Question

11£®Ê¾²¨Æ÷Êǵç×Ó¼¼ÊõÖг£ÓõIJâÁ¿ÒÇÆ÷£¬ÆäʾÒâͼÈçͼËùʾ£¬½ðÊôË¿·¢Éä³öÀ´µÄµç×Ó±»¼ÓËÙºó´Ó½ðÊô°åµÄС¿×´©³ö£¬½øÈëƫתµç³¡£®µç×ÓÔÚ´©³öƫתµç³¡ºóÑØÖ±ÏßÇ°½ø£¬×îºó´òÔÚÓ«¹âÆÁÉÏ£®Éè¼ÓËÙµçѹΪU₁£¬Æ«×ª¼«°å³¤Îªl£¬Æ«×ª¼«°å¼ä¾àΪd£¬µ±µç×Ó¼ÓËÙºó´ÓÁ½½ðÊô°åµÄÖÐÑëÑؼ«°åƽÐз½Ïò½øÈëƫתµç³¡£®Çó£º
£¨1£©Æ«×ªµçѹU₂Ϊ¶à´óʱ£¬µç×ÓÊøÇ¡ºÃ´Óϼ«°å±ßÔµ·É³ö£¿
£¨2£©Èç¹ûƫת¼«°åÓҶ˵½Ó«¹âÆÁµÄ¾àÀëΪL£¬Ôòµç×ÓÊøÔÚÓ«¹âÆÁµÄ×î´óƫת¾àÀëΪ¶àÉÙ£¿

Answer 1

·ÖÎö £¨1£©ÔËÓö¯Äܶ¨ÀíÇóµÃµç×Ó½øÈëƫתµç³¡Ê±µÄ³õËٶȣ»
µ±µç×Ó¾­Æ«×ªµç³¡ºó´ÓÏ°å±ßÔµ³öÀ´Ê±£¬µç×ÓÊø´òÔÚÓ«¹âÆÁÉÏƫת¾àÀë×î´ó£»ÔËÓÃÔ˶¯µÄ·Ö½â£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂɺÍÔ˶¯Ñ§¹«Ê½½áºÏÇó³öƫתµçѹU₂£»
£¨2£©ÀàËÆƽÅ×Ô˶¯µÄÄ©Ëٶȵķ´ÏòÑÓ³¤Ïßͨ¹ýˮƽ·ÖλÒƵÄÖе㣬½áºÏ¼¸ºÎ¹ØϵÁÐʽÇó½âµç×ÓÊøÔÚÓ«¹âÆÁÉϵÄ×î´óƫת¾àÀëy

½â´ð ½â£º£¨1£©ÔÚ¼ÓËٵ糡ÖУ¬Óɶ¯Äܶ¨ÀíµÃ£ºeU₁=$\frac{1}{2}$mv₀²-0£¬½âµÃ£ºv₀=$\sqrt{\frac{2e{U}_{1}}{m}}$£¬
Ҫʹµç×ÓÊø´òÔÚÓ«¹âÆÁÉÏƫת¾àÀë×î´ó£¬µç×Ó¾­Æ«×ªµç³¡ºó±ØÐëÏ°å±ßÔµ³öÀ´£¬µç×ÓÔÚƫתµç³¡ÖÐ×öÀàƽÅ×Ô˶¯£¬
ˮƽ·½Ïò£ºl=v₀t£¬ÊúÖ±·½Ïò£º$\frac{d}{2}$=$\frac{1}{2}$at²=$\frac{1}{2}$$\frac{e{U}_{2}}{md}$t²£¬½âµÃ£ºU₂=$\frac{2{U}_{1}{d}^{2}}{{l}^{2}}$£»
£¨2£©ÀàËÆƽÅ×Ô˶¯µÄÄ©Ëٶȵķ´ÏòÑÓ³¤Ïßͨ¹ýˮƽ·ÖλÒƵÄÖе㣬ÈçͼËùʾ£º

½áºÏ¼¸ºÎ¹Øϵ£¬ÓУº$\frac{\frac{d}{2}}{y}$=$\frac{\frac{l}{2}}{\frac{l}{2}+L}$£¬½âµÃ£ºy=d£¨$\frac{l}{2}$+$\frac{L}{l}$£©£»
´ð£º£¨1£©Æ«×ªµçѹU₂Ϊ$\frac{2{U}_{1}{d}^{2}}{{l}^{2}}$ʱ£¬µç×ÓÊøÇ¡ºÃ´Óϼ«°å±ßÔµ·É³ö£®
£¨2£©Èç¹ûƫת¼«°åÓҶ˵½Ó«¹âÆÁµÄ¾àÀëΪL£¬Ôòµç×ÓÊøÔÚÓ«¹âÆÁµÄ×î´óƫת¾àÀëΪd£¨$\frac{l}{2}$+$\frac{L}{l}$£©£®

µãÆÀ ±¾ÌâÊÇ´øµçÁ£×ÓÏȼÓËÙºóƫתÎÊÌ⣬µç³¡ÖмÓËÙ¸ù¾Ý¶¯Äܶ¨ÀíÇó½â»ñµÃµÄËٶȡ¢Æ«×ªµç³¡ÖÐÀàƽÅ×Ô˶¯µÄÑо¿·½·¨ÊÇÔ˶¯µÄ·Ö½âºÍºÏ³É£¬³£¹æÎÊÌ⣮