Question

11£®ÈçͼËùʾ£¬Ïà¾àΪdµÄƽÐнðÊô°åA¡¢BÊúÖ±·ÅÖã¬ÔÚÁ½°åÖ®¼äˮƽ·ÅÖÃÒ»¾øԵƽ°å£¬Á½°å¼äµçѹΪU=$\frac{3¦Ìmgd}{2q}$£®ÓÐÒ»ÖÊÁ¿m¡¢µçºÉÁ¿+qµÄСÎï¿éÔÚÓë½ðÊô°åAÏà¾àl´¦Óɾ²Ö¹ÊÍ·Å£®Ð¡Îï¿éÓë½ðÊô°åÖ»·¢ÉúÁËÒ»´ÎÅöײ£¬ÅöײºóµçºÉÁ¿±äΪ-$\frac{q}{2}$£¬²¢ÒÔÓëÅöÇ°´óСÏàµÈµÄËٶȷ´·½Ïòµ¯»Ø£®ÒÑ֪СÎï¿éÓë¾øԵƽ°å¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì£¬Èô²»¼ÆСÎï¿éµçºÉÁ¿¶Ôµç³¡µÄÓ°Ïì¡¢Åöײʱ¼äºÍСÎï¿éµÄ´óС£®£¨gΪÖØÁ¦¼ÓËٶȣ©Ôò
£¨1£©Ð¡Îï¿éÓë½ðÊô°åAÅöײǰ˲¼äµÄËٶȴóСÊǶàÉÙ£¿
£¨2£©Ð¡Îï¿éÅöײºó¾­¹ý¶à³¤Ê±¼äÍ£Ö¹Ô˶¯£¿Í£ÔÚ¾àA°å¶à´ó¾àÀë´¦£¿

Answer 1

·ÖÎö ¸ÃÌâµÄÑо¿Çé¾°Êǵ糡£¬Äܹ»¶ÔСÎïÌå½øÐÐÊÜÁ¦·ÖÎö£¬ÔËÓÃÅ£¶ÙµÚ¶þ¶¨ÂɽáºÏÔ˶¯Ñ§¹«Ê½Çó½âÎÊÌ⣮ҪעÒâСÎï¿éÓëA°åÅöײʱÎïÀíÁ¿µÄ¸Ä±ä¶ÔÎÊÌâÑо¿µÄÓ°Ï죮

½â´ð ½â£º£¨1£©¼Óµçѹºó£¬Ð¡Îï¿éÔڵ糡Á¦×÷ÓÃÓëĦ²ÁÁ¦¹²Í¬×÷ÓÃÏÂÏòA°å×öÔȼÓËÙÖ±ÏßÔ˶¯£®µç³¡Ç¿¶ÈΪ£º$E=\frac{U}{d}$
СÎï¿éËùÊܵĵ糡Á¦ÓëĦ²ÁÁ¦·½ÏòÏà·´£¬ÔòºÏÍâÁ¦Îª£ºF_ºÏ=qE-¦Ìmg
¹ÊСÎï¿éÔ˶¯µÄ¼ÓËÙ¶ÈΪ£º${a}_{1}=\frac{{F}_{ºÏ}}{m}=\frac{qU-¦Ìmgd}{md}=\frac{1}{2}¦Ìg$
ÉèСÎï¿éÓëA°åÏàÅöʱµÄËÙ¶ÈΪv₁£¬ÓÉ${v}_{1}^{2}=2{a}_{1}l$
½âµÃ£º${v}_{1}=\sqrt{¦Ìgl}$
£¨2£©Ð¡Îï¿éÓëA°åÏàÅöºóÒÔv₁´óСÏàµÈµÄËٶȷ´µ¯£¬ÒòΪµçºÉÁ¿¼°µçÐԸı䣬µç³¡Á¦´óСÓë·½ÏòÉú±ä»¯£¬Ä¦²ÁÁ¦µÄ·½Ïò·¢Éú¸Ä±ä£¬Ð¡Îï¿éËùÊܵĺÏÍâÁ¦´óСΪ£º${F}_{ºÏ}=¦Ìmg-\frac{qE}{2}$£¬
¼ÓËٶȴóСΪ£º
${a}_{2}=\frac{{F}_{ºÏ}}{m}=\frac{1}{4}¦Ìg$
ÉèСÎï¿éÅöºóµ½Í£Ö¹µÄʱ¼äΪ t£¬×¢Ò⵽ĩËÙ¶ÈΪÁ㣬ÓУº0-v₁=a₂t
½âµÃ£º$t=\frac{{v}_{1}}{{a}_{2}}=4\sqrt{\frac{l}{¦Ìg}}$
ÉèСÎï¿éÅöºóֹͣʱ¾àÀëΪx£¬×¢Ò⵽ĩËÙ¶ÈΪÁ㣬ÓУº
$0-{v}_{1}^{2}=-2{a}_{2}x$
Ôò$x=\frac{{v}^{2}}{2{a}_{2}}=2l$£¬¹Ê¾àÀëA°åΪd=2l
´ð£º£¨1£©Ð¡Îï¿éÓë½ðÊô°åAÅöײǰ˲¼äµÄËٶȴóСÊÇ$\sqrt{¦Ìgl}$£»
£¨2£©Ð¡Îï¿éÅöײºó¾­¹ý$4\sqrt{\frac{l}{¦Ìg}}$ʱ¼äÍ£Ö¹Ô˶¯£¬Í£ÔÚ¾àA°å2l¾àÀë´¦£®

µãÆÀ ±¾Ì⿼²éµç³¡ÖеĶ¯Á¦Ñ§ÎÊÌ⣬ÊÜÁ¦·ÖÎö¡¢ÇóºÏÁ¦¡¢Çó¼ÓËٶȡ¢ÔËÓÃÔ˶¯Ñ§¹«Ê½Çó½âһЩÎïÀíÁ¿£®Òª×¢ÒâÑо¿ÎÊÌâµÄÇé¾°ËæÔ˶¯¹ý³ÌµÄ¸Ä±ä£®