Question

18£®Èçͼ¼×ËùʾµÄ×°ÖÿÉÓÃÑéÖ¤¶¯Á¿Êغ㶨ÂÉ£®Ð±²Û¹ìµÀ¹Ì¶¨ÔÚˮƽ×ÀÃæÉÏ£¬ÔÚÆäÒ»²àÊúÖ±·ÅÖÃÒ»ÌùÓÐ×ø±êÖ½µÄÆÁ£¬×ø±êÖ½ÉÏС·½¸ñµÄ±ß³¤l=9mm£¬ÈÃСÇòÿ´Î´ÓFµãÓɾ²Ö¹ÊÍ·Å£¬´Ó¹ìµÀÄ©¶ËˮƽÅ׳ö£¬Í¨¹ýƵÉÁÕÕÏ෽ʽ¼Ç¼СÇòƽÅ×Ô˶¯¹ý³Ì£®
£¨1£©ÊµÑéÖУ¬ÈÃСÇòA´ÓFµãÓɾ²Ö¹ÊÍ·Å£¬´ÓÄ©¶ËˮƽÅ׳ö£¬Í¨¹ýƵÉÁÕÕÏà²âµÃСÇòAµ½´ï¹ìµÀÄ©¶ËʱµÄËÙ¶Èv_A=0.50m/s£®
£¨2£©°ÑÖ±¾¶ÓëAÇòÏàͬµÄBÇò£¨m_A£¾m_B£©·ÅÖÃÔÚˮƽ¸ßµÍÄ©¶Ë£¬Í¬ÑùÈÃAÇò´ÓFµãÓɾ²Ö¹ÊÍ·Å£¬Á½ÇòÏàÅöºó£®¶¼´Ó¹ìµÀÄ©¶ËˮƽÅ׳ö£¬ÓÃƵÉÁÕÕÏ෽ʽ¼Ç¼ÁËËüÃÇÔ˶¯¹ý³ÌµÄ¸÷ËĸöµãÈçͼÒÒËùʾ£¬Ð´ÅöºóAСÇò×öƽÅ×Ô˶¯µÄ³õËٶȵļÆËãʽΪ£ºv_A¡ä=$\sqrt{gl}$£¨ÓÃl¡¢g±íʾ£©
£¨3£©ÒªÑéÖ¤A¡¢BÁ½ÇòÅöײ¹ý³ÌÖÐϵͳ¶¯Á¿Êغ㣬Ӧ¸ÃÓÐm_Av_A=m_Av_A'+m_Bv_B¡¯µÈʽÔÚʵÑéÔÊÐíÎó²î·¶Î§ÄÚ³ÉÁ¢£¨ÓÃÌâÄ¿Öиø³öµÄ×Öĸ·ûºÅ±íʾ£©£¬Èô´ËµÈʽ³ÉÁ¢£¬ÔòA¡¢BСÇòµÄÖÊÁ¿Ö®±ÈΪ21£º10£®

Answer 1

·ÖÎö £¨2£©Ð¡Çò×öƽÅ×Ô˶¯£¬ÔÚÊúÖ±·½ÏòÓ¦ÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄÍÆÂÛ¿ÉÒÔÇó³öСÇòµÄÔ˶¯Ê±¼ä¼ä¸ô£¬È»ºóÔÙˮƽ·½ÏòÓ¦ÓÃËٶȹ«Ê½¿ÉÒÔÇó³öСÇòµÄ³õËٶȣ®
£¨3£©¸ù¾Ý¶¯Á¿Êغ㶨ÂɽøÐзÖÎö£¬´Ó¶øÃ÷È·¶ÔÓ¦µÄ±í´ïʽ£¬ÔÙ¸ù¾ÝƽÅ×Ô˶¯¹æÂɼÆËã³öСÇòˮƽËٶȣ¬ÔòÓɶ¯Á¿Êغ㶨Âɼ´¿ÉÇóµÃÖÊÁ¿Ö®±È£®

½â´ð ½â£º£¨2£©ÓÉͼ¿ÉÖª£¬AƽÅ×Ô˶¯µÄÏÂÂäÖÐÏàÁÙÁ½µã¼äµÄ¾àÀëΪl£¬ÇÒÏÂÂäÖÐÏàµÈʱ¼äÄڵĸ߶ȲîΪh£»ÔòÓÉƽÅ×Ô˶¯ÊúÖ±·½Ïò×ö×ÔÓÉÂäÌåÔ˶¯£¬¡÷h=h=gT²
ËùÒÔT=$\sqrt{\frac{¡÷h}{g}}$£¬Ôòv_A¡¯=$\frac{l}{T}$=l$\sqrt{\frac{g}{l}}$=$\sqrt{gl}$£»
£¨3£©¸ù¾Ý¶¯Á¿Êغ㶨ÂÉ¿ÉÖª£¬Èç¹û¶¯Á¿Êغ㣬ÔòÓУºm_Av_A=m_Av_A'+m_Bv_B¡¯
¸ù¾Ý£¨2£©Öбí´ïʽ¿ÉÖª£¬v_A'=$\sqrt{10¡Á0.009}$=0.3m/s£»
ͬÀí¿ÉÖªv_B'=$\sqrt{2gl}$=$\sqrt{2¡Á10¡Á0.009}$=0.42m/s£»
ÔòÓɶ¯Á¿Êغã¿ÉµÃ£º
0.5m_A=0.3m_A+0.42m_B
½âµÃ£ºm_A£ºm_B=2.1£º1=21£º10£»
¹Ê´ð°¸Îª£º£¨2£©$\sqrt{gl}$£»£¨3£©21£º10£®

µãÆÀ ±¾Ì⿼²éÀûÓÃƽÅ×Ô˶¯¹æÂÉÑéÖ¤¶¯Á¿Êغ㶨ÂɵÄʵÑ飬ҪעÒâÃ÷È·±¾ÌâÖиø³öµÄËĸöµã²¢²»ÊÇ´ÓƽÅ×Ô˶¯µÄÆðµã¸ø³öµÄ£¬Òò´ËÖ»ÄÜÀûÓÃ$¡÷x=\\;g{T}^{2}$gT²Çó½âʱ¼ä¼ä¸ô£®