Question

5£®ÈçͼËùʾ£¬Èý½ÇÐÎAQCÊDZ߳¤Îª2LµÄµÈ±ßÈý½ÇÐΣ¬P¡¢D·Ö±ðΪAQ¡¢ACµÄÖе㣬ÔÚˮƽÏßQCÏ·½ÊÇˮƽÏò×óµÄÔÈÇ¿µç³¡£»ÇøÓòI£¨ÌÝÐÎPQCD£©ÄÚÓд¹Ö±Ö½ÃæÏòÀïµÄÔÈÇ¿´Å³¡£¬´Å¸ÐӦǿ¶ÈΪB£¬ÇøÓòII£¨Èý½ÇÐÎAPD£©ÄÚÓд¹Ö±Ö½ÃæÏòÀïµÄÔÈÇ¿´Å³¡£¬ÇøÓòIII£¨ÐéÏßPDÖ®ÉÏ£¬Èý½ÇÐÎAPDÒÔÍ⣩Óд¹Ö±Ö½ÃæÏòÍâµÄÔÈÇ¿´Å³¡£¬ÇøÓòII¡¢IIIÄڴŸÐӦǿ¶È´óС¾ùΪ5B£¬Ò»´øÕýµçµÄÁ£×Ó´ÓQµãÕýÏ·½¡¢¾àÀëQµãΪLµÄOµãÒÔijһ³õËÙ¶ÈÉä³ö£¬Ôڵ糡Á¦×÷ÓÃÏ´ÓQC±ßÖеãNÒÔËÙ¶Èv₀´¹Ö±QCÉäÈëÇøÓòI£¬½Ó×Å´ÓPµã´¹Ö±AQÉäÈëÇøÓòIII£¬´Ëºó´øµçÁ£×Ó¾­ÀúһϵÁÐÔ˶¯ºóÓÖÒÔÔ­ËÙÂÊ·µ»ØOµã£®Á£×ÓÖØÁ¦ºöÂÔ²»¼Æ£¬Çó£º
£¨1£©¸ÃÁ£×ӵıȺÉ$\frac{q}{m}$£»
£¨2£©µç³¡Ç¿¶ÈE¼°Á£×Ó´ÓOµãÉä³öʱ³õËÙ¶ÈvµÄ´óС£»
£¨3£©Á£×Ó´ÓOµã³ö·¢µ½Ôٴλص½OµãµÄÕû¸öÔ˶¯¹ý³ÌÖÐËù¾­ÀúµÄʱ¼ät£®

Answer 1

·ÖÎö £¨1£©Á£×ÓÔÚÇøÓò¢ñÄÚ×öÔÈËÙÔ²ÖÜÔ˶¯£¬Ô²ÐÄΪQµã£¬¹Ê°ë¾¶µÈÓÚQN£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÇó½â¼´¿É£»
£¨2£©Á£×Ó´ÓOµ½NÓë´ÓNµ½OÊÇÄæ¹ý³Ì£¬Nµ½O×öÀàƽÅ×Ô˶¯£»¹ÊOµ½NµÄÊúÖ±·ÖÔ˶¯ÊÇÔÈËÙÖ±ÏßÔ˶¯£¬Ë®Æ½·ÖÔ˶¯ÊÇÔȼÓËÙÖ±ÏßÔ˶¯£¬¸ù¾Ý·ÖλÒƹ«Ê½ÁÐʽÇó½â¼´¿É£»
£¨3£©»­³öÁ£×ÓÔڴų¡ÖÐÔ˶¯¹ì¼££¬ÕÒ³ö°ë¾¶ÓëÈý½ÇÐα߳¤µÄ¹Øϵ£¬¶¨³öʱ¼äÓëÖÜÆڵĹØϵ£¬Çó³öʱ¼ä£®

½â´ð ½â£º£¨1£©Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãºqv₀B=m$\frac{{v}_{0}^{2}}{R}$£¬
ÓÉÌâÒâ¿ÉÖª£ºR=L£¬½âµÃ£º$\frac{q}{m}$=$\frac{{v}_{0}}{BL}$£»
£¨2£©Á£×Ó´ÓOµ½N£¬ÓÉÔ˶¯ºÏ³ÉÓë·Ö½âµÄ¹æÂɿɵãºL=v₀t₀£¬$L=\frac{1}{2}at_0^2$
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɿɵãº$a=\frac{qE}{m}$£¬½âµÃ£ºE=2Bv₀£¬
ÓÉÔ˶¯Ñ§¹«Ê½¿ÉµÃ£º$v_x^2=2aL$
Óɹ´¹É¶¨Àí¿ÉµÃ£ºv=$\sqrt{{v}_{0}^{2}+{v}_{x}^{2}}$=$\sqrt{5}$v₀£»
£¨3£©Á£×ÓÔÚµç´Å³¡ÖÐÔ˶¯µÄ×Üʱ¼ä°üÀ¨Èý¶Î£º
µç³¡ÖÐÍù·µµÄʱ¼ät₀¡¢ÇøÓò¢ñÖеÄʱ¼ät₁¡¢ÇøÓò¢òºÍ¢óÖеÄʱ¼ät₂+t₃£®
¸ù¾ÝƽÅ×Ô˶¯¹æÂÉÓÐ${t_0}=\frac{2L}{v_0}$
ÉèÔÚÇøÓò¢ñÖеÄʱ¼äΪt₁£¬Ôò${t_1}=2\frac{2¦ÐL}{{6{v_0}}}=\frac{2¦ÐL}{{3{v_0}}}$
Á£×ÓÔÚÇøÓò¢òºÍ¢óÄÚ×öÔ²ÖÜÔ˶¯£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãºqv₀•5B=m$\frac{{v}_{0}^{2}}{R}$£¬
ÔòÁ£×ÓÔÚÇøÓò¢òºÍ¢óÄÚµÄÔ˶¯¹ì¼£ÈçͼËùʾ£¬×Ü·³ÌΪ$£¨2+\frac{5}{6}£©$¸öÔ²ÖÜ£¬
ÇøÓò¢òºÍ¢óÄÚ×Ü·³ÌΪ£º$s=£¨2+\frac{5}{6}£©¡Á2¦Ðr$£¬${t_2}+{t_3}=\frac{s}{v_0}=\frac{17¦ÐL}{{15{v_0}}}$£¬
¹Ê×Üʱ¼äΪ£º$t={t_1}+{t_2}+{t_3}=\frac{2L}{v_0}+\frac{9}{5}\frac{¦ÐL}{v_0}$
´ð£º£¨1£©¸ÃÁ£×ӵıȺÉ$\frac{q}{m}$Ϊ$\frac{{v}_{0}}{BL}$£»
£¨2£©µç³¡Ç¿¶ÈEΪ2Bv₀£¬Á£×Ó´ÓOµãÉä³öʱ³õËÙ¶ÈvµÄ´óСΪ$\sqrt{5}$v₀£»
£¨3£©Á£×Ó´ÓOµã³ö·¢µ½Ôٴλص½OµãµÄÕû¸öÔ˶¯¹ý³ÌÖÐËù¾­ÀúµÄʱ¼ätΪ$\frac{2L}{{v}_{0}}$+$\frac{9¦ÐL}{5{v}_{0}}$£®

µãÆÀ ±¾ÌâÊôÓÚ´øµçÁ£×ÓÔÚ×éºÏ³¡ÖÐÔ˶¯ÎÊÌ⣬×ÛºÏÐÔ½ÏÇ¿£®´Å³¡ÖÐÔ²ÖÜÔ˶¯Òª»­¹ì¼£·ÖÎöÔ˶¯¹ý³Ì£¬Ì½Ë÷¹æÂÉ£¬Ñ°ÕҰ뾶ÓëÈý½ÇÐαߵĹØϵÊǹؼü£®