Question

10£®ÓÃÈçͼËùʾװÖÃÀ´ÑéÖ¤¶¯Á¿Êغ㶨ÂÉ£¬ÖÊÁ¿Îªm_AµÄ¸ÖÇòAÓÃϸÏßÐü¹ÒÓÚOµã£¬ÖÊÁ¿Îªm_BµÄ¸ÖÇòB·ÅÔÚÀëµØÃæ¸ß¶ÈΪHµÄС֧ÖùNÉÏ£¬Oµãµ½AÇòÇòÐĵľàÀëΪL£¬Ê¹ÐüÏßÔÚAÇòÊÍ·ÅÇ°ÉìÖ±£¬ÇÒÏßÓëÊúÖ±Ï߼нÇΪ¦Á£¬AÇòÊͷźó°Úµ½×îµÍµãʱǡÓëBÇòÕýÅö£¬Åöײºó£¬AÇò°ÑÇáÖÊָʾÕëOCÍÆÒƵ½ÓëÊúÖ±Ï߼нǦ´¦£¬BÇòÂäµ½µØÃæÉÏ£¬µØÃæÉÏÆÌÓÐÒ»ÕŸÇÓи´Ð´Ö½µÄ°×Ö½D£¬±£³Ö¦Á½Ç¶È²»±ä£¬¶à´ÎÖظ´ÉÏÊöʵÑ飬°×Ö½ÉϼǼµ½¶à¸öBÇòµÄÂäµã£®
£¨1£©Í¼ÖÐSÓ¦ÊÇBÇò³õʼλÖõ½ÂäµØµãµÄˮƽ¾àÀ룮
£¨2£©ÎªÁËÑéÖ¤Á½ÇòÅöײ¹ý³Ì¶¯Á¿Êغ㣬Ӧ²âµÃµÄÎïÀíÁ¿ÓÐSºÍm_A¡¢m_B¡¢¦Á¡¢¦Â¡¢H¡¢L¡¢S£®£¨ÓÃ×Öĸ±íʾ£©
£¨3£©ÓòâµÃµÄÎïÀíÁ¿±íʾÅöײǰºóAÇò¡¢BÇòµÄ¶¯Á¿£ºP_A=${m_A}\sqrt{2gL£¨1-cos¦Á£©}$£®P_A¡ä=${m_A}\sqrt{2gL£¨1-cos¦Â£©}$£®P_B=0£®P_B¡ä=m_BS$\sqrt{\frac{g}{2H}}$£®£¨µ±µØµÄÖØÁ¦¼ÓËÙ¶ÈΪg£©

Answer 1

·ÖÎö AÇòÏ°ڹý³Ì»úеÄÜÊغ㣬¸ù¾ÝÊغ㶨ÂÉÁÐʽÇó×îµÍµãËٶȣ»ÇòAÉÏ°Ú¹ý³Ì»úеÄÜÔÙ´ÎÊغ㣬¿ÉÇó½âÅöײºóËٶȣ»ÅöײºóСÇòB×öƽÅ×Ô˶¯£¬¸ù¾ÝƽÅ×Ô˶¯µÄ·ÖλÒƹ«Ê½Çó½âÅöײºóBÇòµÄËٶȣ¬È»ºóÑéÖ¤¶¯Á¿ÊÇ·ñÊغ㼴¿É£®

½â´ð ½â£º£¨1£©BÇòÀ뿪С֧Öùºó×öƽÅ×Ô˶¯£¬SÊÇBÇò×öƽÅ×Ô˶¯µÄˮƽλÒÆ£¬¼´£ºBÇò³õʼλÖõ½ÂäµØµãµÄˮƽ¾àÀ룮
£¨2£©Ð¡Çò´ÓA´¦Ï°ڹý³ÌÖ»ÓÐÖØÁ¦×ö¹¦£¬»úеÄÜÊغ㣬ÓÉ»úеÄÜÊغ㶨Âɵãº
m_AgL£¨1-cos¦Á£©=$\frac{1}{2}$m_Av_A²-0£¬
½âµÃ£ºv_A=$\sqrt{2gL£¨1-cos¦Á£©}$£¬
ÔòP_A=m_Av_A=m_A$\sqrt{2gL£¨1-cos¦Á£©}$£»
СÇòAÓëСÇòBÅöײºó¼ÌÐøÔ˶¯£¬ÔÚAÅöºóµ½´ï×î×ó¶Ë¹ý³ÌÖУ¬»úеÄÜÔÙ´ÎÊغ㣬
ÓÉ»úеÄÜÊغ㶨Âɵãº-m_AgL£¨1-cos¦Â£©=0-$\frac{1}{2}$m_Av_A¡ä²£¬
½âµÃv_A¡ä=$\sqrt{2gL£¨1-cos¦Â£©}$£¬
P_A¡ä=m_Av_A¡ä=m_A$\sqrt{2gL£¨1-cos¦Â£©}$£»
ÅöǰСÇòB¾²Ö¹£¬ÔòP_B=0£»
ÅöײºóBÇò×öƽÅ×Ô˶¯£¬Ë®Æ½·½Ïò£ºS=v_B¡ät£¬ÊúÖ±·½ÏòH=$\frac{1}{2}$gt²£¬
½âµÃv_B¡ä=S$\sqrt{\frac{g}{2H}}$£¬ÔòÅöºóBÇòµÄ¶¯Á¿P_B¡ä=m_Bv_B¡ä=m_BS$\sqrt{\frac{g}{2H}}$£»
Óɶ¯Á¿Êغ㶨ÂÉ¿ÉÖª£¬ÊµÑéÐèÒªÑéÖ¤µÄ±í´ïʽΪ£º
m_A$\sqrt{2gL£¨1-cos¦Á£©}$=m_A$\sqrt{2gL£¨1-cos¦Â£©}$+m_BS$\sqrt{\frac{g}{2H}}$£¬
ʵÑéÐèÒª²âÁ¿µÄÁ¿ÓУºm_A£»m_B£»¦Á£»¦Â£»H£»L£»S£®
¹Ê´ð°¸Îª£º£¨1£©ÂäµØµã£»£¨2£©m_A¡¢m_B¡¢¦Á¡¢¦Â¡¢H¡¢L¡¢S£®£¨3£©${m_A}\sqrt{2gL£¨1-cos¦Á£©}$£»${m_A}\sqrt{2gL£¨1-cos¦Â£©}$£»0£»m_BS$\sqrt{\frac{g}{2H}}$£»£¨3£©m_BS$\sqrt{\frac{g}{2H}}$£®

µãÆÀ ±¾Ì⿼²éÁ˶¯Á¿Êغ㶨ÂɵÄÑé֤ʵÑ飻Öص㿼²éÁËÈ·¶¨ÊµÑéÐèÒª²âÁ¿µÄÁ¿£¬ÖªµÀʵÑéÔ­Àí¡¢Çó³öʵÑéÐèÒªÑéÖ¤µÄ±í´ïʽÊÇÕýÈ·½âÌâµÄ¹Ø¼ü£®