Question

7£®ÈçͼËùʾ£¬Èô½«A¡¢BÁ½¸ö¹â»¬´øµçСÇò¾²Ö¹·ÅÔÚÎÞ×èÁ¦µÄˮƽ¹ÜµÀÄÚ£¬ÆäÖÐAµÄÖÊÁ¿ÎªM£¬BµÄÖÊÁ¿Îªm£¬£¨M£¾m£©£®¿ªÊ¼Ê±Á½ÇòÖ®¼äÏà¾àºÜÔ¶£¬ÏÖÔÚ¸øAÒ»¸ö³õËÙ¶Èv£¬ÈÃÆäÏòÓÒÔ˶¯£® ÒÑÖªÁ½ÇòÖ®¼äÓÉÓÚ´øͬÖÖµçºÉ»áÏ໥Åų⣬ѡȡÎÞÇîԶΪ²Î¿¼Ã棬Á½´øµçСÇòµÄµçÊÆÄÜΪ$\frac{K}{r}$£¬ÆäÖÐK ÎªÒÑÖª³£Êý£¬rΪÁ½ÇòÖ®¼äµÄ¾àÀ룮ÎÊ£º
£¨1£©ÈôÁ½¸ö´øµçСÇòÖ𽥿¿½ü£¬´øµçСÇòAµÄµçÊÆÄÜÈçºÎ±ä»¯£¿
£¨2£©Èç¹ûA²»»á³¬¹ýB£¬¼ÆËãA¡¢B¼äµÄ×îС¾àÀ룿
£¨3£©ÈôÈÃAÄܹ»³¬¹ýB£¬ÇóB×îÖÕµÄËٶȣ¿£¨ÓÃͼʾ»ò¹«Ê½·ÖÎö¶¼¿ÉÒÔ£©

Answer 1

·ÖÎö £¨1£©¸ù¾Ýµç³¡Á¦×ö¹¦µÄÕý¸ºÅжϵçÊÆÄܵı仯£»
£¨2£©ABÔ˶¯¹ý³ÌÖУ¬ÏµÍ³¶¯Á¿Êغ㣬Èç¹ûAÇò²»»á³¬¹ýB£¬µçÊÆÄܺͳõ¶¯ÄÜÈ«²¿×ª»¯ÎªÁ½ÕߵĶ¯ÄÜ£¬¸ù¾Ý¶¯Á¿Êغ㶨ÂÉÒÔ¼°ÄÜÁ¿Êغ㶨ÂÉÁÐʽÇó½â£»
£¨3£©Óɶ¯Á¿ÊغãºÍÄÜÁ¿ÊغãÁÐʽ·ÖÎö¼´¿É£®

½â´ð ½â£º£¨1£©Á½´øµçСÇòÖ𽥿¿½ü£¬µç³¡Á¦×ö¸º¹¦£¬A´øµçСÇòµÄµçÊÆÄÜÖð½¥Ôö´ó£¬
£¨2£©ABÔ˶¯¹ý³ÌÖУ¬ÏµÍ³¶¯Á¿Êغ㣬ÒÔÏòÓÒΪÕý£¬¸ù¾Ý¶¯Á¿ÊغãÓУº
Mv=£¨M+m£©v_¹²
½âµÃ£ºv_¹²=$\frac{Mv}{M+m}$
Èç¹ûAÇò²»»á³¬¹ýB£¬
$\frac{k}{r}$=$\frac{1}{2}M{v^2}-\frac{1}{2}£¨M+m£©{v_¹²}^2$£¬
½âµÃ£º$r=\frac{2k£¨M+m£©}{{Mm{v^2}}}$
£¨3£©Óɶ¯Á¿ÊغãºÍÄÜÁ¿ÊغãµÃ£º
$\begin{array}{l}MV=M{V_A}+m{V_B}\\ \frac{MV_A^2}{2}=\frac{MV_A^2}{2}+\frac{MV_B^2}{2}\end{array}$
»áÓÐÁ½¸ö½â£¬ÉáÈ¥Åöײ½â£¬
×îºóµÈЧһ¸öÍêÈ«µ¯ÐÔÅöײ£¬
×îÖÕBµÄËٶȠv=0 
´ð£º£¨1£©ÈôÁ½¸ö´øµçСÇòÖ𽥿¿½ü£¬A´øµçСÇòµÄµçÊÆÄÜÖð½¥Ôö´ó£»
£¨2£©Èç¹ûA²»»á³¬¹ýB£¬A¡¢B¼äµÄ×îС¾àÀëΪ$\frac{2k£¨M+m£©}{Mm{v}^{2}}$£»
£¨3£©ÈôÈÃAÄܹ»³¬¹ýB£¬B×îÖÕµÄËÙ¶ÈΪ0£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÁ˶¯Á¿Êغ㶨ÂÉÒÔ¼°ÄÜÁ¿Êغ㶨ÂɵÄÓ¦Óã¬ÒªÇóͬѧÃÇÃ÷È·µç³¡Á¦×ö¹¦ÓëµçÊÆÄܱ仯µÄ¹Øϵ£¬µç³¡Á¦×öÕý¹¦µçÊÆÄܼõС£¬µç³¡Á¦×ö¸º¹¦µçÊÆÄÜÔö´ó£®