ÌâÄ¿ÄÚÈÝ
11£®Ä³Í¬Ñ§Éè¼ÆÁË¡°Ì½¾¿¼ÓËÙ¶ÈaÓëÎïÌåËùÊܺÏÁ¦F¼°ÖÊÁ¿mµÄ¹ØÏµ¡±ÊµÑ飮ͼ£¨a£©ÎªÊµÑé×°Öüòͼ£¬AΪС³µ£¬BΪijÖÖ´òµã¼ÆÊ±Æ÷£¬CΪװÓÐϸɰµÄСͰ£¬DΪһ¶Ë´øÓж¨»¬Âֵij¤·½ÐÎľ°å£¬ÊµÑéÖÐÈÏΪϸÉþ¶ÔС³µÀÁ¦FµÈÓÚϸɰºÍСͰµÄ×ÜÖØÁ¿£¬Ð¡³µÔ˶¯µÄ¼ÓËÙ¶Èa¿ÉÓÃÖ½´øÉÏ´ò³öµÄµãÇóµÃ£®¢ÚµçѹӦѡÔñ6Vµµ£®
£¨2£©ÔÚ¡°Ì½¾¿¼ÓËÙ¶ÈaÓëÖÊÁ¿mµÄ¹ØÏµ¡±Ê±£¬±£³ÖϸɰºÍСͰÖÊÁ¿²»±ä£¬¸Ä±äС³µÖÊÁ¿m£¬·Ö±ð¼Ç¼С³µ¼ÓËÙ¶ÈaÓëÆäÖÊÁ¿mµÄÊý¾Ý£®ÔÚ·ÖÎö´¦Àíʱ£¬¸Ã×éͬѧ´æÔÚÁ½ÖÖ·½°¸£»¼×ͬѧÈÏΪӦ¸Ã¸ù¾ÝʵÑéÖвâµÃµÄÊý¾Ý×÷³öС³µ¼ÓËÙ¶ÈaÓëÆäÖÊÁ¿mµÄͼÏó£»ÒÒͬѧÈÏΪӦ¸Ã¸ù¾ÝʵÑéÖвâµÃµÄÊý¾Ý×÷³öС³µ¼ÓËÙ¶ÈaÓëÆäÖÊÁ¿µ¹Êý$\frac{1}{m}$µÄͼÏó£®Á½Î»Í¬Ñ§¶¼°´ÕÕ×Ô¼ºµÄ·½°¸½«ÊµÑéÊý¾ÝÔÚ×ø±êϵÖнøÐÐÁ˱ê×¢£¬µ«ÉÐδÍê³ÉͼÏó£¨Èçͼ1Ëùʾ£©£®
ÄãÈÏΪͬѧÒÒ£¨Ìî¡°¼×¡±¡¢¡°ÒÒ¡±£©µÄ·½°¸¸üºÏÀí£¬²¢ÔÚ´ð¾íÉϼÌÐø°ïÖú¸Ãͬѧ×÷³ö×ø±êÖеÄͼÏó£®
£¨3£©ÔÚ¡°Ì½¾¿¼ÓËÙ¶ÈaÓëºÏÁ¦FµÄ¹ØÏµ¡±Ê±£¬±£³ÖС³µµÄÖÊÁ¿²»±ä£¬¸Ä±äСͰÖÐϸɰµÄÖÊÁ¿£¬¸Ãͬѧ¸ù¾ÝʵÑéÊý¾Ý×÷³öÁ˼ÓËÙ¶ÈaÓëºÏÁ¦FµÄͼÏßÈçͼ2£¬¸ÃͼÏß²»Í¨¹ý×ø±êԵ㣬ÊÔ·ÖÎöͼÏß²»Í¨¹ý×ø±êÔµãµÄÔÒò£®´ð£º¸Ãͬѧδƽºâ£¨»òδÍêȫƽºâ£©Ä¦²ÁÁ¦£®
·ÖÎö £¨1£©¸ù¾Ý´òµã¼ÆÊ±Æ÷µÄ¹¤×÷µçѹ½øÐÐÑ¡Ôñ£»
£¨2£©ÎªÑо¿aÓëmµÄ¹ØÏµ£¬×÷aÓë$\frac{1}{m}$µÄ¹ØÏµ¹ØÏµÍ¼Ïߣ¬×¢ÒâѡȡºÃ±ê¶È£®
£¨3£©Í¼Ïß²»Í¨¹ý×ø±êԵ㣬µ±FΪijһֵʱ£¬¼ÓËÙ¶ÈΪÁ㣬֪ƽºâĦ²ÁÁ¦²»×㣮
½â´ð ½â£º£¨1£©Í¼£¨b£©ÎªÊµÑéÖÐËùÓôòµã¼ÆÊ±Æ÷µÄѧÉúµçÔ´£®ÓÉѧÉúµçÔ´¿ÉÒÔÅжϸÃͬѧѡÓõÄÊÇͼ£¨c£©ÖеÄÒÒ´òµã¼ÆÊ±Æ÷£®
ÉÏÊöͼ£¨b£©µÄ°²×°ÖдæÔڵĴíÎóÓУº¢Ù½ÓÏßÖùÓ¦½ÓÔÚ½»Á÷µçÉÏ¢ÚµçѹӦѡÔñ6Vµµ£®
£¨2£©ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉF=ma¿ÉÖªµ±ºÏÁ¦F²»±äʱmÓëa³É·´±È£¬ÔÚa-mͼÏóÖÐÓ¦¸ÃÊÇË«ÇúÏߣ¬µ«ÊÇʵÑéµÃ³öµÄ¸÷×éÊý¾ÝÊDz»ÊÇÂäÔÚͬһÌõË«ÇúÏßÉÏÊDz»ºÃÅжϵģ¬
µ«ÊÇa-$\frac{1}{m}$µÄ¹ØÏµÊÇÕý±ÈÀýº¯Êý£¬´Ëʱ¸÷×éÊý¾ÝÊDz»ÊÇÂäÔÚͬһÌõÖ±ÏßÉÏÊǷdz£ÈÝÒ×¹Û²ìµÄ£¬
ËùÒÔÒÒͬѧµÄ·½°¸¸üºÏÀí£®ÊµÑéµÃ³öµÄ¸÷×éÊý¾ÝÓ¦¸Ã´óÌåÉÏÂäÔÚͬһÌõÖ±ÏßÉÏ£®
£¨3£©´ÓͼÏó¿ÉÒÔ¿´³öµ±ÓÐÁËÒ»¶¨µÄÀÁ¦Fʱ£¬Ð¡³µµÄ¼ÓËÙ¶ÈÈÔÈ»ÊÇÁ㣬С³µÃ»¶¯ËµÃ÷С³µµÄºÏÁ¦ÈÔÈ»ÊÇÁ㣬¼´Ð¡³µ»¹Êܵ½Ä¦²ÁÁ¦µÄ×÷Óã¬ËµÃ÷Ħ²ÁÁ¦»¹Ã»ÓÐÆ½ºâµô£¬»òÕßÊÇÆ½ºâĦ²ÁÁ¦Á˵«ÊÇÆ½ºâµÄ»¹²»¹»£¬Ã»ÓÐÍêȫƽºâµôĦ²ÁÁ¦£¬
ËùÒÔͼÏß²»Í¨¹ý×ø±êÔµãµÄÔÒòÊÇʵÑéǰ¸Ãͬѧδƽºâ£¨»òδÍêȫƽºâ£©Ä¦²ÁÁ¦£®
¹Ê´ð°¸Îª£º
£¨1£©ÒÒ¡¢½ÓÏßÖùÓ¦½ÓÔÚ½»Á÷µçÉÏ¡¢µçѹӦѡÔñ6Vµµ
£¨2£©ÒÒ¡¢Èçͼ
£¨3£©¸Ãͬѧδƽºâ£¨»òδÍêȫƽºâ£©Ä¦²ÁÁ¦£®
µãÆÀ ±¾Ì⿼²éÁË´òµã¼ÆÊ±Æ÷µÄÓ¦Óü°´ò³öµÄÖ½´øµÄ´¦Àí·½·¨£¬ÓÐÀûÓÚѧÉú»ù±¾ÖªÊ¶µÄÕÆÎÕ£¬Í¬Ê±Ò²¿¼²éÁËѧÉú¶ÔʵÑéÊý¾ÝµÄ´¦Àí·½·¨£¬¼°ÊÔÑéÌõ¼þµÄÕÆÎÕ£¬Æ½ºâĦ²ÁÁ¦µÄ·½·¨£®
| A£® | 2v0 | B£® | 4v0 | C£® | $\frac{{v}_{0}}{2}$ | D£® | $\frac{\sqrt{2}}{2}$v0 |
| A£® | ÒÒ½Ó°ôʱÔÚ½ÓÁ¦ÇøÐè±¼³ö8mµÄ¾àÀë | |
| B£® | ÒÒ½Ó°ôʱÔÚ½ÓÁ¦ÇøÐè±¼³ö16mµÄ¾àÀë | |
| C£® | ÒÒÓ¦ÔÚ¾àÀë¼×16mʱÆðÅÜ | |
| D£® | ÒÒÓ¦ÔÚ¾àÀë¼×24mʱÆðÅÜ |
| A£® | ÊÖ¶ÔË®µÄ×÷ÓÃÁ¦´óÓÚË®¶ÔÊÖµÄ×÷ÓÃÁ¦ | |
| B£® | ÊÖ¶ÔË®µÄ×÷ÓÃÁ¦Ð¡ÓÚË®¶ÔÊÖµÄ×÷ÓÃÁ¦ | |
| C£® | ÊÖ¶ÔË®ÏòºóµÄ×÷ÓÃÁ¦ºÍË®¶ÔÊÖÏòǰµÄ×÷ÓÃÁ¦ÊÇÒ»¶ÔƽºâÁ¦ | |
| D£® | ÊÖ¶ÔË®ÏòºóµÄ×÷ÓÃÁ¦ºÍË®¶ÔÊÖÏòǰµÄ×÷ÓÃÁ¦ÊÇ×÷ÓÃÁ¦Óë·´×÷ÓÃÁ¦ |