Question

3£®ÈçͼËùʾ£¬Á£×ÓÔ´S¿ÉÒÔ²»¶Ï²úÉúÖÊÁ¿Îªm¡¢µçºÉÁ¿Îª+qµÄÁ£×Ó£¨ÖØÁ¦²»¼Æ£©£®Á£×Ó´ÓO₁¿×Æ®½øÒ»¸öˮƽ·½ÏòµÄ¼ÓËٵ糡£¨³õËÙ²»¼Æ£©£¬ÔÙ¾­¹ýС¿×O₂½øÈëÏ໥Õý½»µÄÔÈÇ¿µç³¡ºÍÔÈÇ¿´Å³¡ÇøÓò£¬µç³¡Ç¿¶È´óСΪE£¬´Å¸ÐӦǿ¶È´óСΪB₁£¬·½ÏòÈçͼ£®ÐéÏßPQ¡¢MNÖ®¼ä´æÔÚ×ÅˮƽÏòÓÒµÄÔÈÇ¿´Å³¡£¬´Å³¡·¶Î§×ã¹»´ó£¬´Å¸ÐӦǿ¶È´óСΪB₂£®Ò»¿éÕÛ³ÉÖ±½ÇµÄÓ²ÖÊËÜÁÏƬabc£¨²»´øµç£¬¿í¶ÈºÍºñ¶È¶¼ºÜС¿ÉºöÂÔ£¬ab±ß¡¢bc±ßΪËÜÁÏƬ£¬ac±ßΪȱ¿Ú£©·ÅÖÃÔÚPQ¡¢MNÖ®¼ä£¬½ØÃæͼÈçͼ£¬a¡¢cÁ½µã·Ö±ðλÓÚPQ¡¢MNÉÏ£¬ab=bc=L£¬¦Á=45¡ã£®Á£×ÓÄÜÑØͼÖÐÐéÏßO₂O₃µÄÑÓ³¤Ïß½øÈëPQ¡¢MNÖ®¼äµÄÇøÓò£®

£¨1£©Çó¼ÓËÙµçѹU₁£»
£¨2£©¼ÙÉèÁ£×ÓÓëÓ²ÖÊËÜÁÏƬÏàÅöºó£¬ËٶȴóС²»±ä£¬·½Ïò×ñÑ­¹âµÄ·´É䶨ÂÉ£¬ÄÇôÁ£×ÓÓëËÜÁÏƬµÚÒ»´ÎÏàÅöºóµ½µÚ¶þ´ÎÏàÅöÇ°×öʲôÔ˶¯£¿
£¨3£©Á£×ÓÔÚPQ¡¢MNÖ®¼äµÄÇøÓòÖÐÔ˶¯µÄ×Üʱ¼ätºÍ×Ü·³Ìs£®

Answer 1

·ÖÎö £¨1£©Á£×Ó¾­¹ý¸´ºÏ³¡Ê±£¬µç³¡Á¦ÏòÏ£¬ÂåÂ××ÈÁ¦ÏòÉÏ£¬¶¼ÓëËٶȴ¹Ö±£¬¹ÊºÏÁ¦ÎªÁ㣬¸ù¾ÝƽºâÌõ¼þÁÐʽÇó½âËٶȣ»
£¨2£©Á£×ÓÓë´Å³¡µÚÒ»´ÎÅöײºó£¬ËÙ¶ÈÏòÉÏ£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬ÔÚÓëac±ß´¹Ö±µÄƽÃæÄÚ×öÔÈËÙÔ²ÖÜÔ˶¯£¬¾­¹ýһȦºó£¬Óëab±ßÄÚ²àÅöײ£¬ÅöײºóˮƽÏòÓÒÔ˶¯£¬Óëbc±ß¶þ´ÎÅöײºó£¬ÔÚÓëac±ß´¹Ö±µÄƽÃæÄÚ×öÔÙ´ÎÔÈËÙÔ²ÖÜÔ˶¯£¬ÓÖ¾­¹ýһȦºó£¬Óëb±ßÍâ²àÅöײ£¬Ë®Æ½ÏòÓÒÀ뿪´Å³¡£®
£¨3£©ÏÈ·ÖÎö³öÔ˶¯¹ì¼££¬ÔÙ·ÖÔÈËÙÖ±ÏßÔ˶¯ºÍÔÈËÙÔ²ÖÜÔ˶¯ÌÖÂÛ£¬¶ÔÓÚÔÈËÙÔ²ÖÜÔ˶¯£¬ÏȼÆËã°ë¾¶ºÍÖÜÆÚ£¬ÔÙ¸ù¾Ý¹ì¼£¼ÆË㣮

½â´ð ½â£º£¨1£©Á£×ÓÔÚÕý½»³¡ÖÐ×öÔÈËÙÔ˶¯£¬Eq=qv₀B₁£¬
½âµÃ£ºv₀=$\frac{E}{{B}_{1}}$£¬
Óɶ¯Äܶ¨ÀíµÃ£ºqU₁=$\frac{1}{2}$mv₀²-0£¬
½âµÃ£ºU₁=$\frac{m{E}^{2}}{2q{B}_{1}^{2}}$£»
£¨2£©Á£×ÓÅöµ½abºóÒÔ´óСΪv₀µÄËٶȴ¹Ö±´Å³¡·½ÏòÔ˶¯£¬ÔÚÂåÂØ×È×÷ÓÃÏÂÔÚ´¹Ö±Óڴų¡µÄƽÃæÄÚ×öÔÈËÙÔ²ÖÜÔ˶¯£¬×ª¹ýÒ»Öܺó´ïµ½abµÄϲ¿£®   
£¨3£©ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãºqv₀B₂=m$\frac{{v}_{0}^{2}}{R}$£¬
½âµÃ£ºR=$\frac{mE}{q{B}_{1}{B}_{2}}$£¬
Á£×ÓÔڴų¡ÖÐ×öÔ²ÖÜÔ˶¯µÄÖÜÆÚΪ£ºT=$\frac{2¦Ðm}{q{B}_{2}}$£¬
Á£×ÓÔڴų¡Öй²Åö°å2´Î£¬×öÔ²ÖÜÔ˶¯µÄʱ¼äΪ£ºt₁=2T=$\frac{4¦Ðm}{q{B}_{2}}$£¬
×öÔ²ÖÜÔ˶¯µÄ·³ÌΪ£ºs₁=2•2¦ÐR=$\frac{4¦ÐmE}{q{B}_{1}{B}_{2}}$£¬
ÔÚˮƽ·½ÏòÉÏÔ˶¯µÄ·³ÌΪ£ºs₂=$\sqrt{2}$R£¬
¾­ÀúµÄʱ¼äΪ£ºt₂=$\frac{s}{{v}_{0}}$=$\frac{\sqrt{2}{B}_{1}L}{E}$£¬
ÔòÁ£×ÓÔÚPQ¡¢MNÖ®¼äµÄÇøÓòÖÐÔ˶¯µÄ×Üʱ¼äΪ£ºt=t₁+t₂=$\frac{4¦Ðm}{q{B}_{2}}$+$\frac{\sqrt{2}{B}_{1}L}{E}$£¬
×Ü·³ÌΪ£ºs=s₁+s₂=$\frac{4¦ÐmE}{q{B}_{1}{B}_{2}}$+$\sqrt{2}$R£»
´ð£º£¨1£©¼ÓËÙµçѹU₁Ϊ$\frac{m{E}^{2}}{2q{B}_{1}^{2}}$£»
£¨2£©×öÔÈËÙÔ²ÖÜÔ˶¯£®
£¨3£©Á£×ÓÔÚPQ¡¢MNÖ®¼äµÄÇøÓòÖÐÔ˶¯µÄ×Üʱ¼ätΪ$\frac{4¦Ðm}{q{B}_{2}}$+$\frac{\sqrt{2}{B}_{1}L}{E}$£¬×Ü·³ÌsΪ$\frac{4¦ÐmE}{q{B}_{1}{B}_{2}}$+$\sqrt{2}$R£®

µãÆÀ ±¾ÌâÖеĸ´ºÏ³¡¾ßÓÐËÙ¶ÈÑ¡ÔñµÄ¹¦ÄÜ£¬½øÈë´Å³¡ÇøÓòºó£¬¸ù¾Ý¶¯Á¦Ñ§¹æÂÉÏÈÈ·¶¨Ô˶¯¹ì¼££¬ÔÙ½øÐмÆË㣮