Question

3£®ÈçͼËùʾ£¬Ö½ÃæÄÚÖ±ÏßCD¡¢MN¡¢FGÏ໥ƽÐУ¬¼ä¾àΪd£¬ÔÚÖ±ÏßCD¡¢MNÖ®¼äµÄÇøÓòÄÚÓÐƽÐÐÓÚCDµÄÔÈÇ¿µç³¡£¬ÔÚÖ±ÏßMN¡¢FGÖ®¼äµÄÇøÓòÄÚÓд¹Ö±ÓÚÖ½ÃæÏòÀïµÄÔÈÇ¿´Å³¡£®ÏÖÓÐÖÊÁ¿Îªm£¬µçÁ¿ÎªqµÄ´øÕýµçÁ£×Ó´ÓCD±ßijµãOÒÔ³õËÙ¶Èv₀£¬ÑØ´¹Ö±ÓÚCDµÄ·½ÏòÉäÈëµç³¡£¬À뿪µç³¡½øÈë´Å³¡Ê±ËٶȴóСΪv=2v₀£¬´ÓÖ±ÏßFG´¦À뿪´Å³¡Ê±Ëٶȷ½ÏòÓëÖ±ÏßFGÖ®¼äµÄ¼Ð½ÇΪ¦Â=60?£¬²»¼ÆÁ£×ÓËùÊÜÖØÁ¦£¬µç¡¢´Å³¡ÇøÓò×ã¹»´ó£®Çó£º
£¨1£©Á£×Óͨ¹ýµç³¡µÄʱ¼ä£»
£¨2£©µç³¡Ç¿¶ÈµÄ´óС£»
£¨3£©´Å¸ÐӦǿ¶ÈµÄ´óС£®

Answer 1

·ÖÎö £¨1£©´øµçÁ£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬¸ù¾Ý´¹Ö±µç³¡·½ÏòÉϵÄÔÈËÙÖ±ÏßÔ˶¯¹æÂÉ¿ÉÇóµÃʱ¼ä£»
£¨2£©ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÇóµÃ¼ÓËٶȣ¬ÔÙÀàƽÅ×Ô˶¯µÄ¹æÂÉ¿ÉÇóµÃµç³¡Ç¿¶È£»
£¨3£©¸ù¾Ý¼¸ºÎ¹Øϵ¿ÉÃ÷È·´øµçÁ£×ÓÔڴų¡ÖÐÔ˶¯°ë¾¶£»ÔÙÓÉÂåÂ××ÈÁ¦³äµ±ÏòÐÄÁ¦ÁÐʽ¿ÉÇóµÃ´Å¸ÐӦǿ¶ÈµÄ´óС£®

½â´ð ½â£º£¨1£©ÉèÁ£×Óͨ¹ýµç³¡µÄʱ¼äΪt£¬ÓÉÔÈËÙÔ˶¯¹«Ê½µÃ£ºd=v₀t
µÃ£º$t=\frac{d}{v_0}$
£¨2£©ÉèÁ£×ÓÀ뿪µç³¡Ê±ËÙ¶ÈÑص糡·½ÏòµÄ·ÖÁ¿Îªv_y£¬ÓÉËٶȷֽâ¿ÉµÃ£º${v_y}=\sqrt{{v^2}-v_0^2}=\sqrt{3}{v_0}$
Éèµç³¡Ç¿¶È´óСΪE£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº${a_y}=\frac{qE}{m}$
ÓÉÔȱäËÙÔ˶¯¹«Ê½µÃ£ºv_y=a_yt
ÁªÁ¢ÒÔÉϸ÷ʽµÃ£º$E=\frac{{\sqrt{3}mv_0^2}}{qd}$
£¨3£©ÉèÁ£×ÓÀ뿪µç³¡Ê±Ëٶȷ½ÏòÓëµç´Å³¡±ß½çMN¼äµÄ¼Ð½ÇΪ¦È£¬ÓÉËٶȺϳɿɵãº$sin¦È=\frac{v_0}{v}=\frac{1}{2}$¦È=30?
Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÈçͼËùʾ£¬Ô²ÐÄ¿ÉÄÜΪO₁»òO₂£¬À뿪´Å³¡µÄµã¿ÉÄÜΪPµã»òQµã£®Éè´ÓPµãÀ뿪´Å³¡µÄ¹ìµÀ°ëΪr₁£¬´ÓQµãÀ뿪´Å³¡µÄ¹ìµÀ°ëΪr₂£¬Óɼ¸ºÎ֪ʶ¿ÉµÃ£ºd=r₁cos¦È+r₁cos¦Â
 d=r₂cos¦È-r₂cos¦Â
ÓÉÂåÂØ×ÈÁ¦¹«Ê½µÃ¼°ÔÈËÙÔ²ÖÜÔ˶¯¹«Ê½µÃ£º$qvB=m\frac{v^2}{r}$
ÁªÁ¢ÒÔÉϸ÷ʽµÃ£º${B_1}=\frac{{£¨\sqrt{3}+1£©m{v_0}}}{qd}$
   ${B_2}=\frac{{£¨\sqrt{3}-1£©m{v_0}}}{qd}$
´ð£º£¨1£©Á£×Óͨ¹ýµç³¡µÄʱ¼äΪ$\frac{d}{{v}_{0}}$£»
£¨2£©µç³¡Ç¿¶ÈµÄ´óС$\frac{\sqrt{3}m{v}_{0}^{2}}{qd}$£»
£¨3£©´Å¸ÐӦǿ¶ÈµÄ´óС¿ÉÄÜΪ$\frac{£¨\sqrt{3}+1£©m{v}_{0}}{qd}$»ò$\frac{£¨\sqrt{3}-1£©m{v}_{0}}{qd}$£®

µãÆÀ ±¾Ì⿼²é´øµçÁ£×ÓÔڵ糡ºÍ´Å³¡ÖеÄÔ˶¯¹æÂÉ£¬Òª×¢ÒâÃ÷È·Ôڵ糡ÖÐÒ»°ã¸ù¾ÝÔ˶¯µÄºÏ³ÉºÍ·Ö½â¹æÂɽ⣻¶øÔڴų¡ÖÐҪעÒâÃ÷È·Ô²ÖÜÔ˶¯¹æÂÉ£¬Ã÷È·¼¸ºÎ¹Øϵ¿ÉÂåÂ××ÈÁ¦³äµ±ÏòÐÄÁ¦µÄÓ¦Óã®