Question

10£®ÈçͼËùʾ£¬Ôڹ⻬µÄˮƽµØÃæÉÏ·ÅÖÃA¡¢BÁ½Ð¡³µ£¬A¡¢BÁ½Ð¡³µÖÊÁ¿½ÔΪM£¬ÔÚA³µµÄÓÒ¶ËÓÐÒ»ÖÊÁ¿ÎªmµÄСÎï¿é£¬M=2m£®ÏÖA³µÓëСÎï¿éÒ»ÆðÒÔËÙ¶Èv₀ÏòÓÒÔ˶¯£¬A³µÓëB³µÅöײºóСÎï¿é»¬µ½B³µÉÏ£¬×îÖÕСÎï¿éÓëB³µÒ»ÆðÒÔËÙ¶È$\frac{4}{5}{v_0}$ÏòÓÒÔ˶¯£®£¨ºöÂÔ¿ÕÆø×èÁ¦¡¢Åöײʱ¼ä£©Çó£º
¢ÙA³µ×îºóµÄËٶȣ»
¢ÚСÎï¿éÔÚB³µÉÏ»¬¶¯µÄ¹ý³ÌÖп˷þĦ²ÁÁ¦×öµÄ¹¦£®

Answer 1

·ÖÎö ¢ÙA³µÓëB³µÅöײ¹ý³ÌÖУ¬ÏµÍ³¶¯Á¿Êغ㣬ÒÔÏòÓÒΪÕý£¬¸ù¾Ý¶¯Á¿Êغ㶨ÂÉÁÐʽÇó½â¼´¿É£»
¢ÚСÎï¿éÔÚB³µÉÏ»¬¶¯µÄ¹ý³ÌÖУ¬¸ù¾Ý¶¯Äܶ¨ÀíÇó½â¼´¿É£®

½â´ð ½â£º¢ÙA³µÓëB³µÅöײ¹ý³ÌÖУ¬ÏµÍ³¶¯Á¿Êغ㣬ÒÔÏòÓÒΪÕý£¬¸ù¾Ý¶¯Á¿Êغ㶨Âɵãº
£¨m+M£©v₀=Mv_A+£¨M+m£©v£¬
ÆäÖÐv=$\frac{4}{5}{v}_{0}$
½âµÃ£º${v}_{A}=\frac{3}{10}{v}_{0}$
¢ÚСÎï¿éÔÚB³µÉÏ»¬¶¯µÄ¹ý³ÌÖУ¬¸ù¾Ý¶¯Äܶ¨ÀíµÃ£º
W=$\frac{1}{2}m{{v}_{0}}^{2}-\frac{1}{2}m{v}^{2}=\frac{9}{50}m{{v}_{0}}^{2}$
´ð£º¢ÙA³µ×îºóµÄËÙ¶ÈΪ$\frac{3}{10}{v}_{0}$£»
¢ÚСÎï¿éÔÚB³µÉÏ»¬¶¯µÄ¹ý³ÌÖп˷þĦ²ÁÁ¦×öµÄ¹¦Îª$\frac{9}{50}m{{v}_{0}}^{2}$£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÁ˶¯Á¿Êغ㶨ÂÉÒÔ¼°¶¯Äܶ¨ÀíµÄÖ±½ÓÓ¦Óã¬ÒªÇóͬѧÃÇÄÜÕýÈ··ÖÎöÎïÌåµÄÔ˶¯Çé¿ö£¬ÖªµÀÓ¦Óö¯Á¿Êغ㶨ÂÉʱҪÏȹ涨Õý·½Ïò£¬ÄѶȲ»´ó£¬ÊôÓÚ»ù´¡Ì⣮