Question

14£®¹ýɽ³µÊÇÈËÃÇϲ°®µÄÒ»Ïî»î¶¯£¬Ä³Ò»ÓÎÀÖ³¡µÄ¹ýɽ³µ¿É¼ò»¯ÎªÈçͼµÄÄ£ÐÍ£ºÈçͼËùʾ£¬¼×¡¢ÒÒÁ½¸ö¹â»¬µÄÔ²ÐιìµÀ°²ÖÃÔÚͬһÊúֱƽÃæÉÏ£¬°ë¾¶·Ö±ðΪR=1mºÍr=0.6m£¬ÔÚÁ½¹ìµÀÖ®¼äÓÐÒ»Ìõ³¤ÎªL=3mˮƽ¹ìµÀCDÏàͨ£¬Ò»ÖÊÁ¿Îª1kgµÄСÇòÒÔÒ»¶¨µÄËÙ¶ÈÏÈ»¬Éϼ׹ìµÀ£¬Í¨¹ýCD¶ÎºóÓÖ»¬ÉÏÒÒ¹ìµÀ£¬×îºó´ÓÒÒ¹ìµÀ×îµÍµã»¬Àë¹ìµÀ£¬Ð¡ÇòÔ˶¯¹ý³ÌÖÐһֱδÍÑÀë¹ìµÀ£¬ÇÒСÇòÓëˮƽ¹ìµÀ¼äµÄ¶¯Ä¦²ÁÒòÊý¦Ì=0.2£¬ÎÊ£º
£¨1£©Ð¡Çò¸Õ½øÈë¼×¹ìµÀʱµÄËÙ¶ÈV₀ÖÁÉÙΪ¶à´ó£¿
£¨2£©ÈôСÇòÒÔ£¨1£©ÎÊÖеÄ×îСËٶȽøÈë¼×¹ìµÀ£¬ÔòСÇò¾­¹ýÒÒ¹ìµÀ×îµÍµãʱ¶Ô¹ìµÀµÄѹÁ¦F¶à´ó£¿

Answer 1

·ÖÎö £¨1£©Ð¡ÇòÔÚÁ½Ô²¹ìµÀµÄ×î¸ßµã¶Ô¹ìµÀµÄѹÁ¦Ç¡ºÃΪÁ㣬¶¼ÓÉÖØÁ¦ÌṩÏòÐÄÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öСÇò¾­¹ýÔ²ÐιìµÀ×î¸ßµãʱµÄËÙÂÊ£®µ±Ð¡Çò´ÓCµ½´ï¼×Ô²ÐιìµÀµÄ×î¸ßµãµÄ¹ý³ÌÖУ¬Ö»ÓÐÖØÁ¦×ö¹¦£¬¸ù¾Ý»úеÄÜÊغ㶨ÂÉÇó½âСÇò¸Õ½øÈë¼×¹ìµÀʱµÄËÙ¶Èv₀£®
£¨2£©¸ù¾Ý¶¯Äܶ¨ÀíÇóСÇò¾­¹ýÒÒ¹ìµÀ×îµÍµãʱµÄËٶȣ¬ÔÙÓÉÅ£¶Ù¶¨ÂÉÇóСÇò¶Ô¹ìµÀµÄѹÁ¦£®

½â´ð ½â£º£¨1£©ÉèСÇòÇ¡ºÃͨ¹ý¼×¹ìµÀ×î¸ßµãµÄËÙ¶ÈΪv₁£¬ÔòÓÐ
mg=m$\frac{{v}_{1}^{2}}{R}$
½âµÃ v₁=$\sqrt{gR}$
È¡¹ìµÀ×îµÍµãËùÔÚˮƽÃæΪ²Î¿¼Æ½Ã棬´ÓCµ½¼×¹ìµÀµÄ×î¸ßµãµÄ‰c£¬ÓÉ»úеÄÜÊغ㶨ÂÉÓÐ
$\frac{1}{2}$mv₀₁²=mg•2R+$\frac{1}{2}$mv₁²
½âµÃ v₀₁=$\sqrt{5gR}$=$\sqrt{5¡Á10¡Á1}$=5$\sqrt{2}$m/s
СÇòÇ¡ºÃͨ¹ýÒÒ¹ìµÀ×î¸ßµãʱµÄËÙ¶È v₂=$\sqrt{gr}$=$\sqrt{6}$m/s
´ÓCµ½ÒÒ¹ìµÀ×î¸ßµãµÄ¹ý³Ì£¬Óɶ¯Äܶ¨ÀíµÃ
-mg•2r=-¦ÌmgL=$\frac{1}{2}$mv₂²-$\frac{1}{2}$mv₀₂²£¬½âµÃ v₀₂=$\sqrt{42}$m/s£¼v₀₁
ËùÒÔСÇò¸Õ½øÈë¼×¹ìµÀʱµÄËÙ¶Èv₀ÖÁÉÙΪ5$\sqrt{2}$m/s£®
£¨2£©ÈôСÇòÒÔ£¨1£©ÎÊÖеÄ×îСËٶȽøÈë¼×¹ìµÀ£¬ÉèСÇò¾­¹ýÒÒ¹ìµÀ×îµÍµãʱËÙ¶ÈΪv_D£®
´ÓCÔ˶¯µ½DµÄ¹ý³Ì£¬Óɶ¯Äܶ¨ÀíµÃ
-¦ÌmgL=$\frac{1}{2}$mv_D²-$\frac{1}{2}$mv₀₁²£®
ÔÚDµã£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵÃ
F¡ä-mg=m$\frac{{v}_{D}^{2}}{r}$
ÁªÁ¢¿ÉµÃ F¡ä=$\frac{220}{3}$N
¸ù¾ÝÅ£¶ÙµÚÈý¶¨ÂÉÖª£¬Ð¡Çò¾­¹ýÒÒ¹ìµÀ×îµÍµãʱ¶Ô¹ìµÀµÄѹÁ¦ F=F¡ä=$\frac{220}{3}$N
´ð£º
£¨1£©Ð¡Çò¸Õ½øÈë¼×¹ìµÀʱµÄËÙ¶Èv₀ÖÁÉÙΪ5$\sqrt{2}$m/s£®
£¨2£©Ð¡Çò¾­¹ýÒÒ¹ìµÀ×îµÍµãʱ¶Ô¹ìµÀµÄѹÁ¦FΪ$\frac{220}{3}$N£®

µãÆÀ ±¾ÌâµÄ¹Ø¼üÒª·ÖÎöÇå³þСÇòµÄÔ˶¯¹ý³Ì£¬°ÑÎÕÔ²ÖÜÔ˶¯×î¸ßµãµÄÁÙ½çÌõ¼þ£ºÖØÁ¦µÈÓÚÏòÐÄÁ¦£¬ÔËÓûúеÄÜÊغ㶨ÂɺͶ¯Äܶ¨ÀíÑо¿£®ÒªÖªµÀÔÚÊúֱƽÃæÄÚ£¬Ð¡ÇòÑع⻬Բ¹ìµÀµÄÔ˶¯Ä£ÐÍÓëÇáÉþË©µÄÇòµÄÔ˶¯Ä£ÐÍÏàËÆ£®