Question

12£®ÈçͼËùʾ£¬MN¡¢PQÊÇÁ½ÌõÔÚˮƽÃæÄÚ¡¢Æ½ÐзÅÖõĹ⻬½ðÊôµ¼¹ì£¬µ¼¹ìµÄÓҶ˽ÓÀíÏë±äѹÆ÷µÄÔ­ÏßȦ£¬±äѹÆ÷µÄ¸±ÏßȦÓë×èֵΪRµÄµç×è×é³É±ÕºÏ»Ø·£¬±äѹÆ÷µÄÔ­¸±ÏßȦÔÑÊýÖ®±Èn₁£ºn₂=k£¬µ¼¹ì¿í¶ÈΪL£®ÖÊÁ¿ÎªmµÄµ¼Ìå°ôab´¹Ö±MN¡¢PQ·ÅÔÚµ¼¹ìÉÏ£¬ÔÚˮƽÍâÁ¦×÷ÓÃÏ£¬´Ót=0ʱ¿Ì¿ªÊ¼Íù¸´Ô˶¯£¬ÆäËÙ¶ÈËæʱ¼ä±ä»¯µÄ¹æÂÉÊÇv=v_msin£¨$\frac{2¦Ð}{T}$t£©£¬ÒÑÖª´¹Ö±¹ìµÀƽÃæµÄÔÈÇ¿´Å³¡µÄ´Å¸ÐӦǿ¶ÈΪB£¬µ¼¹ì¡¢µ¼Ìå°ô¡¢µ¼ÏߺÍÏßȦµÄµç×è¾ù²»¼Æ£¬µçÁ÷±íΪÀíÏë½»Á÷µç±í£¬µ¼Ìå°ôʼÖÕÔڴų¡ÖÐÔ˶¯£®ÔòÏÂÁÐ˵·¨ÖÐÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® ÔÚt=$\frac{T}{4}$ʱ¿ÌµçÁ÷±íµÄʾÊýΪ$\frac{{BLv_m^{\;}}}{{\sqrt{2}{k^2}R}}$
• B£® µ¼Ìå°ôÁ½¶ËµÄ×î´óµçѹΪBLv_m
• C£® µç×èRÉÏÏûºÄµÄ¹¦ÂÊΪ$\frac{{{B^2}{L^2}v_m^2}}{{2{k^2}R}}$
• D£® ´Ót=0ÖÁt=$\frac{T}{4}$µÄʱ¼äÄÚˮƽÍâÁ¦Ëù×öµÄ¹¦Îª$\frac{{{B^2}{L^2}v_m^2}}{{8{k^2}R}}$T

Answer 1

·ÖÎö °ô²úÉúµÄÊǽ»Á÷µç£¬µçÁ÷±íÏÔʾµÄÊÇÓÐЧֵ£¬¸ù¾ÝµçѹÓëÔÑÊý³ÉÕý±È£¬µçÁ÷ÓëÔÑÊý³É·´±È£¬½áºÏ¹¦Âʹ«Ê½ÖðÏî·ÖÎö¼´¿É£®

½â´ð ½â£ºA¡¢t=$\frac{T}{4}$µÄʱ¿Ì°ôµÄËÙ¶ÈΪV_m£¬¸ÐÓ¦µç¶¯ÊÆE=BLV_m£¬¸±ÏßȦµÄµçѹΪ${U}_{2}^{\;}$=BL$\frac{{v}_{m}^{\;}}{k}$£¬µçÁ÷Ϊ${I}_{2}^{\;}$=BL$\frac{{v}_{m}^{\;}}{\sqrt{2}kR}$£¬µçÁ÷ÓëÔÑÊý³É·´±È£¬ËùÒÔµçÁ÷±íµÄʾÊýΪI=$\frac{BL{v}_{m}^{\;}}{\sqrt{2}{k}_{\;}^{2}R}$£¬AÕýÈ·£»
B¡¢µ±ËÙ¶È×î´óʱ£¬µ¼Ìå°ôÁ½¶ËµÄ×î´óµçѹΪ${E}_{m}^{\;}$=BLV_m£¬BÕýÈ·£»
C¡¢µç×èRÉÏÏûºÄµÄ¹¦ÂÊΪP=£¨BL$\frac{{v}_{m}^{\;}}{\sqrt{2}kR}$£©²R=$\frac{{B}_{\;}^{2}{L}_{\;}^{2}{v}_{m}^{2}}{2{k}_{\;}^{2}R}$£¬CÕýÈ·£»
D¡¢´Ót=0ÖÁt=$\frac{T}{4}$µÄʱ¼äÄÚˮƽÍâÁ¦Ëù×öµÄ¹¦µÈÓÚR²úÉúµÄÈÈÁ¿Ó붯ÄÜÖ®ºÍ£¬¼´W=$\frac{1}{2}m{v}_{0}^{2}$+${I}_{\;}^{2}R\frac{T}{4}$=$\frac{1}{2}m{v}_{0}^{2}$+$\frac{{B}_{\;}^{2}{L}_{\;}^{2}{v}_{m}^{2}}{8{k}_{\;}^{2}R}$T£¬¹ÊD´íÎó£»
¹ÊÑ¡£ºABC£®

µãÆÀ ±¾Ì⿼²éÁ˽»Á÷µçµÄ²úÉúºÍ±äѹÆ÷µÄÔ­Àí£¬½áºÏ¹¦ÂʵÈ֪ʶµã£¬ÄѶȽϴó£®