Question

13£®ÈçͼËùʾ£¬MN¡¢PQÊÇÁ½¸ùÊúÖ±·ÅÖõļä¾àΪLµÄ×ã¹»³¤¹â»¬Æ½ÐнðÊôµ¼¹ì£¬ÐéÏßÒÔÉÏÓд¹Ö±Ö½ÃæÏòÍâµÄ„òÇ¿´Å³¡I£¬ÐéÏßÒÔÏÂÓд¹Ö±Ö½ÃæÏòÄÚµÄÔÈÇ¿´Å³¡H£¬Á½´Å³¡ÇøÓòµÄ´Å¸ÐӦǿ¶È¾ùΪB£®½ðÊô°ôabÖÊÁ¿ÎªM£¬µç×èΪR£¬¾²Ö¹·ÅÔÚIÖе¼¹ìÉϵÄˮƽͻÆðÉÏ£»½ðÊô°ôcdÖÊÁ¿Îªm£¬µç×èҲΪR£®ÈÃcdÔÚ¢òÖÐij´¦ÎÞ³õËÙÊÍ·Å£¬µ±cdÏÂÂä¾àÀëΪmʱǡºÃ¶ÔÍ»ÆðûÓÐѹÁ¦£®ÒÑÖªÁ½¸ù½ðÊô°ôʼÖÕˮƽÇÒÓë½ðÊôµ¼¹ì½Ó´¥Á¼ºÃ£¬½ðÊôµ¼¹ìµÄµç×è²»¼Æ£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£®Çó£º
£¨1£©µ±cdÏÂÂä¾àÀëΪhʱ£¬Í¨¹ýabµÄµçÁ÷I£®
£¨2£©µ±cdÏÂÂä¾àÀëΪhʱ£¬cdµÄËٶȴóСv
£¨3£©´ÓcdÊͷŵ½ÏÂÂä¾àÀëΪh£¬¹ý³ÌÖУ¬abÉϲúÉúµÄ½¹¶úÈÈQ_ab£®£¨½á¹ûÓàB¡¢L¡¢M¡¢m¡¢R¡¢h¡¢g ±íʾ£©

Answer 1

·ÖÎö £¨1£©µ¼Ìå°ôcdÏ»¬¹ý³ÌÖÐabËùÊܵݲÅàÁ¦ÓëÖØÁ¦Æ½ºâ£¬¸ù¾ÝƽºâÌõ¼þºÍ°²ÅàÁ¦¹«Ê½½áºÏÇó½â£®
£¨2£©¸ù¾Ý·¨À­µÚµç´Å¸ÐÓ¦¶¨ÂɺÍÅ·Ä·¶¨ÂɽáºÏÇó½âµ¼Ìå°ôcdÔ˶¯Ê±µÄËٶȴóС£®
£¨3£©ÓÉ×ÜÄÜÁ¿Êغã¿ÉÖª£º»úеÄܵļõСµÈÓÚÄÚÄܵÄÔö¼Ó£¬¾Ý´Ë¿ÉÇóµÃ½¹¶úÈÈQ_ab£®

½â´ð ½â£º£¨1£©µ¼Ìå°ôcdÏ»¬¹ý³ÌÖÐabËùÊܵݲÅàÁ¦ÓëÖØÁ¦Æ½ºâ£¬ÔòÓУºMg=BIL
ÔòµÃ£ºI=$\frac{Mg}{BL}$
£¨2£©Éèµ¼Ìå°ôcdÔ˶¯Ê±µÄËٶȴóСΪv
¸ÐÓ¦µç¶¯ÊƵĴóСΪ£ºE=Blv
¸ù¾Ý±ÕºÏÅ·Ä·¶¨ÂɵãºI=$\frac{E}{2R}$
ÔòµÃ£ºv=$\frac{2MgR}{{B}^{2}{L}^{2}}$
¡¡£¨3£©ÓÉÄÜÁ¿Êغã¿ÉÖª£º$mgh=\frac{1}{2}m{v}^{2}+{Q}_{ab}+{Q}_{cd}$¡¡
ÓÖÒòab£¬cd´®Áª£¬ÇÒµç×èÏàµÈ£¬¹ÊQ_ab=Q_cd
½âµÃ£ºQ=$\frac{1}{2}$mgh-$\frac{m{M}^{2}{g}^{2}{R}^{2}}{{B}^{4}{L}^{4}}$
´ð£º£¨1£©µ±cdÏÂÂä¾àÀëΪhʱ£¬Í¨¹ýabµÄµçÁ÷IΪ$\frac{Mg}{BL}$£®
£¨2£©µ±cdÏÂÂä¾àÀëΪhʱ£¬cdµÄËٶȴóСvΪ$\frac{2MgR}{{B}^{2}{L}^{2}}$
£¨3£©´ÓcdÊͷŵ½ÏÂÂä¾àÀëΪh£¬¹ý³ÌÖУ¬abÉϲúÉúµÄ½¹¶úÈÈQ_abΪ$\frac{1}{2}$mgh-$\frac{m{M}^{2}{g}^{2}{R}^{2}}{{B}^{4}{L}^{4}}$£®

µãÆÀ ´ËÌâ¹Ø¼üÒªÀíÇå¹ý³Ì£¬ÖªµÀ½ðÊô¸ËÔÈËÙÖ±ÏßÔ˶¯Ê±£¬ËùÊܵÄÖØÁ¦Óë°²ÅàÁ¦Æ½ºâ£®