Question

13£®ÔÚÊúֱƽÃæÄÚ½¨Á¢Ò»Æ½ÃæÖ±½Ç×ø±êϵxoy£¬xÖáÑØˮƽ·½Ïò£¬Èçͼ¼×Ëùʾ£®×ø±êϵµÄµÚÒ»ÏóÏÞÄÚÓÐÒ»Õý½»µÄÔÈÇ¿µç³¡ºÍÔÈÇ¿´Å³¡£¬µç³¡·½ÏòÊúÖ±ÏòÉÏ£¬³¡Ç¿ÎªE₁£¬´Å³¡·½Ïò´¹Ö±Ö½Ã棬´Å¸ÐӦǿ¶ÈB₀=$\frac{3+\sqrt{3}}{10}$T£¬·½Ïò°´Í¼ÒÒËùʾ¹æÂɱ仯£¨ÒÔ´¹Ö±Ö½ÃæÏòÍâµÄ´Å³¡·½ÏòΪÕýÏò£©£¬µÚ¶þÏóÏÞÄÚÓÐһˮƽÏòÓÒµÄÔÈÇ¿µç³¡£¬³¡Ç¿E₂=2E₁£®Ò»¸ö±ÈºÉ$\frac{q}{m}$=10²C/kgµÄ´øÕýµçµÄÁ£×Ó£¨¿ÉÊÓΪÖʵ㣩ÒÔv_.0=4m/sµÄËÙ¶ÈÔÚ-xÉϵÄAµãÊúÖ±ÏòÉÏÅ׳ö£¬Ç¡ÄÜÒÔv₁=8m/sËٶȴÓ+yÉϵÄCµãˮƽ½øÈëµÚÒ»ÏóÏÞ£®È¡Á£×Ó¸Õ½øÈëµÚÒ»ÏóÏÞʱt=0£®£¨È¡g=10m/s²£©ÊÔÇó£º

£¨1£©AC¼äµçÊƲîU_AC¼°E₂µÄ´óС£»
£¨2£©Í¨¹ý¼ÆËãÅжϴøµçÁ£×Ó½øÈëµÚÒ»ÏóÏÞºó×öºÎÖÖÔ˶¯£¿
£¨3£©ÎªÈ·±£Á£×Ó²»ÔÙÔ½¹ýOC½øÈëµÚ¶þÏóÏÞ£¬Ôò½»±ä´Å³¡ÖÜÆÚ×î´óÖµT_mΪ¶àÉÙ£¿

Answer 1

·ÖÎö £¨1£©½«Á£×ÓÔÚµÚ¶þÏóÏÞÄÚµÄÔ˶¯·Ö½âΪˮƽ·½ÏòºÍÊúÖ±·½Ïò£¬µÃ³öÁ½¸ö·½ÏòÉϵÄÔ˶¯¹æÂÉ£¬½áºÏÔ˶¯Ñ§¹«Ê½ºÍÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö´øµç΢Á£Ô˶¯µ½CµãµÄ×Ý×ø±êÖµh¼°µç³¡Ç¿¶ÈE₂£¬´Ó¶ø¿ÉÇóµÃAC¼äµçÊƲ
£¨2£©¸ù¾ÝÖØÁ¦Óëµç³¡Á¦µÄ¹Øϵ£¬·ÖÎöÁ£×ÓµÄÔ˶¯Çé¿ö£®
£¨3£©µ±½»±ä´Å³¡ÖÜÆÚÈ¡×î´óÖµ¶øÁ£×Ó²»ÔÙÔ½¹ýyÖáʱ£¬¸ù¾Ý¼¸ºÎ¹ØϵÇó³öT_m£®

½â´ð ½â£º£¨1£©ÉèOC¸ßΪh£¬OA³¤ÎªL£¬Á£×ÓÔÚµÚ¶þÏóÏÞÔ˶¯Ê±¼äΪt₁£¬Ôò
 ÔÚÊúÖ±·½Ïò£ºv₀=gt
 ÔÚˮƽ·½Ïò£ºL=$\frac{1}{2}$v₁t£¬v₁=$\frac{q{E}_{2}}{m}$t
ÓÖ U_AC=E₂L
´úÈëÊý¾Ý¿ÉµÃ£ºh=0.8m£¬L=1.6m£¬E₂=0.2V/m£¬
µÃ£ºU_AC=0.32V
£¨2£©Á£×ÓÔÚµÚÒ»ÏóÏÞÔ˶¯Ê±ÊÜÖØÁ¦mg¡¢µç³¡Á¦E₁qºÍÂåÂ××ÈÁ¦×÷Óã¬Òòmg-qE₁=0£¬¹ÊÁ£×Ó×öÔÈËÙÔ²ÖÜÔ˶¯Ô˶¯£®
£¨3£©ÉèÁ£×ÓÔ˶¯Ô²¹ìµÀ°ë¾¶ÎªR£¬ÖÜÆÚΪT£®
Ôò qv₁B₀=m$\frac{{v}_{1}^{2}}{R}$
¿ÉµÃR=$\frac{m{v}_{1}}{q{B}_{0}}$
ÔÈËÙÔ²ÖÜÔ˶¯µÄÖÜÆÚ T=$\frac{2¦Ðm}{q{B}_{0}}$£¬´úÈëB₀µÃ£ºT=$\frac{¦Ð£¨3-\sqrt{3}£©}{30}$s                                 
µ±½»±ä´Å³¡ÖÜÆÚÈ¡×î´óÖµ¶øÁ£×Ó²»½øÈëµÚÒ»ÏóÏÞʱ¿É×÷ÈçͼÔ˶¯ÇéÐΣº
ÓÉͼ¿ÉÖªT₀=$\frac{5}{6}$T=$\frac{£¨3-\sqrt{3}£©¦Ð}{36}$s
´ð£º£¨1£©AC¼äµçÊƲîU_ACÊÇ0.32V£¬E₂µÄ´óСΪ0.2V/m£»
£¨2£©Í¨¹ý¼ÆËãÅжϴøµçÁ£×Ó½øÈëµÚÒ»ÏóÏÞºó×öÔÈËÙÔ²ÖÜÔ˶¯Ô˶¯£®
£¨3£©ÎªÈ·±£Á£×Ó²»ÔÙÔ½¹ýOC½øÈëµÚ¶þÏóÏÞ£¬Ôò½»±ä´Å³¡ÖÜÆÚ×î´óÖµT_mΪ$\frac{£¨3-\sqrt{3}£©¦Ð}{36}$s£®

µãÆÀ ±¾ÌâÖÐÖʵãÔÚ¸´ºÏ³¡Ô˶¯£¬·ÖÎöÊÜÁ¦Çé¿ö£¬È·¶¨ÖʵãµÄÔ˶¯Çé¿öÊǽâÌâµÄ»ù´¡£®½áºÏÁ£×ÓÔ˶¯µÄÖÜÆÚÐÔÒÔ¼°ÁÙ½ç״̬£¬ÔËÓÃÊýѧ¼¸ºÎ֪ʶ×ÛºÏÇó½â£®