Question

6£®ÈçͼÔÚÕæ¿ÕÖдæÔÚ×ÅÊúÖ±ÏòϵÄÔÈÇ¿µç³¡£¬³¡Ç¿ÎªE£®Ò»¸ù¾øԵϸÏß³¤ÎªL£¬Ò»¶Ë¹Ì¶¨ÔÚͼÖеÄOµã£¬ÁíÒ»¶Ë¹Ì¶¨ÓÐÒ»¸öÖÊÁ¿Îªm¡¢´øµçÁ¿Îª+q¡¢¿ÉÊÓΪµãµçºÉµÄСÇò£¬Oµã¾àÀëµØÃæµÄ¸ß¶ÈΪH£¬½«Ð¡ÇòÀ­ÖÁÓëOµãµÈ¸ßµÄλÖÃA´¦´Ó¾²Ö¹ÊÍ·Å£®Çó£º
£¨1£©Ð¡ÇòÔ˶¯µ½OµãÕýÏ·½BµãʱµÄËٶȴóС
£¨2£©´Ë¿ÌϸÏ߶ÔBµã´¦µÄСÇòµÄÀ­Á¦´óС
£¨3£©ÈôСÇòͨ¹ýBµãʱ£¬Ï¸ÏßÇ¡ºÃ¶Ï¿ª£¬ÇóСÇòÂäµØµãÓëOµãµÄˮƽλÒÆx£®

Answer 1

·ÖÎö £¨1£©´ÓAµ½B¸ù¾Ý¶¯Äܶ¨Àí¼´¿ÉÇó³öOµãÕýÏ·½BµãµÄËٶȴóС£»
£¨2£©ÔÚBµã£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó½âϸÏ߶ÔBµã´¦µÄСÇòµÄÀ­Á¦´óС£»
£¨3£©Ï¸Ï߶Ͽªºó£¬Ð¡Çò×öÀàƽÅ×Ô˶¯£¬ÓÉÀàƽÅ×Ô˶¯µÄ֪ʶºÍÅ£¶ÙµÚ¶þ¶¨Âɼ´¿ÉÇó½â£»

½â´ð ½â£º£¨1£©´ÓAµ½B¹ý³Ì£¬Óɶ¯Äܶ¨ÀíµÃ£º
mgL+qEL=$\frac{1}{2}$mv²-0 
СÇòµ½´ïBµãʱµÄËÙ¶ÈΪ£º
$v=\sqrt{\frac{2£¨mg+qE£©L}{m}}$
£¨2£©ÔÚBµã£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº
T-mg-qE=$m\frac{{v}_{\;}^{2}}{L}$
½âµÃ£ºT=3£¨mg+qE£©
£¨3£©¶ÔСÇòÔÚÉþ¶Ï¿ªºóµÄÀàƽÅ×Ô˶¯£º
ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÓУºqE+mg=ma
ÊúÖ±·½ÏòÉÏÓУº$H-L=\frac{1}{2}a{t}_{\;}^{2}$
ˮƽ·½ÏòÉÏÓУºx=vt
ÁªÁ¢½âµÃ£º$x=2\sqrt{£¨H-L£©L}$
´ð£º£¨1£©Ð¡ÇòÔ˶¯µ½OµãÕýÏ·½BµãʱµÄËٶȴóСΪ$\sqrt{\frac{2£¨mg+qE£©L}{m}}$
£¨2£©´Ë¿ÌϸÏ߶ÔBµã´¦µÄСÇòµÄÀ­Á¦´óСΪ3£¨mg+qE£©
£¨3£©ÈôСÇòͨ¹ýBµãʱ£¬Ï¸ÏßÇ¡ºÃ¶Ï¿ª£¬ÇóСÇòÂäµØµãÓëOµãµÄˮƽλÒÆxΪ$2\sqrt{£¨H-L£©L}$

µãÆÀ ±¾Ì⿼²éÁ˶¯Äܶ¨ÀíÒÔ¼°Å£¶ÙµÚ¶þ¶¨ÂÉ£¬ÖªµÀСÇò×öÔ²ÖÜÔ˶¯Ñذ뾶·½ÏòÉϵĺÏÁ¦ÌṩÏòÐÄÁ¦£¬×¢ÒâÀàƽÅ×Ô˶¯µÄ´¦Àí·½·¨£®