Question

12£®Èçͼ¼×ËùʾµÄ×°ÖýÐ×ö°¢ÌØÎéµÂ»ú£¬ÊÇ°¢ÌØÎéµÂ£¨G£®Atwood1746-1807£©´´ÖƵÄÒ»ÖÖÖøÃûÁ¦Ñ§ÊµÑé×°Öã¬ÓÃÀ´Ñо¿ÔȱäËÙÖ±ÏßÔ˶¯µÄ¹æÂÉ£®Ä³Í¬Ñ§¶Ô¶Ô¸Ã×°ÖüÓÒԸĽøºóÓÃÀ´Ñé֤ţ¶ÙµÚ¶þ¶¨ÂÉ£¬ÈçͼÒÒËùʾ£®
£¨1£©ÊµÑéʱ£¬¸Ãͬѧ½øÐÐÁËÈçϲÙ×÷£º
1¡¢½«ÖÊÁ¿¾ùΪM£¨AµÄÖÊÁ¿°üÀ¨µ²¹âƬ¡¢BµÄÖÊÁ¿°üÀ¨¹Ò¹³£©µÄÖØÎïÓÃϸÏßÁ¬½Óºó£¬¿ç·ÅÔÚ¶¨»¬ÂÖÉÏ£¬Ê¹Æä´¦ÓÚ¾²Ö¹×´Ì¬£®²âÁ¿³öµ²¹âƬµÄÉϱíÃæµ½¹âµçÃÅÖÐÐĵľàÀëh£®
2¡¢ÔÚBµÄ϶˹ÒÉÏÖÊÁ¿ÎªmµÄ¹³ÂëC£¬ÈÃϵͳ£¨ÖØÎïA¡¢BÒÔ¼°¹³ÂëC£©ÖеÄÎïÌåÓɾ²Ö¹¿ªÊ¼Ô˶¯£¬¼Ç¼µ²¹âƬµ²¹âµÄʱ¼äΪt£®
3¡¢µ²¹âƬµÄ¿í¶ÈΪd£¬¼ÆËã³öA¡¢BµÄËٶȴóСΪ$\frac{d}{¡÷t}$£¬¼ÓËٶȴóСΪ$\frac{{d}^{2}}{2h£¨¡÷t£©^{2}}$£®
£¨2£©¸ù¾ÝÅ£¶ÙÔ˶¯µÚ¶þ¶¨ÂÉ£¬Ó¦¸ÃÂú×ãµÄµÈʽÊÇmg=£¨2M+m£©$\frac{{d}^{2}}{2h£¨¡÷t£©^{2}}$  £¨ÒÑÖªÖØÁ¦¼ÓËÙ¶ÈΪg£©

Answer 1

·ÖÎö £¨1£©¸ù¾ÝËٶȹ«Ê½¿ÉÇóµÃ˲½øËٶȣ¬ÔÙ¶ÔϵͳµÄÔ˶¯¹ý³Ì·ÖÎö£¬¼´¿ÉÇóµÃ¼ÓËٶȣ»
£¨2£©¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇóµÃºÏÁ¦£¬ÔÙÓÉÊÜÁ¦·ÖÎöÃ÷È·ºÏÁ¦µÄ´óС£¬Ôò¿ÉµÃ³ö¶ÔÓ¦µÄ±í´ïʽ£®

½â´ð ½â£º£¨1¡¢2£©ÐèÒª²âÁ¿ÏµÍ³ÖØÁ¦ÊÆÄܵı仯Á¿£¬ÔòÓ¦¸Ã²âÁ¿³öµ²¹âƬÖÐÐĵ½¹âµçÃÅÖÐÐĵľàÀ룬ϵͳµÄÄ©ËÙ¶ÈΪ£ºv=$\frac{d}{¡÷t}$£¬
ÓÉv²=2ah¿ÉµÃ£ºa=$\frac{{d}^{2}}{2h£¨¡÷t£©^{2}}$
£¨4£©¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵã¬ÏµÍ³ËùÊܵĺÏÁ¦Îªmg£¬Ôòϵͳ¼ÓËÙ¶ÈΪ£ºmg=£¨2M+m£©a£»
½âµÃ£ºmg=£¨2M+m£©$\frac{{d}^{2}}{2h£¨¡÷t£©^{2}}$
¹Ê´ð°¸Îª£º£¨1£©3¡¢$\frac{d}{¡÷t}$£»$\frac{{d}^{2}}{2h£¨¡÷t£©^{2}}$£»
£¨2£©mg=£¨2M+m£©$\frac{{d}^{2}}{2h£¨¡÷t£©^{2}}$

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÖªµÀʵÑéµÄÔ­Àí£¬·ÖÎöʵÑé·½·¨£¬ÕÆÎÕÕûÌå·¨ÔÚÅ£¶ÙµÚ¶þ¶¨ÂÉÖеÄÔËÓã®