Question

20£®ÈçͼËùʾ£¬Ò»¸ù³¤ÎªLµÄ¾øÔµÇáÉþµÄÒ»¶Ë¹Ì¶¨ÔÚOµã£¬ÁíÒ»¶ËÁ¬½Ó×ÅÒ»¸ö´øÕýµçµÄСÇò£¬Ð¡Çò¿ÉÊÓΪÖʵ㣬ÆäÖÊÁ¿Îªm£¬µçºÉÁ¿Îªq£®ÔÚOµãÕýÉÏ·½ºÍÕýÏ·½¾àOµãL´¦£¬¸÷¹Ì¶¨Ò»¸ö¾øÔµµ¯ÐÔµ²°åAºÍB£¬Á½¸öµ²°å³ß´çºÜС£¬¾ùÊúÖ±·ÅÖã®´Ë×°Öô¦ÔÚÒ»¸öÊúÖ±ÔÈÇ¿µç³¡ÖУ¬µç³¡Ç¿¶ÈµÄ´óСΪE=$\frac{mg}{q}$£¬·½Ïò×î³õÊúÖ±ÏòÉÏ£®ÏÖ½«Ð¡ÇòÀ­µ½OµãÓÒ²àͬһ¸ß¶ÈÇÒ¾àOµãL´¦£¬¸øËüÒ»¸öÊúÖ±ÏòÉϵijõËÙ¶Èv₀=$\sqrt{2gL}$£®´ËºóСÇòÔÚA¡¢BÖ®¼äµÄÓÒ²àÇøÓòÊúÖ±ÃæÄÚ×öÔ²ÖÜÔ˶¯£¬²¢²»Ê±ÓëA¡¢Bµ²°åÅöײ£¬ÔÚСÇòÓëA¡¢Bµ²°åÅöײʱ£¬Í¨¹ýÁ½µ²°åÉÏ°²×°µÄ´«¸ÐÆ÷ºÍ¿ØÖƵç·£¬¿ØÖƵ糡·½ÏòÔÚÅöºó˲¼ä·´Ïò£¬²»¼ÆÅöײÖеÄÄÜÁ¿Ëðʧ£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£¬Çó£º
£¨1£©Ð¡ÇòÓëAµ²°åµÚÒ»´ÎÅöǰ˲¼ä£¬ÉþÖÐÀ­Á¦F₁Ϊ¶àÉÙ£¿
£¨2£©Ð¡ÇòÓëBµ²°åµÚÒ»´ÎÅöǰ˲¼ä£¬ÉþÖеÄÀ­Á¦F₂Ϊ¶àÉÙ£¿
£¨3£©ÈôÇáÉþ¿ÉÒÔ³ÐÊܵÄ×î´óÀ­Á¦Îª50mg£¬ÔòÔÚÉþ¶Ï֮ǰ£¬Ð¡ÇòÓëBµ²°åÅöײÁ˶àÉٴΣ¿

Answer 1

·ÖÎö £¨1£©Ð¡ÇòÊܵ½µÄÖØÁ¦ºÍµç³¡Á¦Ö®ºÍΪÁ㣬¹ÊСÇòÒÔv₀×öÔÈËÙÔ²ÖÜÔ˶¯£¬¹ÊÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÇóµÄÀ­Á¦
£¨2£©µÚÒ»´ÎÅöºóÀûÓö¯Äܶ¨ÀíÇóµÄµ½´ïBµãµÄËٶȣ¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÇóµÄÀ­Á¦
£¨3£©ÔÚÒÔºóµÄÅöײ¹ý³ÌÖмäµÄÔ˶¯ÀûÓö¯Äܶ¨ÀíÇóµÄÅöײʱµÄËٶȣ¬ÀûÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉÇóµÄÀ­Á¦£¬¼´¿ÉÅжϣ®

½â´ð ½â£º£¨1£©Ð¡ÇòµÚÒ»´ÎÓëAÅö֮ǰ£¬qE=mgÇÒ·½ÏòÏà·´£¬×öÔÈËÙÔ²ÖÜÔ˶¯
ËùÒÔСÇòÓëA°åµÚÒ»´ÎÅöÇ°£¬ËÙ¶ÈΪ${v}_{0}=\sqrt{2gL}$
${F}_{1}=\frac{{mv}_{0}^{2}}{L}=2mg$
СÇò´ÓÓëA°åµÚÒ»´ÎÅöºóµ½ÓëB°åµÚÒ»´ÎÅöÇ°µÄ¹ý³ÌÖÐ
$£¨qE+mg£©2L=\frac{1}{2}{mv}_{B1}^{2}-\frac{1}{2}{mv}_{0}^{2}$
½âµÃ${v}_{B1}=\sqrt{10gL}$
СÇòÓëB°åµÚÒ»´ÎÅöÇ°${T}_{B1}-qE-mg=\frac{{mv}_{B1}^{2}}{L}$
½âµÃ£ºT_B1=12mg
£¨3£©Ð¡Çò´ÓÓëB°åµÚÒ»´ÎÅöºóµ½ÓëA°åµÚ¶þ´ÎÅöÇ°£¬qE=mgÇÒ·½ÏòÏà·´£¬×öÔÈËÙÔ²ÖÜÔ˶¯£®
ÇòÓëA°åµÚ¶þ´ÎÅöÇ°${V}_{A2}={V}_{B1}=\sqrt{10gL}$
´ËʱϸÉþÖÐÀ­Á¦  ${T}_{A2}=\frac{{mv}_{A2}^{2}}{L}=10mg$
СÇò´ÓÓëA°åµÚ¶þ´ÎÅöºóµ½ÓëB°åµÚ¶þ´ÎÅöÇ°µÄ¹ý³ÌÖÐ$£¨qE+mg£©2L=\frac{1}{2}{mv}_{B2}^{2}-\frac{1}{2}{mv}_{A2}^{2}$
${v}_{B2}=\sqrt{18gL}$
СÇòÓëB°åµÚ¶þ´ÎÅöÇ°${T}_{B2}-qE-mg=\frac{{mv}_{B2}^{2}}{L}$
½âµÃT_B2=20mg
×ÛÉÏ·ÖÎö¿ÉÖª£¬Ð¡Çòÿ´ÎÓëA£¬B°åÅöÇ°£¬ÉþÖÐÀ­Á¦±ÈÉÏÒ»´ÎÅöÇ°Ôö¼Ó¡÷T=8mg
ÔòСÇòÓëBµµ°åµÚn´ÎÅöÃ棬ÉþÖÐÀ­Á¦T_Bn=T_B1+£¨n-1£©¡÷T=£¨8n+4£©mg
ÈôÉþ¶Ï£¬ÔòT_Bn¡Ý50mg
ÁªÁ¢µÃ£ºn¡Ý5.75
ËùÒÔСÇòÔÚÉþ¶ÏÇ°ÓëBµ²°åÅöײÁË5´Î£®
´ð£º£¨1£©Ð¡ÇòÓëAµ²°åµÚÒ»´ÎÅöǰ˲¼ä£¬ÉþÖÐÀ­Á¦F₁Ϊ2mg
£¨2£©Ð¡ÇòÓëBµ²°åµÚÒ»´ÎÅöǰ˲¼ä£¬ÉþÖеÄÀ­Á¦F₂Ϊ12mg
£¨3£©ÈôÇáÉþ¿ÉÒÔ³ÐÊܵÄ×î´óÀ­Á¦Îª50mg£¬ÔòÔÚÉþ¶Ï֮ǰ£¬Ð¡ÇòÓëBµ²°åÅöײÁË5´Î

µãÆÀ ±¾ÌâҪעÒâµç³¡Á¦ÓëÖØÁ¦×ö¹¦µÄÌص㣬¶þÁ¦×ö¹¦¾ùÓë·¾¶Î޹أ¬¹Ø¼üÊÇץסÔÚСÇòÏòÉÏÔ˶¯Ê±ÖØÁ¦Óëµç³¡Á¦´óСÏàµÈ·½ÏòÏà·´£¬µç³¡Á¦ºÍÖØÁ¦×ö¹¦Ö®ºÍΪÁ㣬ÏòÏÂÔ˶¯Ê±ÖØÁ¦ºÍµç³¡Á¦×öÕý¹¦¼´¿É