Question

20£®ÈçͼËùʾ£¬³¤ÎªL¡¢Äڱڹ⻬µÄÖ±¹ÜÓëˮƽµØÃæ³É30¡ã½Ç¹Ì¶¨·ÅÖ㮽«Ò»ÖÊÁ¿ÎªmµÄСÇò¹Ì¶¨Ôڹܵף¬ÓÃÒ»ÇáÖʹ⻬ϸÏß½«Ð¡ÇòÓëÖÊÁ¿ÎªM=kmµÄСÎï¿éÏàÁ¬£¬Ð¡Îï¿éÐü¹ÒÓڹܿڣ®ÏÖ½«Ð¡ÇòÊÍ·Å£¬Ò»¶Îʱ¼äºó£¬Ð¡Îï¿éÂäµØ¾²Ö¹²»¶¯£¬Ð¡Çò¼ÌÐøÏòÉÏÔ˶¯£¬Í¨¹ý¹Ü¿ÚµÄתÏò×°Öúó×öƽÅ×Ô˶¯£¬Ð¡ÇòÔÚתÏò¹ý³ÌÖÐËÙÂʲ»±ä£®£¨ÖØÁ¦¼ÓËÙ¶ÈΪg£©
£¨1£©ÇóСÎï¿éÏÂÂä¹ý³ÌÖеļÓËٶȴóС£»
£¨2£©ÇóСÇò´Ó¹Ü¿ÚÅ׳öʱµÄËٶȴóС£»
£¨3£©ÇóСÇòƽÅ×Ô˶¯µÄˮƽλÒƵıí´ïʽ£®

Answer 1

·ÖÎö £¨1£©·Ö±ð¶ÔmºÍMÔËÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉ£¬×¥×¡Á½ÕߵļÓËٶȴóСÏàµÈ£¬Çó³öСÎï¿éµÄ¼ÓËٶȴóС£®Ò²¿ÉÒÔ¶ÔÕûÌåÔËÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉ£®
£¨2£©¸ù¾ÝËÙ¶ÈλÒƹ«Ê½Çó³öÎï¿éÂäµØʱСÇòµÄËٶȣ¬ÔÙ¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öľ¿éÂäµØºóСÇòµÄ¼ÓËٶȣ¬ÔËÓÃËÙ¶ÈλÒƹ«Ê½Çó³öСÇòÀ뿪¹Ü¿ÚµÄËٶȣ®
£¨3£©¸ù¾Ý¸ß¶ÈÇó³öƽÅ×Ô˶¯µÄʱ¼ä£¬ÔÙ¸ù¾Ý³õËٶȺÍʱ¼äÇó³öƽÅ×Ô˶¯µÄˮƽλÒÆ£®

½â´ð ½â£º£¨1£©ÉèϸÏßÖеÄÕÅÁ¦ÎªT£¬¶ÔСÇòºÍСÎï¿é¸÷×ÔÊÜÁ¦·ÖÎö£º

¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵãº
¶ÔM£ºMg-T=Ma
¶Ôm£ºT-mgsin30¡ã=ma
ÇÒM=km£¬½âµÃ£ºa=$\frac{2k-1}{2£¨k+1£©}$g£»
£¨2£©ÉèMÂäµØʱµÄËٶȴóСΪv£¬mÉä³ö¹Ü¿ÚʱËٶȴóСΪv₀£¬MÂäµØºómµÄ¼ÓËÙ¶ÈΪa₀£®
¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÓУºmgsin30¡ã=ma₀
¶ÔÓÚmÔȼÓËÙÖ±ÏßÔ˶¯ÓУºv²=2aLsin30¡ã
¶ÔÓÚСÎï¿éÂäµØ¾²Ö¹²»¶¯£¬Ð¡Çòm¼ÌÐøÏòÉÏ×öÔȼõËÙÔ˶¯ÓУºv²-v₀²=2a₀L£¨1-sin30¡ã£©
½âµÃ£ºv₀=$\sqrt{\frac{£¨k-2£©gL}{2£¨k+1£©}}$  £¨k£¾2£©£»
£¨3£©Ð¡Çò×öƽÅ×Ô˶¯£¬
ˮƽ·½Ïò£ºx=v₀t£¬
ÊúÖ±·½Ïò£ºLsin30¡ã=$\frac{1}{2}$gt²£¬
½âµÃ£ºx=L$\sqrt{\frac{k-2}{2£¨k+1£©}}$£»
´ð£º£¨1£©Ð¡Îï¿éÏÂÂä¹ý³ÌÖеļÓËٶȴóСΪ$\frac{2k-1}{2£¨k+1£©}$g£»
£¨2£©Ð¡Çò´Ó¹Ü¿ÚÅ׳öʱµÄËٶȴóСΪ$\sqrt{\frac{£¨k-2£©gL}{2£¨k+1£©}}$  £¨k£¾2£©£»
£¨3£©Ð¡ÇòƽÅ×Ô˶¯µÄˮƽλÒƵıí´ïʽΪx=L$\sqrt{\frac{k-2}{2£¨k+1£©}}$£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÀíÇåСÇòµÄÔ˶¯¹ý³Ì£¬ÔËÓÃÅ£¶Ù¶¨ÂÉÇó½â£®Ð¡Çò¾­ÀúÁËÔȼÓËÙÖ±ÏßÔ˶¯¡¢ÔȼõËÙÖ±ÏßÔ˶¯£¬Æ½Å×Ô˶¯£®