£¬Òò´ËҪʹÏñÄܹ»³ÉÔÚ¹âÆÁµÄÖÐÑ룬Ӧ½«¹âÆÁÏòϵ÷£¬Ê¹ËüµÄÖÐÐĺÍÖòÑ桢͹͸¾µµÄÖÐÐÄÔÚͬһ¸ß¶ÈÉÏ£»
£¨2£©ÒÑÖª¹âÆÁÉϵõ½Ò»µÈ´óÇåÎúµÄÏñ£¬ËùÒÔÀ¯ÖòÒ»¶¨ÊÇÔÚ2±¶½¹¾à´¦£¬¼´2f=20cm£¬f=10cm£»
£¨3£©Ê¹ÖòÑæÏò×óÒƶ¯5cmºó£¬´Ëʱu=25cm£¬¼´u£¾2f£¬³Éµ¹Á¢¡¢ËõСµÄʵÏñ£¬´ËʱÏñ¾àf£¼v£¼2f£¬Òò´ËÐèÒª½«¹âÆÁ×óÒÆ£»
£¨4£©Í¹Í¸¾µ³ÉʵÏñʱ£¬ËùÓÐ͸¹ý͸¾µµÄ¹â»á¾Ûµ½¹âÆÁÉϳÉÏñ£¬µ±½«Í¸¾µµÄÏ°벿·Öµ²×¡ºó£¬Õû¸öÎïÌå·¢³öµÄ¹âËäÓÐÒ»²¿·Ö±»µ²×¡£¬µ«×Ü»áÓÐÒ»²¿·Ö¹âͨ¹ýÉϰ벿·Ö͹͸¾µ¶ø»á¾Û³ÉÏñ£¬Òò´Ë£¬ÏñÓëÔÀ´Ïàͬ£»ÓÉÓÚ͸¾µµÄÒ»°ë±»ÕÚס£¬Òò´ËÕÛÉä³öµÄ¹âÏßÓëÔÀ´Ïà±È¼õÉÙÁËÒ»°ë£¬¹ÊÁÁ¶È»á¼õÈõ£®
£¨5£©´ÓÀ¯Öòµ½Í¹Í¸¾µ¾àÀëµÈÓÚ2±¶½¹¾à´¦¿ªÊ¼£¬Ïò½¹µã·½ÏòÒƶ¯À¯Öò£¬´ËʱÎï¾à¼õС£¬ÔòÏñ¾àÔö´ó£¬¼´Ïñµ½Í¸¾µµÄ¾àÀëÔö´ó£¬Ïñ±ä´ó£®
£¨6£©ÎïÌå´Ëʱ¾à͸¾µµÄ¾àÀëÓпÉÄÜÇ¡ºÃΪһ±¶½¹¾à£¬´ËʱÎïÌå²»³ÉÏñ£®ËùÒÔ¹âÆÁÉÏûÓÐÇåÎúµÄÏñ£®
ÎïÌå´Ëʱ¾à͸¾µµÄ¾àÀëÓпÉÄÜСÓÚÒ»±¶½¹¾à£¬ÎïÌå³ÉµÄÊÇÕýÁ¢·Å´óµÄÐéÏñ£¬ÓÉÓÚÐéÏñ²»ÊÇÓÉʵ¼Ê¹âÏß»á¾Û¶ø³É£¬ËùÒÔ¹âÆÁÉÏÒ²²»»áÓÐÇåÎúµÄÏñ£®
ÎïÌå´ËʱµÄ¾àÀ뼴ʹ´óÓÚÒ»±¶½¹¾à£¬³ÉʵÏñ£¬ÈôÀ¯Öò¡¢Í¹Í¸¾µ¡¢¹âÆÁµÄÖÐÐIJ»ÔÚͬһ¸ß¶ÈÉÏ£¬´Ëʱ¹âÆÁÉÏÒ²²»»áÓÐÇåÎúµÄÏñ£®¹ÊÓÐÒÔÏÂÈýÖÖ¿ÉÄÜ£º
¢ÙÎïÌå¾à͸¾µµÄ¾àÀëΪһ±¶½¹¾à£¬ÎïÌå²»³ÉÏñ£»
¢ÚÎïÌå¾à͸¾µµÄ¾àÀëСÓÚÒ»±¶½¹¾à£¬ÎïÌå³ÉµÄÊÇÕýÁ¢·Å´óµÄÐéÏñ£»
¢ÛÀ¯Öò¡¢Í¹Í¸¾µ¡¢¹âÆÁµÄÖÐÐIJ»ÔÚͬһ¸ß¶ÈÉÏ£»
£¨7£©Èç¹û×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£¬ÎïÌå·ÅÔÚ×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±µÄÒ»±¶½¹¾àÒÔÄÚ£¬Ò»¶¨ÄÜÆð·Å´óµÄ×÷Óã®°ÑÊÖ·ÅÔÚ×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±µÄºóÃ棬´ÓÇ°Ãæ¿´ÊÖÊÇ·ñÊÇ·Å´óµÄ£¬Èç¹ûÊÇ·Å´óµÄ£¬Ôò×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£®
¹Ê´ð°¸Îª£º£¨1£©Ï£»Í¹Í¸¾µ£»Í¬Ò»¸ß¶È£»£¨2£©10£»£¨3£©×ó£»µ¹Á¢£»ËõС£»Êµ£»£¨4£©±ä°µ£»
£¨5£©Ôö´ó£»£¨6£©ÎïÌå¾à͸¾µµÄ¾àÀëСÓÚÒ»±¶½¹¾à£»£¨7£©°ÑÊÖ·ÅÔÚ×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±µÄºóÃ棬´ÓÇ°Ãæ¿´ÊÖÊÇ·ñÊÇ·Å´óµÄ£¬Èç¹ûÊÇ·Å´óµÄ£¬Ôò×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£®
£¨2£©ÒÑÖª¹âÆÁÉϵõ½Ò»µÈ´óÇåÎúµÄÏñ£¬ËùÒÔÀ¯ÖòÒ»¶¨ÊÇÔÚ2±¶½¹¾à´¦£¬¼´2f=20cm£¬f=10cm£»
£¨3£©Ê¹ÖòÑæÏò×óÒƶ¯5cmºó£¬´Ëʱu=25cm£¬¼´u£¾2f£¬³Éµ¹Á¢¡¢ËõСµÄʵÏñ£¬´ËʱÏñ¾àf£¼v£¼2f£¬Òò´ËÐèÒª½«¹âÆÁ×óÒÆ£»
£¨4£©Í¹Í¸¾µ³ÉʵÏñʱ£¬ËùÓÐ͸¹ý͸¾µµÄ¹â»á¾Ûµ½¹âÆÁÉϳÉÏñ£¬µ±½«Í¸¾µµÄÏ°벿·Öµ²×¡ºó£¬Õû¸öÎïÌå·¢³öµÄ¹âËäÓÐÒ»²¿·Ö±»µ²×¡£¬µ«×Ü»áÓÐÒ»²¿·Ö¹âͨ¹ýÉϰ벿·Ö͹͸¾µ¶ø»á¾Û³ÉÏñ£¬Òò´Ë£¬ÏñÓëÔÀ´Ïàͬ£»ÓÉÓÚ͸¾µµÄÒ»°ë±»ÕÚס£¬Òò´ËÕÛÉä³öµÄ¹âÏßÓëÔÀ´Ïà±È¼õÉÙÁËÒ»°ë£¬¹ÊÁÁ¶È»á¼õÈõ£®
£¨5£©´ÓÀ¯Öòµ½Í¹Í¸¾µ¾àÀëµÈÓÚ2±¶½¹¾à´¦¿ªÊ¼£¬Ïò½¹µã·½ÏòÒƶ¯À¯Öò£¬´ËʱÎï¾à¼õС£¬ÔòÏñ¾àÔö´ó£¬¼´Ïñµ½Í¸¾µµÄ¾àÀëÔö´ó£¬Ïñ±ä´ó£®
£¨6£©ÎïÌå´Ëʱ¾à͸¾µµÄ¾àÀëÓпÉÄÜÇ¡ºÃΪһ±¶½¹¾à£¬´ËʱÎïÌå²»³ÉÏñ£®ËùÒÔ¹âÆÁÉÏûÓÐÇåÎúµÄÏñ£®
ÎïÌå´Ëʱ¾à͸¾µµÄ¾àÀëÓпÉÄÜСÓÚÒ»±¶½¹¾à£¬ÎïÌå³ÉµÄÊÇÕýÁ¢·Å´óµÄÐéÏñ£¬ÓÉÓÚÐéÏñ²»ÊÇÓÉʵ¼Ê¹âÏß»á¾Û¶ø³É£¬ËùÒÔ¹âÆÁÉÏÒ²²»»áÓÐÇåÎúµÄÏñ£®
ÎïÌå´ËʱµÄ¾àÀ뼴ʹ´óÓÚÒ»±¶½¹¾à£¬³ÉʵÏñ£¬ÈôÀ¯Öò¡¢Í¹Í¸¾µ¡¢¹âÆÁµÄÖÐÐIJ»ÔÚͬһ¸ß¶ÈÉÏ£¬´Ëʱ¹âÆÁÉÏÒ²²»»áÓÐÇåÎúµÄÏñ£®¹ÊÓÐÒÔÏÂÈýÖÖ¿ÉÄÜ£º
¢ÙÎïÌå¾à͸¾µµÄ¾àÀëΪһ±¶½¹¾à£¬ÎïÌå²»³ÉÏñ£»
¢ÚÎïÌå¾à͸¾µµÄ¾àÀëСÓÚÒ»±¶½¹¾à£¬ÎïÌå³ÉµÄÊÇÕýÁ¢·Å´óµÄÐéÏñ£»
¢ÛÀ¯Öò¡¢Í¹Í¸¾µ¡¢¹âÆÁµÄÖÐÐIJ»ÔÚͬһ¸ß¶ÈÉÏ£»
£¨7£©Èç¹û×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£¬ÎïÌå·ÅÔÚ×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±µÄÒ»±¶½¹¾àÒÔÄÚ£¬Ò»¶¨ÄÜÆð·Å´óµÄ×÷Óã®°ÑÊÖ·ÅÔÚ×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±µÄºóÃ棬´ÓÇ°Ãæ¿´ÊÖÊÇ·ñÊÇ·Å´óµÄ£¬Èç¹ûÊÇ·Å´óµÄ£¬Ôò×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£®
¹Ê´ð°¸Îª£º£¨1£©Ï£»Í¹Í¸¾µ£»Í¬Ò»¸ß¶È£»£¨2£©10£»£¨3£©×ó£»µ¹Á¢£»ËõС£»Êµ£»£¨4£©±ä°µ£»
£¨5£©Ôö´ó£»£¨6£©ÎïÌå¾à͸¾µµÄ¾àÀëСÓÚÒ»±¶½¹¾à£»£¨7£©°ÑÊÖ·ÅÔÚ×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±µÄºóÃ棬´ÓÇ°Ãæ¿´ÊÖÊÇ·ñÊÇ·Å´óµÄ£¬Èç¹ûÊÇ·Å´óµÄ£¬Ôò×°ÂúÇåË®µÄ͸Ã÷²£Á§¾Æ±¾ßÓÐ͹͸¾µµÄÐÔÖÊ£®
µãÆÀ£ºÍ¹Í¸¾µ³ÉÏñµÄ¼¸ÖÖÇé¿öºÍ͹͸¾µ³ÉʵÏñµÄʵÑé½áÂÛÊǽâ¾ö͹͸¾µ³ÉÏñÏ°ÌâµÄ»ù´¡ÄÚÈÝ£¬Ò»¶¨ÒªÊìÁ·ÕÆÎÕ£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿