Question

4£®ÈçͼËùʾ£¬ÒÔˮƽµØÃ潨Á¢xÖᣬÓÐÒ»¸öÖÊÁ¿Îªm=1kgµÄľ¿é·ÅÔÚÖÊÁ¿ÎªM=2kgµÄ³¤Ä¾°å×ó¶Ë£¬Ä¾°å³¤L=11.5m£®ÒÑ֪ľ°åÓëµØÃæµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì₁=0.1£¬mÓëMÖ®¼äµÄĦ²ÁÒòËئÌ₂=0.9£¨Éè×î´ó¾²Ä¦²ÁÁ¦µÈÓÚ»¬¶¯Ä¦²ÁÁ¦£©£®mÓëM±£³ÖÏà¶Ô¾²Ö¹¹²Í¬ÏòÓÒÔ˶¯£¬Ä¾°åµÄ×ó¶ËAµã¾­¹ý×ø±êÔ­µãOʱµÄËÙ¶ÈΪV₀=10m/s£¬ÔÚ×ø±êΪX=21m´¦µÄPµãÓÐÒ»µ²°å£¬Ä¾°åÓëµ²°åÅöײºóÁ¢¼´ÒÔÔ­ËÙÂÊ·´Ïòµ¯»Ø£¬¶øľ¿éÔÚ´Ë˲¼äËٶȱ£³Ö²»±ä£¬ÅöºóÁ¢¿Ì³·È¥µ²°å£¬gÈ¡10m/s²£¬Çó£º

£¨1£©Ä¾°åÅöµ²°åʱµÄËÙ¶Èv₁£»
£¨2£©Åöײºó¾­¾­¶à³¤Ê±¼äľ¿éÏòÓÒµÄËٶȼõΪÁ㣻´Ëʱľ°åµÄËٶȴóС£®

Answer 1

·ÖÎö £¨1£©¶ÔÕûÌå·ÖÎö£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öÕûÌåÔȼõËÙÖ±ÏßÔ˶¯µÄ¼ÓËٶȴóС£¬½áºÏËÙ¶ÈλÒƹ«Ê½Çó³öľ°åÅöµ²°åʱµÄËٶȴóС£®
£¨2£©Åöºó£¬M·´µ¯Ïò×ó×ö¼õËÙ£¬mÏòÓÒ¼õËÙ£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ·Ö±ðÇó³öMºÍmµÄ¼ÓËٶȴóС£¬½áºÏËÙ¶Èʱ¼ä¹«Ê½Çó³öľ¿éÏòÓÒËٶȼõΪÁãµÄʱ¼ä£¬¸ù¾ÝËÙ¶Èʱ¼ä¹«Ê½Çó³ö´Ëʱľ°åµÄËٶȴóС£®

½â´ð ½â£º£¨1£©Ä¾°åÅöµ²°åÇ°£¬¶Ôľ¿éºÍľ°å×é³ÉµÄϵͳ£¬ÓУº
¦Ì₁£¨m+M£©g=£¨M+m£©a₁£¬
¸ù¾ÝËÙ¶ÈλÒƹ«Ê½µÃ£º${{v}_{0}}^{2}-{{v}_{1}}^{2}=2{a}_{1}£¨x-L£©$£¬
´úÈëÊý¾Ý½âµÃv₁=9m/s£®
£¨2£©ÅöºómÏòÓÒ¼õËÙ£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÖª£º${a}_{m}={¦Ì}_{2}g=0.9¡Á10m/{s}^{2}=9m/{s}^{2}$£¬
MÏò×ó¼õËÙ£¬ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵ㺦Ì₁£¨M+m£©g+¦Ì₂mg=Ma_M£¬
´úÈëÊý¾Ý½âµÃ£º${a}_{M}=6m/{s}^{2}$£®
ÅöºómÔ˶¯ÖÁֹͣʱ¼äΪ£º${t}_{1}=\frac{{v}_{1}}{{a}_{m}}=\frac{9}{9}s=1s$£¬
´ËʱMµÄËÙ¶ÈΪ£ºv_M=v₁-a_Mt₁=9-6¡Á1m/s=3m/s£®
´ð£º£¨1£©Ä¾°åÅöµ²°åʱµÄËÙ¶ÈΪ9m/s£»
£¨2£©Åöײºó¾­¾­1sʱ¼äľ¿éÏòÓÒµÄËٶȼõΪÁ㣬´Ëʱľ°åµÄËٶȴóСΪ3m/s£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÀíÇåľ¿éºÍľ°åÔÚÕû¸ö¹ý³ÌÖеÄÔ˶¯¹æÂÉ£¬½áºÏÅ£¶ÙµÚ¶þ¶¨ÂɺÍÔ˶¯Ñ§¹«Ê½×ÛºÏÇó½â£¬ÖªµÀ¼ÓËÙ¶ÈÊÇÁªÏµÁ¦Ñ§ºÍÔ˶¯Ñ§µÄÇÅÁº£®