Question

9£®ÖÊÁ¿ÎªmµÄСÀîÏëÍƶ¯¼ÒÀïµÄ¾àÀëǽ±ÚΪdµÄÒ³÷£¬µ«Ê¹³öÁ˳ÔÄ̵ÄÁ¦ÆøÒ²ÍƲ»¶¯£®Ëû±ãÏëµ½¸ö·½·¨È¥³¢ÊÔ£¬Èçͼ¼×Ëùʾ£¬Óó¤¶È¾ùΪLµÄA¡¢BÁ½¿é³¤ÌõÐη½Ä¾°å´î³ÉÒ»¸öÈË×ÖÐμܣ¬È»ºóËûÇá¾­Õ¾ÉÏÖÐÑëC´¦£¬²¢±£³Ö¾²Ö¹£¬·¢ÏÖ´ËʱÒ³÷»¹ÊDZ£³Ö¾²Ö¹×´Ì¬£¬¼ò»¯Çé¾°ÈçͼÒÒËùʾ£®A¡¢BÊÓΪ²»¼ÆÖÊÁ¿µÄ¹â»¬Ó²Ä¾°å£¬²¢½«C´¦Á¬½ÓÊÓΪ¹â»¬½ÂÁ´Á¬½Ó£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£®

£¨1£©Çóľ°åA¶ÔµØÃæµÄѹÁ¦F_NµÄ´óС£®
£¨2£©ÇóÒ³÷´ËʱËùÊܵÄĦ²ÁÁ¦F_fµÄ´óС£®

Answer 1

·ÖÎö £¨1£©ÈË´¦ÓÚ¾²Ö¹×´Ì¬£¬ÊÜÁ¦Æ½ºâ£¬¶ÔÈËÊÜÁ¦·ÖÎö£¬¸ù¾ÝƽºâÌõ¼þÇó½âľ°åA¶ÔÈ˵Ä×÷ÓÃÁ¦ÔÚÊúÖ±·½ÏòµÄ·ÖÁ¿£¬¼´ÎªÄ¾°åA¶ÔµØÃæµÄѹÁ¦F_NµÄ´óС£»
£¨2£©ÉèA°åÓëÊúÖ±·½ÏòµÄ¼Ð½ÇΪ¦È£¬¶ÔÒ³÷ÊÜÁ¦·ÖÎö£¬Ò³÷¾²Ö¹£¬ÊÜÁ¦Æ½ºâ£¬Ä¾°åAÊܵ½µÄ×÷ÓÃÁ¦ÔÚˮƽ·½ÏòµÄ·ÖÁ¿ÓëÒ³÷ËùÊܵÄĦ²ÁÁ¦´óСÏàµÈ£®

½â´ð ½â£º£¨1£©ÈË´¦ÓÚ¾²Ö¹×´Ì¬£¬ÊÜÁ¦Æ½ºâ£¬ÈËÊܵ½ÖØÁ¦£¬Á½°å¶ÔÈ˵ÄÖ§³ÖÁ¦£¬¸ù¾ÝƽºâÌõ¼þµÃ£º
ÿ¸ö°å¶ÔÈ˵ÄÖ§³ÖÁ¦ÔÚÊúÖ±·½ÏòµÄ·ÖÁ¿µÈÓÚÖØÁ¦µÄÒ»°ë£¬Ôò
2F_N=mg£¬
½âµÃ£º${F}_{N}=\frac{mg}{2}$£¬
Ôòľ°åA¶ÔµØÃæµÄѹÁ¦µÄΪ$\frac{mg}{2}$£¬
£¨2£©ÉèA°åÓëÊúÖ±·½ÏòµÄ¼Ð½ÇΪ¦È£¬¸ù¾Ý¼¸ºÎ¹ØϵµÃ£º$tan¦È=\frac{\frac{d}{2}}{\sqrt{{L}^{2}-£¨\frac{d}{2}£©^{2}}}$=$\frac{d}{2\sqrt{{L}^{2}-{£¨\frac{d}{2}£©}^{2}}}$
Ò³÷´¦ÓÚ¾²Ö¹×´Ì¬£¬ÊÜÁ¦Æ½ºâ£¬Ë®Æ½·½ÏòÓУº
F_f=$\frac{mg}{2}tan¦È$=$\frac{dmg}{4\sqrt{{L}^{2}-{£¨\frac{d}{2}£©}^{2}}}$
´ð£º£¨1£©Ä¾°åA¶ÔµØÃæµÄѹÁ¦F_NµÄ´óСΪ$\frac{mg}{2}$£®
£¨2£©Ò³÷´ËʱËùÊܵÄĦ²ÁÁ¦F_fµÄ´óСΪ$\frac{dmg}{4\sqrt{{L}^{2}-{£¨\frac{d}{2}£©}^{2}}}$£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÁ˹²µãÁ¦Æ½ºâÌõ¼þµÄÖ±½ÓÓ¦Óã¬ÒªÇóͬѧÃÇÄÜÕýÈ··ÖÎöÎïÌåµÄÊÜÁ¦Çé¿ö£¬×¢Ò⼸ºÎ¹ØϵÔÚ½âÌâÖеÄÓ¦Óã¬ÄѶÈÊÊÖУ®