Question

15£®ÈçͼËùʾ±ØÐëÊǰ뾶ΪrµÄ$\frac{1}{4}$Ô²»¡ÐεĹ⻬ÇÒ¾øÔµµÄ¹ìµÀ£¬Î»ÓÚÊúֱƽÃæÄÚ£¬Æä϶ËÓëˮƽ¾øÔµ¹ìµÀƽ»¬Á¬½Ó£¬Õû¸ö¹ìµÀ´¦ÔÚÊÇˮƽÏò×óµÄÔÈÇ¿µç³¡ÖУ¬µç³¡Ç¿¶ÈΪE£¬½ñÓÐÒ»ÖÊÁ¿Îªm£¬´øÕýµçqµÄС»¬¿é£¨Ìå»ýºÜС¿ÉÒÔÊÓΪÖʵ㣩£¬´ÓCµãÓɾ²Ö¹ÊÍ·Å£¬»¬µÀˮƽ¹ìµÀÉϵÄAµãʱËٶȼõΪÁ㣬ÈôÒÑÖª»¬¿éÓëˮƽ¹ìµÀ¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£¬ºöÂÔÒòĦ²Á¶øÔì³ÉµÄµçÁ¿Ëðʧ£®
£¨1£©»¬¿éͨ¹ýBµãʱµÄËٶȴóС£»
£¨2£©»¬¿é´ÓCµã»¬µ½AµãµçÊÆÄܱ仯µÄÖµÊǶà´ó£¿
£¨3£©ÊÔ·ÖÎö£¬»¬¿éÔÚˮƽÃæÉϾ­¹ý·µÄ×î´óÖµÊǶàÉÙ£¿

Answer 1

·ÖÎö £¨1£©Ð¡»¬¿é´ÓCµ½BµÄ¹ý³ÌÖУ¬Ö»ÓÐÖØÁ¦ºÍµç³¡Á¦¶ÔËü×ö¹¦£¬¸ù¾Ý¶¯Äܶ¨ÀíÇó½â£®
£¨2£©¶ÔÕû¸ö¹ý³ÌÑо¿£¬ÖØÁ¦×öÕý¹¦£¬Ë®Æ½ÃæÉÏĦ²ÁÁ¦×ö¸º¹¦£¬µç³¡Á¦×ö¸º¹¦£¬¸ù¾Ý¶¯Äܶ¨ÀíÇó³öˮƽ¹ìµÀÉÏA¡¢BÁ½µãÖ®¼äµÄ¾àÀë¼°µç³¡Á¦×ö¹¦£®

½â´ð ½â£º£¨1£©Ð¡»¬¿é´ÓCµ½BµÄ¹ý³ÌÖУ¬Ö»ÓÐÖØÁ¦ºÍµç³¡Á¦¶ÔËü×ö¹¦£¬
  É軬¿éͨ¹ýBµãʱµÄËÙ¶ÈΪv_B£¬¸ù¾Ý¶¯Äܶ¨ÀíÓУº
   mgR-qER=$\frac{1}{2}{mv}_{B}^{2}$                    
½âµÃ£ºv_B=$\sqrt{\frac{2£¨mg-qE£©R}{m}}$               
  £¨2£©´ÓCµ½AÓɶ¯Äܶ¨Àí¿ÉÖª
mgR-qE£¨x+R£©-¦Ìmgx=0-0
x=$\frac{mgR-qER}{qE+¦Ìmg}$
µçÊÆÄܱ仯Ϊ$E=qE•£¨x+R£©=\frac{qE£¨mgR+¦ÌmgR£©}{qE+¦Ìmg}$
´ð£º£¨1£©»¬¿éͨ¹ýBµãʱµÄËٶȴóСΪ$\sqrt{\frac{2£¨mg-qE£©R}{m}}$£»
£¨2£©»¬¿é´ÓCµã»¬µ½AµãµçÊÆÄܱ仯µÄÖµÊÇ$\frac{mgR-qER}{qE+¦Ìmg}$
£¨3£©ÊÔ·ÖÎö£¬»¬¿éÔÚˮƽÃæÉϾ­¹ý·µÄ×î´óÖµÊÇ$\frac{qE£¨mgR+¦ÌmgR£©}{qE+¦Ìmg}$

µãÆÀ ±¾Ì⿼²é·ÖÎöºÍ´¦ÀíÎïÌåÔÚ¸´ºÏ³¡Ô˶¯µÄÄÜÁ¦£®¶ÔÓڵ糡Á¦×ö¹¦W=qEd£¬dΪÁ½µãÑص糡Ïß·½ÏòµÄ¾àÀë