Question

15£®ÈçͼËùʾ£¬Ä³¹Ì¶¨Ð±ÃæÇã½ÇΪ30¡ã£¬Ð±Ãæ×ã¹»³¤£¬¶¥ÉÏÓÐÒ»¶¨»¬ÂÖ£¬¿ç¹ý¶¨»¬ÂÖµÄϸÉþÁ½¶Ë·Ö±ðÓëÎïÌåA¡¢BÁ¬½Ó£¬AÖÊÁ¿ÎªM=4kg£¬BÖÊÁ¿Îªm=1kg£®¿ªÊ¼Ê±£¬½«B°´ÔÚµØÉϲ»¶¯£¬È»ºó·Å¿ªÊÖ£¬ÈÃAÑØбÃæE»¬¶øBÉÏÉý£¬ËùÓÐĦ²ÁºöÂÔ²»¼Æ£®µ±AÑØбÃæÏ»¬x₁=5mºó£®Ï¸ÉþͻȻ¶ÏÁË£®£¨ÉèB²»Ó붨»¬ÂÖÏàÅö£¬g=10m/s²£©
£¨1£©Ï¸Ïßδ¶Ïʱ£¬A¡¢BµÄ¼ÓËٶȴóСa£»
£¨2£©Ï¸Ïßδ¶Ïʱ£®Éþ×ÓµÄÀ­Á¦T£»
£¨3£©Ï¸Éþ¶Ïʱ£¬A¡¢BµÄËÙ¶ÈV_A¡¢V_B£»
£¨4£©Ï¸Éþ¶Ïºó£¬AÓëBµÄ¼ÓËÙ¶Èa₁ºÍa₂£»
£¨5£©Îï¿éBÉÏÉýµÄ×î´ó¸ß¶ÈH£®

Answer 1

·ÖÎö £¨1£©Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÒÔÇó³ö¼ÓËٶȣ®
£¨2£©Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÒÔÇó³öÉþ×ÓµÄÀ­Á¦£®
£¨3£©Ó¦ÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄËٶȹ«Ê½¿ÉÒÔÇó³öÎïÌåµÄËٶȣ®
£¨4£©Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÒÔÇó³öA¡¢BµÄ¼ÓËٶȣ®
£¨5£©Ó¦ÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄËÙ¶ÈλÒƹ«Ê½¿ÉÒÔÇó³öBÉÏÉýµÄ×î´ó¸ß¶È£®

½â´ð ½â£º£¨1£©¶ÔABϵͳ£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº
a=$\frac{Mgsin30¡ã-mg}{M+m}$=$\frac{4¡Á10¡Ásin30¡ã-1¡Á10}{4+1}$=2m/s²£»
£¨2£©¶ÔB£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº
T-mg=ma£¬½âµÃ£ºT=m£¨g+a£©=1¡Á£¨10+2£©=12N£»
£¨3£©ÎïÌå×ö³õËÙ¶ÈΪÁãµÄÔȼÓËÙÖ±ÏßÔ˶¯£¬
ÓÉÔȱäËÙÖ±ÏßÔ˶¯µÄËÙ¶ÈλÒƹ«Ê½µÃ£¬
ÎïÌåµÄËٶȣºv_A=v_B=$\sqrt{2a{x}_{1}}$=$\sqrt{2¡Á2¡Á5}$=2$\sqrt{5}$m/s£»
£¨4£©Éþ×Ó¶ÏÁѺó£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº
¶ÔA£ºa_A=$\frac{Mgsin30¡ã}{M}$=$\frac{4¡Á10¡Ásin30¡ã}{4}$=5m/s²£¬
B×öÊúÖ±ÉÏÅ×Ô˶¯£¬¼ÓËٶȣºa_B=10m/s²£»
£¨5£©BÉÏÉýµÄ×î´ó¸ß¶È£ºH=x₁+$\frac{{v}_{B}^{2}}{2g}$=5+$\frac{£¨2\sqrt{5}£©^{2}}{2¡Á10}$=6m£»
´ð£º£¨1£©Ï¸Ïßδ¶Ïʱ£¬A¡¢BµÄ¼ÓËٶȴóСaΪ2m/s²£»
£¨2£©Ï¸Ïßδ¶Ïʱ£®Éþ×ÓµÄÀ­Á¦T´óСΪ12N£»
£¨3£©Ï¸Éþ¶Ïʱ£¬A¡¢BµÄËÙ¶ÈV_AΪ2$\sqrt{5}$m/s£¬·½Ïò£ºÑØбÃæÏòÏ£¬V_BΪ2$\sqrt{5}$m/s£¬·½Ïò£ºÊúÖ±ÏòÉÏ£»
£¨4£©Ï¸Éþ¶Ïºó£¬AÓëBµÄ¼ÓËÙ¶Èa₁Ϊ2m/s²£¬·½Ïò£ºÑØбÃæÏòÏ£¬a₂Ϊ2m/s²£¬·½Ïò£ºÊúÖ±ÏòÏ£»
£¨5£©Îï¿éBÉÏÉýµÄ×î´ó¸ß¶ÈHΪ6m£®

µãÆÀ ±¾Ì⿼²éÁËÅ£¶ÙµÚ¶þ¶¨ÂɵÄÓ¦Ó㬿¼²éÁËÇó¼ÓËٶȡ¢ËÙ¶ÈÓëλÒÆÎÊÌ⣬·ÖÎöÇå³þÎïÌåµÄÔ˶¯¹ý³ÌÊǽâÌâµÄÇ°ÌᣬӦÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉÓëÔ˶¯Ñ§¹«Ê½¿ÉÒÔ½âÌ⣮