ÌâÄ¿ÄÚÈÝ

£¨1£©¢ñ£®ÔÚ¡°»¥³É½Ç¶ÈµÄÁ½¸öÁ¦µÄºÏ³É¡±ÊµÑéÖУ¬ÓÃÁ½¸öµ¯»É³Ó·Ö±ð¹³×¡Ï¸ÉþÌ×£¬»¥³É½Ç¶ÈµØÀ­ÏðƤÌõ£¬Ê¹ËüÉ쳤µ½Ä³Ò»Î»ÖÃOµã£¬ÎªÁËÈ·¶¨Á½¸ö·ÖÁ¦µÄ´óСºÍ·½Ïò£¬ÕâÒ»²½²Ù×÷ÖбØÐë¼Ç¼µÄÊÇ______
A£®ÏðƤÌõ¹Ì¶¨¶ËµÄλÖá¡¡¡¡¡¡¡¡¡ B£®ÃèÏÂOµãλÖúÍÁ½ÌõϸÉþÌ׵ķ½Ïò
C£®ÏðƤÌõÉ쳤ºóµÄ×ܳ¤¶È¡¡¡¡¡¡¡¡ D£®Á½¸öµ¯»É³ÓµÄ¶ÁÊý
¢ò£®×öʵÑéʱ£¬¸ù¾Ý²âÁ¿½á¹ûÔÚ°×Ö½ÉÏ»­³öÈçͼ1ËùʾµÄͼ£¬ÆäÖÐOΪÏðƤ½îÓëϸÉþµÄ½áµã£®Í¼ÖеÄ______ÊÇF1ºÍF2µÄºÏÁ¦µÄÀíÂÛÖµ£»______ÊÇF1ºÍF2µÄºÏÁ¦µÄʵ¼Ê²âÁ¿Öµ£®
£¨2£©ÔÚÈçͼÒÒͬÖÖ²ÄÁÏÁ½Ä¾°åͨ¹ýһС¶ÎÔ²»¡Á¬½Ó³ÉÒ»¸öбÃæºÍˮƽÃ沿·Ö£¬ÏÖÒª²âÁ¿Õý·½ÌåСÌú¿éA¡¢BºÍÕâľ°å¼äµÄ¶¯Ä¦²ÁÒòÊý¦Ì£¬ÀûÓÃÁËÈçÏÂÆ÷²ÄºÍ·½·¨£º£¨Ë®Æ½²¿·Ö×ã¹»³¤£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£©
¢ñ£®Óà 20 ¸öµÈ·Ö¿Ì¶ÈµÄÓα꿨³ß²â¶¨Ð¡Ìú¿éAµÄ±ß³¤dÈçͼ±û£¬²âµÃ³¤¶ÈΪd=______cm£®
¢ò£®¹âµç¼ÆʱÆ÷ÊÇÒ»ÖÖÑо¿ÎïÌåÔ˶¯µÄ³£ÓüÆʱÆ÷£¬Æä½á¹¹Èçͼ¼×Ëùʾ£¬a¡¢b ·Ö±ðÊǹâµçÃŵļ¤¹â·¢ÉäºÍ½ÓÊÕ×°Ö㬵±ÓÐÎïÌå´Ó a¡¢b ¼äͨ¹ýʱ£¬¹âµç¼ÆʱÆ÷¾Í¿ÉÒÔÏÔʾÎïÌåµÄµ²¹âʱ¼ä£®´Ó¶ø¿ÉÒÔËãµÃÎïÌåµÄËٶȣ®

½«Ð±ÃæÌåÖÃÓÚˮƽ×ÀÃæÉÏ£¬Ð±Ã涥¶Ë P Ðü¹ÒһǦ´¹Ïߣ¬Q Ϊ׶¼âÓë×ÀÃæµÄ½Ó´¥µã£¬1ºÍ 2 Êǹ̶¨ÔÚбÃæÉϵÄÁ½¸ö¹âµçÃÅ£¨ÓëÖ®Á¬½ÓµÄµç·δ»­³ö£©£¬ÈÃСÌú¿éAÓÉPµãÑØбÃ滬Ï£¬Ð¡Ìú¿éͨ¹ý¹âµçÃÅ 1¡¢2 µÄʱ¼ä·Ö±ðΪ¡÷t1¡¢¡÷t2£¬ÓÃÃ׳߲âµÃ l¡¢2 Ö®¼äµÄ¾àÀëΪ L£¬ÔòСÌú¿éÏ»¬¹ý³ÌÖеļÓËÙ¶Èa=______£»£¨ÓÃÌâÖÐ×Öĸ±íʾ£© ÔÙÀûÓÃÃ׳߲â³ö______¡¢______£¬¾Í¿ÉÒÔ²âµÃ¶¯Ä¦²ÁÒòÊý¦Ì1£®
¢ó£®ÈôÔÙ²âÌú¿éBºÍ°å¼ä¶¯Ä¦²ÁÒòÊý¦Ì2ʱ£¬¹âµç¼ÆʱÆ÷³öÏÖ¹ÊÕϲ»ÄÜʹÓã¬ÏÖÖ»ÀûÓÃÃ׳ßÍê³ÉʵÑ飬ÈôÒѲâµÃPQ¸ßΪh£¬ÔòÖ»ÐèÒªÔÙ²â______£®£¨ÒªÇóÖ»ÄÜÔÙ²âÒ»¸öÎïÀíÁ¿£©
²âµÃµÄ¶¯Ä¦²ÁÒòÊý¦Ì2=______£¨ÓÃÒÑÖªÁ¿ºÍ²â¶¨µÄÎïÀíÁ¿Ëù¶ÔÓ¦µÄ×Öĸ±íʾ£©

½â£º£¨1£©I¡¢¸ÃʵÑéµÄʵÑéÄ¿µÄÊÇÑéÖ¤Á¦µÄƽÐÐËıßÐζ¨Ôò£¬Òª¸ù¾ÝÁ½¸öµ¯»ÉÀ­ÏðƤ½îʱÁ½¸öÀ­Á¦µÄ´óСºÍ·½Ïò×ö³öƽÐÐËıßÐÎÇó³öÆäºÏÁ¦´óС£¬È»ºóÓëÒ»¸öµ¯»ÉÀ­ÏðƤ½îʱµÄÀ­Á¦´óС½øÐбȽϣ¬×îºóµÃ³ö½áÂÛ£¬¹ÊÐèÒª¼Ç¼µÄÊÇÁ½µ¯Á¦µÄ´óСºÍ·½Ïò£¬¹ÊAC´íÎó£¬BDÕýÈ·£®
¹ÊÑ¡BD£®
±¾ÊµÑé²ÉÓÃÁË¡°µÈЧ·¨¡±£¬F1ÓëF2µÄºÏÁ¦µÄʵ¼ÊÖµ²âÁ¿ÖµÎªÒ»¸öµ¯»ÉÀ­ÉþÌ×ʱµÄµ¯»ÉµÄµ¯Á¦´óСºÍ·½Ïò£¬¶øÀíÂÛÖµÊÇͨ¹ýƽÐÐËıßÐζ¨ÔòµÃµ½µÄÖµ£®
¹Ê´ð°¸Îª£ºF£¬F¡ä£®
£¨2£©I¡¢Óα꿨³ßµÄÖ÷³ß¶ÁÊýΪ£º2cm£¬Óαê¶ÁÊýµÈÓÚ£º0.05¡Á4mm=0.20mm=0.020cm£¬ËùÒÔ×îÖÕ¶ÁÊýΪ£º2cm+0.20cm=2.020cm£¬¼´2.0200cm£®
¹Ê´ð°¸Îª£º2.020£®
II¡¢Ìú¿éͨ¹ý¹âµçÃÅ1ʱµÄËÙ¶ÈΪ£º£¬Í¨¹ý¹âµçÃÅ2ʱµÄËÙ¶ÈΪ£º£¬
¸ù¾ÝËٶȺÍλÒƹØϵʽ£ºµÃ£º

СÌú¿éÏ»¬¹ý³ÌÖÐÊÜÖØÁ¦¡¢Ö§³ÖÁ¦ºÍĦ²ÁÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵãº
=gsin¦È-¦Ìgcos¦È ¦ÈΪбÃæÇã½Ç£¬ËùÒÔÓУº
¸ù¾Ý¼¸ºÎ֪ʶ¿ÉÖª£ºÔÙÀûÓÃÃ׳߲â³öбÃæµÄ¸ßH£¬Ð±ÃæµÄ³¤S£¬¾Í¿ÉÒÔ²âµÃ¶¯Ä¦²ÁÒòÊý ¦Ì£®
¹Ê´ð°¸Îª£º£»PQµÄ¾àÀëh£¬Ð±Ã沿·Ö³¤s£®
£¨4£©ÈÃСÌú¿éÓɶ¥¶Ë´Ó¾²Ö¹»¬Ï£¬»¬ÖÁˮƽ°åÉϵÄCµãͣϣ¬²â³ö¶¥¶ËµÄ¸ß¶ÈhºÍСÌú¿éÔÚÕû¸ö¹ý³ÌÖеÄˮƽλÒÆl
ÔËÓö¯Äܶ¨ÀíÑо¿Ð¡Ìú¿éÓɶ¥¶Ë´Ó¾²Ö¹»¬Ï£¬»¬ÖÁˮƽ°åÉϵÄCµãͣϣ¬
mgh-¦Ìmgcos¦È?L-¦ÌmgL¡ä=0-0=0£¬LΪбÃæµÄ³¤¶È£¬L¡äΪÔÚˮƽÃæÉÏ»¬ÐеľàÀ룮

Lcos¦ÈΪбÃæÔÚˮƽ·½ÏòµÄ³¤¶È£¬ËùÒÔl=Lcos¦È+L¡äΪСÌú¿éÔÚÕû¸ö¹ý³ÌÖеÄˮƽλÒÆ£®
¼´£º
¹Ê´ð°¸Îª£º»¬¿é×Ô¿ªÊ¼µ½Í£ÏµÄˮƽλÒÆL£¬£®
·ÖÎö£º£¨1£©I¡¢¸ù¾Ý¸ÃʵÑéµÄʵÑéÔ­ÀíÒÔ¼°ÊµÑéÄ¿µÄ¿ÉÒÔÃ÷È·¸ÃʵÑéÐèÒª¼Ç¼µÄÊý¾Ý£»
II¡¢¸ÃʵÑé²ÉÓÃÁË¡°µÈЧ·¨¡±£¬ÓÉÓÚʵÑéÎó²îµÄ´æÔÚ£¬µ¼ÖÂF1ÓëF2ºÏ³ÉµÄʵ¼ÊÖµÓëÓëÀíÂÛÖµ´æÔÚ²î±ð£®
£¨2£©I¡¢Óα꿨³ß¶ÁÊýµÄ·½·¨ÊÇÖ÷³ß¶ÁÊý¼ÓÉÏÓαê¶ÁÊý£¬²»Ðè¹À¶Á£®ÓαêµÄÁã¿Ì¶ÈÏß³¬¹ýÖ÷³ßÉϵĿ̶ÈÊýΪÖ÷³ß¶ÁÊý£¬Óαê¶ÁÊýµÈÓڷֶȳËÒÔ¶ÔÆëµÄ¸ùÊý£®
II¡¢Ìú¿éͨ¹ý¹âµçÃŵÄʱ¼ä·Ç³£Ð¡£¬Òò´Ë¿ÉÒÔƽ¾ùËٶȴúÌæÆäͨ¹ýµÄ˲ʱËٶȣ¬¾Ý´Ë¿ÉÒÔÇó³öÌú¿éͨ¹ý¹âµçÃÅʱµÄËٶȴóС£»Ìú¿é×öÔȱäËÙÖ±ÏßÔ˶¯£¬¸ù¾ÝËٶȺÍλÒƹØϵʽ¿ÉÒÔÇó³öС³µµÄ¼ÓËٶȴóС£®
III¡¢ÔËÓö¯Äܶ¨ÀíÑо¿Ð¡Ìú¿éÓɶ¥¶Ë´Ó¾²Ö¹»¬Ï£¬»¬ÖÁˮƽ°åÉϵÄCµãÍ£ÏÂÁгöµÈʽ£¬½áºÏ¼¸ºÎ¹ØϵÇó½â£®
µãÆÀ£º£¨1£©I¡¢±¾Ì⿼²éÁË¡°»¥³É½Ç¶ÈµÄÁ½¸öÁ¦µÄºÏ³É¡±ÊµÑéÖеĻù±¾²Ù×÷£¬ÊÇÒ»µÀ¿¼²é»ù±¾ÊµÑé²Ù×÷µÄºÃÌ⣮
II¡¢ÕÆÎÕʵÑéÔ­Àí£¬´Ó¶à¸ö½Ç¶ÈÀ´Àí½âºÍ·ÖÎöʵÑ飬Ìá¸ß·ÖÎö½â¾öÎÊÌâµÄÄÜÁ¦£®
£¨2£©I¡¢½â¾ö±¾ÌâµÄ¹Ø¼üÕÆÎÕÓα꿨³ßµÄ¶ÁÊý·½·¨£¬Óα꿨³ß¶ÁÊýµÄ·½·¨ÊÇÖ÷³ß¶ÁÊý¼ÓÉÏÓαê¶ÁÊý£¬²»Ðè¹À¶Á£®
II¡¢¼ÓÉî¶Ôƽ¾ùËٶȺÍ˲ʱËٶȵÄÀí½â£¬Ö»Óе±Ê±¼ä¼ä¸ô¡÷tÇ÷ÏòÓÚÁãʱ£¬´ËʱµÄËٶȿÉÒÔÈÏΪÊÇ˲ʱËٶȣ¬ÊìÁ·Ó¦ÓÃÔ˶¯Ñ§¹«Ê½Çó½âʵÑéÎÊÌ⣮
III¡¢ÎïÌåÑØбÃæÏ»¬ÊÇÒ»¸öÖØÒªµÄÎïÀíÄ£ÐÍ£¬Ò»¶¨Òª¶Ô¸Ã¹ý³ÌÖÐĦ²ÁÁ¦¡¢µ¯Á¦¡¢ÖØÁ¦ÑØбÃæµÄ·ÖÁ¦¡¢¼ÓËٶȵÈÎïÀíÁ¿µÄ±ä»¯·ÖÎö͸³¹£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

£¨12·Ö£©ÔÚÖ¤Á¦µÄƽÐÐËıßÐζ¨ÔòʵÑéÖУº
£¨1£©ÎªÊ¹ÏðƤ½îÑØÊúÖ±·½ÏòÉ쳤£¬ÄÇô»¥³É½Ç¶ÈµÄÁ½µ¯»É³ÓËùÊ©µÄÁ¦F1ºÍF2±ØÐ루¡¡¡¡£©
A£®µÈ´ó                      B. »¥Ïà´¹Ö±
C£®Ë®Æ½·ÖÁ¦µÈ´ó·´Ïò          D. ÊúÖ±·ÖÁ¦µÈ´ó
£¨2£©£®ÈçͼËùʾ£¬ÓÃA£¬BÁ½¸ö²âÁ¦¼ÆÀ­ÏðƤÌõµÄD¶Ë£¨O¶Ë¹Ì¶¨£©£¬µ±°ÑD¶ËÀ­µ½E´¦Ê±£¬¦Á£«¦Â=90¡ã£»È»ºó±£³ÖAµÄ¶ÁÊý²»±ä£¬µ±¦Á½ÇÓÉͼÖÐËùʾµÄÖµÖð½¥±äСʱ£¬ÒªÊ¹D¶ËÈÔÔÚE´¦£¬¿É²ÉÓõİ취ÊÇ£¨¡¡¡¡£©

A£®Ôö´óBµÄ¶ÁÊý£¬¼õС¦Â½Ç    B£®¼õСBµÄ¶ÁÊý£¬¼õС½Ç¦Â
C£®¼õСBµÄ¶ÁÊý£¬Ôö´ó¦Â½Ç    D£®Ôö´óBµÄ¶ÁÊý£¬Ôö´ó¦Â½Ç
£¨3£©£®ÔÚ×ö¡°»¥³É½Ç¶ÈµÄÁ½¸öÁ¦µÄºÏ³É¡±ÊµÑéʱ£¬ÒÔÏÂ˵·¨ÖдíÎóµÄÓУ¨¡¡¡¡£©
A£®ÓÃÁ½Ö»µ¯»É³ÓÀ­ÏðƤ½îʱ£¬Ó¦Ê¹Á½Ï¸ÉþÌ×Ö®¼äµÄ¼Ð½ÇΪ90o£¬ÒÔ±ãËã³öºÏÁ¦µÄ´óС
B£®ÓÃÁ½Ö»µ¯»É³ÓÀ­ÏðƤ½îʱ£¬½áµãµÄλÖñØÐëÓëÓÃÒ»Ö»µ¯»É³ÓÀ­Ê±½áµãµÄλÖÃÖغÏ
C£®ÈôÓÃÁ½Ö»µ¯»É³ÓÀ­Ê±ºÏÁ¦µÄͼʾFÓëÓÃÒ»Ö»µ¯»É³ÓÀ­Ê±À­Á¦µÄͼʾF¡¯²»ÍêÈ«Öغϣ¬ËµÃ÷¡°Á¦µÄºÏ³É¡±µÄƽÐÐËıßÐζ¨Ôò²»Ò»¶¨ÆÕ±é³ÉÁ¢
D£®ÈôF1ºÍF2µÄ·½Ïò²»±ä£¬¶ø´óС¸÷Ôö¼Ó1N£¬ÔòºÏÁ¦FµÄ·½Ïò²»±ä£¬´óСҲÔö¼Ó1N

£¨12·Ö£©ÔÚÖ¤Á¦µÄƽÐÐËıßÐζ¨ÔòʵÑéÖУº

£¨1£©ÎªÊ¹ÏðƤ½îÑØÊúÖ±·½ÏòÉ쳤£¬ÄÇô»¥³É½Ç¶ÈµÄÁ½µ¯»É³ÓËùÊ©µÄÁ¦F1ºÍF2±ØÐ루¡¡¡¡£©

A£®µÈ´ó                      B. »¥Ïà´¹Ö±

C£®Ë®Æ½·ÖÁ¦µÈ´ó·´Ïò          D. ÊúÖ±·ÖÁ¦µÈ´ó

£¨2£©£®ÈçͼËùʾ£¬ÓÃA£¬BÁ½¸ö²âÁ¦¼ÆÀ­ÏðƤÌõµÄD¶Ë£¨O¶Ë¹Ì¶¨£©£¬µ±°ÑD¶ËÀ­µ½E´¦Ê±£¬¦Á£«¦Â=90¡ã£»È»ºó±£³ÖAµÄ¶ÁÊý²»±ä£¬µ±¦Á½ÇÓÉͼÖÐËùʾµÄÖµÖð½¥±äСʱ£¬ÒªÊ¹D¶ËÈÔÔÚE´¦£¬¿É²ÉÓõİ취ÊÇ£¨¡¡¡¡£©

A£®Ôö´óBµÄ¶ÁÊý£¬¼õС¦Â½Ç    B£®¼õСBµÄ¶ÁÊý£¬¼õС½Ç¦Â

C£®¼õСBµÄ¶ÁÊý£¬Ôö´ó¦Â½Ç    D£®Ôö´óBµÄ¶ÁÊý£¬Ôö´ó¦Â½Ç

£¨3£©£®ÔÚ×ö¡°»¥³É½Ç¶ÈµÄÁ½¸öÁ¦µÄºÏ³É¡±ÊµÑéʱ£¬ÒÔÏÂ˵·¨ÖдíÎóµÄÓУ¨¡¡¡¡£©

A£®ÓÃÁ½Ö»µ¯»É³ÓÀ­ÏðƤ½îʱ£¬Ó¦Ê¹Á½Ï¸ÉþÌ×Ö®¼äµÄ¼Ð½ÇΪ90o£¬ÒÔ±ãËã³öºÏÁ¦µÄ´óС

B£®ÓÃÁ½Ö»µ¯»É³ÓÀ­ÏðƤ½îʱ£¬½áµãµÄλÖñØÐëÓëÓÃÒ»Ö»µ¯»É³ÓÀ­Ê±½áµãµÄλÖÃÖغÏ

C£®ÈôÓÃÁ½Ö»µ¯»É³ÓÀ­Ê±ºÏÁ¦µÄͼʾFÓëÓÃÒ»Ö»µ¯»É³ÓÀ­Ê±À­Á¦µÄͼʾF¡¯²»ÍêÈ«Öغϣ¬ËµÃ÷¡°Á¦µÄºÏ³É¡±µÄƽÐÐËıßÐζ¨Ôò²»Ò»¶¨ÆÕ±é³ÉÁ¢

D£®ÈôF1ºÍF2µÄ·½Ïò²»±ä£¬¶ø´óС¸÷Ôö¼Ó1N£¬ÔòºÏÁ¦FµÄ·½Ïò²»±ä£¬´óСҲÔö¼Ó1N