Question

20£®Æ½ÐаåµçÈÝÆ÷ABÁ½¼«°åÖ®¼äµçѹΪU£¬¼ä¾àΪd£®Ï¼«°åÓëÒ»¸öÖ±¾¶ÎªLµÄ°ëÔ²ÐνðÊôͨµÀÏàÁ¬£¬½ðÊôͨµÀÓÐÁ½¸öͬÐĵİëÔ²ÐνðÊôƬCD×é³É£¬Ô²ÐÄÌùÔÚO¡ä´¦£¬Á½¸ö½ðÊôƬ±Ë´Ë¿¿½üÓÖ²»½Ó´¥£¬Öмä´æÔÚ¾¶Ïòµç³¡£¬¼´µç³¡´óСÏàµÈ£¬·½Ïò¶¼Ö¸ÏòO¡ä£®°ëÔ²ÐÎͨµÀÓëϼ«°å½Ó´¥µãÓÐС¿×ÏàÁ¬Í¨£®ÏÖ´ÓÕý¶ÔB°åС¿×½ô¿¿A°åµÄO´¦Óɾ²Ö¹ÊÍ·ÅÒ»¸öÖÊÁ¿Îªm¡¢µçºÉÁ¿ÎªqµÄ´øÕýµç΢Á££¨Î¢Á£µÄÖØÁ¦²»¼Æ£©£¬Á£×ÓÔÚ°ëÔ²ÐιìµÀ¼äÔ˶¯¶ø²»»á·¢ÉúÅöײ£®
£¨1£©Çó³ö΢Á£´©¹ýB°åС¿×½øÈë°ëÔ²ÐιìµÀʱµÄËٶȴóСºÍ°ëÔ²ÐνðÊôͨµÀÄڵĵ糡ǿ¶È´óС£®
£¨2£©´ÓÊÍ·Å΢Á£¿ªÊ¼¼Æʱ£¬¾­¹ý¶à³¤Ê±¼ä΢Á£Í¨¹ý°ëÔ²ÐνðÊô°å¼äµÄ×îµÍµãPµã£¿
£¨3£©Èô°Ñ°ëÔ²ÐιìµÀÄڵĵ糡¸ÄΪ´Å³¡£¬ÔòÐèÒªÒ»¸öʲôÑùµÄ´Å³¡¿ÉÒÔʵÏÖÎÞÅöײͨ¹ý°ëÔ²ÐιìµÀ£¿

Answer 1

·ÖÎö £¨1£©ÏÈÓÉAB¼äµç³¡¼ÓËÙºó½øÈë°ëÔ²ÐνðÊôͨµÀ×÷ÔÈËÙÔ²ÖÜÔ˶¯£¬Ïȸù¾Ý¶¯Äܶ¨ÀíÇó³ö¼ÓËٶȵõ½µÄËٶȣ®ÔÙ¸ù¾Ýµç³¡Á¦³äµ±ÏòÐÄÁ¦£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÇó½â°ëÔ²ÐνðÊôͨµÀÄڵĵ糡ǿ¶È£®
£¨2£©ÓÉλÒƵÈÓÚƽ¾ùËٶȳËÒÔʱ¼ä£¬ÁÐʽÇó³ö΢Á£ÔÚAB¼äÔ˶¯µÄʱ¼ä£®ÔÙÓÉÔ²ÖÜÔ˶¯µÄ¹æÂÉÇó³ö΢Á£´ÓCµ½PµÄʱ¼ä£®
£¨3£©Èô°Ñ°ëÔ²ÐιìµÀÄڵĵ糡¸ÄΪ´Å³¡£¬Î¢Á£Ôڴų¡ÖÐ×÷ÔÈËÙÔ²ÖÜÔ˶¯£¬°ë¾¶Îª$\frac{L}{2}$£¬ÓÉÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬ÁÐʽÇó³ö´Å¸ÐӦǿ¶ÈµÄ´óС£¬ÓÉ×óÊÖ¶¨ÔòÅжϴų¡µÄ·½Ïò£®

½â´ð ½â£º£¨1£©Î¢Á£ÔÚAB¼ä¼ÓËÙ¹ý³Ì£¬Óɶ¯Äܶ¨ÀíµÃ£ºqU=$\frac{1}{2}m{v}^{2}$¡­¢Ù
µÃ£ºv=$\sqrt{\frac{2qU}{m}}$
΢Á£ÔÚ°ëÔ²ÐνðÊôͨµÀ×÷ÔÈËÙÔ²ÖÜÔ˶¯£¬µç³¡Á¦³äµ±ÏòÐÄÁ¦£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵãºqE=m$\frac{{v}^{2}}{\frac{L}{2}}$¡­¢Ú
ÁªÁ¢¢Ù¢Ú½âµÃ£ºE=$\frac{4U}{L}$
£¨2£©Éè΢Á£ÔÚAB¼äÔ˶¯Ê±¼äΪt₁£¬´ÓCÔ˶¯µ½PµÄʱ¼äΪt₂£®
ÔòÔÚAB¼ä£¬ÓУºd=$\frac{v}{2}{t}_{1}$£¬
µÃ£ºt₁=d$\sqrt{\frac{2m}{qU}}$
´ÓCÔ˶¯µ½PµÄʱ¼äΪ£ºt₂=$\frac{\frac{¦Ð}{2}•\frac{L}{2}}{v}$=$\frac{¦ÐL}{4}$$\sqrt{\frac{m}{2qU}}$
¹ÊÓУºt=t₁+t₂=d$\sqrt{\frac{2m}{qU}}$+$\frac{¦ÐL}{4}$$\sqrt{\frac{m}{2qU}}$=£¨d+$\frac{¦ÐL}{8}$£©$\sqrt{\frac{2m}{qU}}$
£¨3£©Èô°Ñ°ëÔ²ÐιìµÀÄڵĵ糡¸ÄΪ´Å³¡£¬ÓÉ×óÊÖ¶¨ÔòÅжÏÖª£¬´Å³¡·½Ïò±ØÐë´¹Ö±Ö½ÃæÏòÀÉè´Å¸ÐӦǿ¶È´óСΪB£®
¸ù¾ÝqvB=m$\frac{{v}^{2}}{\frac{L}{2}}$
µÃ£ºB=$\frac{2}{L}$$\sqrt{\frac{2mU}{q}}$
´ð£º£¨1£©Î¢Á£´©¹ýB°åС¿×½øÈë°ëÔ²ÐιìµÀʱµÄËٶȴóСΪ$\sqrt{\frac{2qU}{m}}$£¬°ëÔ²ÐνðÊôͨµÀÄڵĵ糡ǿ¶È´óСΪ$\frac{4U}{L}$£®
£¨2£©´ÓÊÍ·Å΢Á£¿ªÊ¼¼Æʱ£¬¾­¹ý£¨d+$\frac{¦ÐL}{8}$£©$\sqrt{\frac{2m}{qU}}$ʱ¼ä΢Á£Í¨¹ý°ëÔ²ÐνðÊô°å¼äµÄ×îµÍµãPµã£®
£¨3£©Èô°Ñ°ëÔ²ÐιìµÀÄڵĵ糡¸ÄΪ´Å³¡£¬ÔòÐèÒªÒ»¸ö´¹Ö±Ö½ÃæÏòÀï¡¢´Å¸ÐӦǿ¶ÈΪ$\frac{2}{L}$$\sqrt{\frac{2mU}{q}}$µÄ´Å³¡¿ÉÒÔʵÏÖÎÞÅöײͨ¹ý°ëÔ²ÐιìµÀ£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÒªÃ÷ȷ΢Á£µÄÔ˶¯Çé¿ö£¬ÅжÏÆäÊÜÁ¦Çé¿ö£¬ÔËÓö¯Á¦Ñ§·½·¨´¦Àí£®¶ÔÓÚÔ²ÖÜÔ˶¯£¬¹Ø¼üҪȷ¶¨ÏòÐÄÁ¦µÄÀ´Ô´£®