Question

14£®ÈçͼËùʾ£¬Ð¡Çòa¡¢bÓó¤¶È¾ùΪLµÄϸÏßÐü¹ÒÓÚͬһ¹Ì¶¨µãO£®ÈÃÇòa¾²Ö¹Ï´¹£¬½«ÇòbÏòÓÒÀ­Æð£¬Ê¹Ï¸ÏßˮƽÉìÖ±£¬Óɾ²Ö¹ÊÍ·ÅÇòb£¬Á½ÇòÅöºóÕ³ÔÚÒ»ÆðÏò×ó°Ú¶¯£¬´ËºóϸÏßÓëÊúÖ±·½ÏòÖ®¼äµÄ×î´óÆ«½Ç¦È=60¡ã£®ºöÂÔ¿ÕÆø×èÁ¦£¬ÖØÁ¦¼ÓËٶȴóСΪg£®
£¨1£©ÇóÁ½ÇòÅöײǰ˲¼ä£¬Ð¡ÇòbµÄËٶȴóС£»
£¨2£©ÇóÁ½ÇòµÄÖÊÁ¿Ö®±È£»
£¨3£©ÈôÒÔСÇòÔ˶¯µÄ×îµÍµãËùÔÚµÄˮƽÃæΪÁãÊÆÄÜÃ棬Çóa¡¢bÁ½Çò×é³ÉµÄϵͳÔÚÅöײǰºóµÄ»úеÄÜÖ®±È£®

Answer 1

·ÖÎö £¨1£©bÇòÏ°ڹý³ÌÖУ¬Ö»ÓÐÖØÁ¦×ö¹¦£¬ÓÉ»úеÄÜÊغ㶨ÂÉÇó³öÅöÇ°bÇòµÄËٶȣ»
£¨2£©Á½ÇòÅöײ¹ý³ÌÖж¯Á¿Êغ㣬Óɶ¯Á¿Êغ㶨ÂÉÁз½³Ì£®ÅöºóÁ½ÇòÏò×ó°Ú¶¯¹ý³ÌÖУ¬ÕûÌåµÄ»úеÄÜÊغ㣬ÓÉ»úеÄÜÊغ㶨ÂÉÁÐʽ£¬ÁªÁ¢¿ÉÇóµÃÁ½ÇòµÄÖÊÁ¿Ö®±È£»
£¨3£©¶ÔÓÚÁ½ÇòÅöײǰºó£¬ÓÉ»úеÄÜÊغ㶨ÂɵóöËüÃǵĻúеÄÜ£¬ÔÙÇóϵͳÔÚÅöײǰºóµÄ»úеÄÜÖ®±È£®

½â´ð ½â£º£¨1£©ÉèÇòaµÄÖÊÁ¿Îªm₁£¬ÇòbµÄÖÊÁ¿Îªm₂£®µ±Çòb°Úµ½×îµÍµã£¬µ«Î´ÓëÇòaÏàÅöʱµÄËٶȴóСΪv£®Óɶ¯Äܶ¨ÀíµÃ
  m₂gL=$\frac{1}{2}{m}_{2}{v}^{2}$
½âµÃ v=$\sqrt{2gL}$
£¨2£©ÉèÅöºó˲¼äÁ½ÇòµÄ¹²Í¬ËÙ¶ÈΪv¡ä£®ÔÚÁ½Çò´ÓÅöײºóµ½Ïò×ó°Úµ½×î¸ßλÖõĹý³ÌÖУ¬Óɶ¯Äܶ¨ÀíµÃ
-£¨m₁+m₂£©gL£¨1-cos60¡ã£©=0-$\frac{1}{2}£¨{m}_{1}+{m}_{2}£©v{¡ä}^{2}$
½âµÃ v¡ä=$\sqrt{gL}$
¶ÔÓÚÅöײ¹ý³Ì£¬ÒÔˮƽÏò×óΪÕý·½Ïò£¬Óɶ¯Á¿Êغ㶨ÂɵÃ
   m₂v=£¨m₁+m₂£©v¡ä
½âµÃ $\frac{{m}_{1}}{{m}_{2}}$=$\sqrt{2}$-1
£¨3£©a¡¢bÁ½Çò×é³ÉµÄϵͳÔÚÅöײǰµÄ»úеÄÜΪ E₁=m₂gL
a¡¢bÁ½Çò×é³ÉµÄϵͳÔÚÅöײºóµÄ»úеÄÜΪ E₂=m₂gL£¨1-cos60¡ã£©
½áºÏ $\frac{{m}_{1}}{{m}_{2}}$=$\sqrt{2}$-1
½âµÃ $\frac{{E}_{1}}{{E}_{2}}$=$\sqrt{2}$
´ð£º
£¨1£©Á½ÇòÅöײǰ˲¼ä£¬Ð¡ÇòbµÄËٶȴóСÊÇ$\sqrt{2gL}$£»
£¨2£©Á½ÇòµÄÖÊÁ¿Ö®±ÈΪ$\sqrt{2}$-1£»
£¨3£©a¡¢bÁ½Çò×é³ÉµÄϵͳÔÚÅöײǰºóµÄ»úеÄÜÖ®±ÈΪ$\sqrt{2}$£º1£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÊÇÒªÃ÷ȷСÇòÔÚÏ°ڻòÉÏ°Ú¹ý³ÌÖлúеÄÜÊغ㣬Åöײ¹ý³ÌÖж¯Á¿Êغ㣬Óɶ¯Äܶ¨Àí£¨»ò»úеÄÜÊغ㶨ÂÉ£©¡¢¶¯Á¿Êغ㶨Âɼ´¿ÉÕýÈ·½âÌ⣮