Question

8£®Ò»ÖÊÁ¿Îª2mµÄÎïÌåP¾²Ö¹Óڹ⻬ˮƽµØÃæÉÏ£¬Æä½ØÃæÈçͼËùʾ£®Í¼ÖÐabΪ´Ö²ÚµÄˮƽÃ棬³¤¶ÈΪL£»bcΪһ¹â»¬Ð±Ã棬бÃæºÍˮƽÃæͨ¹ýÓëabºÍbc¾ùÏàÇеij¤¶È¿ÉºöÂԵĹ⻬Բ»¡Á¬½Ó£®ÏÖÓÐÒ»ÖÊÁ¿ÎªmµÄľ¿éÒÔ´óСΪv₀µÄˮƽ³õËٶȴÓaµãÏò×óÔ˶¯£¬ÔÚбÃæÉÏÉÏÉýµÄ×î´ó¸ß¶ÈΪh£¬·µ»ØºóÔÚµ½´ïaµãÇ°ÓëÎïÌåPÏà¶Ô¾²Ö¹£®ÖØÁ¦¼ÓËÙ¶ÈΪg£®Çó
£¨1£©Ä¾¿éÔÚ×î¸ßµãʱµÄËÙ¶È
£¨2£©Ä¾¿éÔÚab¶ÎÊܵ½µÄĦ²ÁÁ¦f£»
£¨3£©Ä¾¿é×îºó¾àaµãµÄ¾àÀës£®

Answer 1

·ÖÎö £¨1£©Ä¾¿é´ÓaÔ˶¯µ½Ð±ÃæÉÏ×î¸ßµãµÄ¹ý³ÌÖУ¬Ä¾¿éÓëÎïÌåP×é³ÉµÄϵͳ£¬Ë®Æ½·½Ïò²»ÊÜÍâÁ¦£¬Ë®Æ½·½ÏòµÄ¶¯Á¿Êغ㣬ľ¿éÔÚ×î¸ßµãʱ£¬Á½ÕßÓй²Í¬Ëٶȣ¬Óɶ¯Á¿Êغ㶨ÂÉÇó½â£®
£¨2£©½áºÏÄÜÁ¿Êغ㶨ÂÉÇó³öľ¿éÔÚab¶ÎÊܵ½µÄĦ²ÁÁ¦£®
£¨3£©Ä¾¿é·µ»ØÓëÎïÌåPµÚ¶þ´Î´ïµ½¹²Í¬ËÙ¶ÈÓëµÚÒ»´Î´ïµ½¹²Í¬µÄËÙ¶ÈÏàͬ£¬¶ÔÈ«¹ý³ÌÔËÓÃÄÜÁ¿Êغ㶨ÂÉÇó³öľ¿é×îºó¾àaµãµÄ¾àÀës£®

½â´ð ½â£º£¨1£©Ä¾¿éÔÚ×î¸ßµãʱ£¬Éèľ¿éºÍÎïÌåP¹²Í¬ËÙ¶ÈΪv£¬Á½ÎïÌå´Ó¿ªÊ¼µ½µÚÒ»´Îµ½´ï¹²Í¬Ëٶȹý³Ì£¬È¡Ë®Æ½Ïò×óΪÕý·½Ïò£¬ÓÉˮƽ·½Ïò¶¯Á¿ÊغãµÃ£º
mv₀=£¨m+2m£©v¡­¢Ù
µÃ£ºv=$\frac{1}{3}{v}_{0}$
£¨2£©ÓÉÄÜÁ¿Êغ㶨Âɵãº
   $\frac{1}{2}$mv₀²=$\frac{1}{2}$£¨m+2m£©v²+mgh+fL¡­¢Ú
Óɢ٢ڵãºf=$\frac{m£¨{v}_{0}^{2}-3gh£©}{3L}$¡­¢Û
£¨2£©Ä¾¿é·µ»ØÓëÎïÌåPµÚ¶þ´Î´ïµ½¹²Í¬ËÙ¶ÈÓëµÚÒ»´ÎÏàͬ£¨¶¯Á¿Êغ㣩£¬¶ÔÈ«¹ý³Ì£¬ÓÉÄÜÁ¿ÊغãµÃ£º
   $\frac{1}{2}$mv₀²=$\frac{1}{2}$£¨m+2m£©v²+f£¨2L-s£©¡­¢Ü
Óɢڢۢܵãºs=$\frac{{v}_{0}^{2}-6gh}{{v}_{0}^{2}-3gh}$L£®
´ð£º£¨1£©Ä¾¿éÔÚ×î¸ßµãʱµÄËÙ¶ÈÊÇ$\frac{1}{3}{v}_{0}$£®
£¨2£©Ä¾¿éÔÚab¶ÎÊܵ½µÄĦ²ÁÁ¦fÊÇ$\frac{m£¨{v}_{0}^{2}-3gh£©}{3L}$£»
£¨3£©Ä¾¿é×îºó¾àaµãµÄ¾àÀësÊÇ$\frac{{v}_{0}^{2}-6gh}{{v}_{0}^{2}-3gh}$L£®

µãÆÀ ±¾Ìâ×ÛºÏÔËÓÃÁ˶¯Á¿Êغ㶨ÂɺÍÄÜÁ¿Êغ㶨ÂÉ£¬¹Ø¼üÑ¡ÔñÑо¿µÄ¹ý³Ì£¬¸ù¾ÝÁ½´óÊغ㶨ÂÉÁбí´ïʽ½øÐÐÇó½â£®Òª×¢ÒâĦ²ÁÉúÈÈÓëÏà¶ÔλÒÆÓйأ®