Question

14£®ÈçͼËùʾ£¬Ò»ÖÊÁ¿M=0.4kgµÄСÎï¿éBÔÚ×ã¹»³¤µÄ¹â»¬Ë®Æ½Ì¨ÃæÉϾ²Ö¹²»¶¯£¬ÆäÓÒ²à¹Ì¶¨ÓÐÒ»ÇáÖÊˮƽµ¯»É£¨´¦ÓÚÔ­³¤£©£®Ì¨ÃæµÄÓÒ±ßƽ»¬¶Ô½ÓÓÐÒ»µÈ¸ßµÄˮƽ´«ËÍ´ø£¬´«ËÍ´øʼÖÕÒÔ¦Ô=1m/sµÄËÙÂÊÄæʱÕëת¶¯£®ÁíÒ»ÖÊÁ¿m=0.1kgµÄСÎï¿éAÒÔËٶȦÔ₀=4m/sˮƽ»¬ÉÏ´«ËÍ´øµÄÓҶˣ®ÒÑÖªÎï¿éAÓë´«ËÍ´øÖ®¼äµÄ¶¯Ä¦²ÁÒòÊý¦Ì=0.1£¬´«ËÍ´ø×óÓÒÁ½¶ËµÄ¾àÀël=3.5m£¬»¬¿éA¡¢B¾ùÊÓΪÖʵ㣬ºöÂÔ¿ÕÆø×èÁ¦£¬È¡g=10m/s²£®
£¨1£©ÇóÎï¿éAµÚÒ»´Îµ½´ï´«ËÍ´ø×ó¶ËʱËٶȴóС£»
£¨2£©ÇóÎï¿éAµÚÒ»´ÎѹËõµ¯»É¹ý³ÌÖе¯»ÉµÄ×î´óµ¯ÐÔÊÆÄÜE_pm£»
£¨3£©Îï¿éA»á²»»áµÚ¶þ´ÎѹËõµ¯»É£¿

Answer 1

·ÖÎö £¨1£©Îï¿éA´Ó´«ËÍ´øµÄÓҶ˻¬µ½×ó¶ËµÄ¹ý³Ì£¬¸ù¾Ý¶¯Äܶ¨ÀíÇó½â£»
£¨2£©Îï¿éAµÚÒ»´ÎѹËõµ¯»É¹ý³ÌÖУ¬µ±Îï¿éAºÍBµÄËÙ¶ÈÏàµÈʱ£¬µ¯»ÉµÄµ¯ÐÔÊÆÄÜ×î´ó£¬¸ù¾Ý¶¯Á¿Êغ㶨ÂɺͻúеÄÜÊغ㶨ÂÉÁÐʽÇó½â£»
£¨3£©Îï¿éAµÚÒ»´ÎѹËõµ¯»ÉÇ°ºó¶¯Á¿ºÍ¶¯ÄܾùÊغ㣬¸ù¾Ý¶¯Á¿Êغ㶨ÂɺͻúеÄÜÊغ㶨ÂÉÁÐʽÇó½âÅöײºóµÄËٶȣ¬ÔÙ¸ù¾Ý¶¯Äܶ¨ÀíÁÐʽÇó³öËٶȼõΪÁãµÄλÒÆ£¬ÔÙÎï¿éAµÚ¶þ´ÎÏò×óµ½´ï´«ËÍ´ø×ó¶ËʱµÄËٶȣ¬´Ó¶øÅжÏÊÇ·ñ»áµÚ¶þ´ÎѹËõµ¯»É£®

½â´ð ½â£º£¨1£©Îï¿éA´Ó´«ËÍ´øµÄÓҶ˻¬µ½×ó¶ËµÄ¹ý³Ì£¬¸ù¾Ý¶¯Äܶ¨ÀíÓУº
$\frac{1}{2}$m¦Ô₁²-$\frac{1}{2}$m¦Ô₀²=-¦Ìmgl
´úÈëÊý¾Ý½âµÃ£º¦Ô₁=3m/s
ÒòΪ¦Ô₁£¾¦Ô
ËùÒÔÎï¿éAµÚÒ»´Îµ½´ï´«ËÍ´ø×ó¶ËʱËٶȴóСΪ3m/s£®
£¨2£©Îï¿éAµÚÒ»´ÎѹËõµ¯»É¹ý³ÌÖУ¬µ±Îï¿éAºÍBµÄËÙ¶ÈÏàµÈʱ£¬µ¯»ÉµÄµ¯ÐÔÊÆÄÜ×î´ó£¬¸ù¾Ý¶¯Á¿Êغ㶨ÂÉÓУºm¦Ô₁=£¨ M+m £©¦Ô¡ä
¸ù¾Ý»úеÄÜÊغ㶨ÂÉÓУºE_pm=$\frac{1}{2}$m¦Ô₁²-$\frac{1}{2}$£¨ M+m £© ¦Ô¡ä²
´úÈëÊý¾Ý½âµÃ£ºE_pm=0.36J£®
£¨3£©Îï¿éAµÚÒ»´ÎѹËõµ¯»ÉÇ°ºó¶¯Á¿ºÍ¶¯ÄܾùÊغ㣬ÓУº
m¦Ô₁=m¦Ô₁¡ä+M¦Ô₂¡ä
$\frac{1}{2}$m¦Ô₁²=$\frac{1}{2}$m¦Ô₁¡ä²+$\frac{1}{2}$M¦Ô₂¡ä²
½âµÃ£º¦Ô₁¡ä=$\frac{m-M}{m+M}$¦Ô₁=-1.8m/s£¬¦Ô₂¡ä=$\frac{2m}{m+M}$¦Ô₁
´úÈëÊý¾Ý½âµÃ£º¦Ô₁¡ä=-1.8m/s£¬¦Ô₂¡ä=1.2m/s
¸ù¾Ý¶¯Äܶ¨ÀíÓУº0-$\frac{1}{2}$m ¦Ô₁¡ä²=-¦Ìmgl₁
´úÈëÊý¾Ý½âµÃ£ºl₁=1.62m
ÒòΪl₁£¼l
ËùÒÔÎï¿éAµÚ¶þ´ÎÏò×óµ½´ï´«ËÍ´ø×ó¶ËʱµÄËٶȦÔ₁¡å=¦Ô=1m/s
¸ù¾Ý¦Ô₁¡å£¼¦Ô₂¡ä£¬¿ÉµÃÎï¿éA²»»áµÚ¶þ´ÎѹËõµ¯»É£®
´ð£º£¨1£©Îï¿éAµÚÒ»´Îµ½´ï´«ËÍ´ø×ó¶ËʱËٶȴóСΪ3m/s£»
£¨2£©Îï¿éAµÚÒ»´ÎѹËõµ¯»É¹ý³ÌÖе¯»ÉµÄ×î´óµ¯ÐÔÊÆÄÜE_pmΪ0.36J£»
£¨3£©Îï¿éA²»»áµÚ¶þ´ÎѹËõµ¯»É£®

µãÆÀ ±¾ÌâÊǶà¹ý³ÌÎÊÌ⣬·ÖÎö»¬¿é¾­ÀúµÄ¹ý³Ì£¬ÔËÓö¯Á¿Êغ㣬ÄÜÁ¿Êغ㡢¶¯Äܶ¨Àí·ÖÎöºÍ¼ÆË㣬¹Ø¼üÊÇ·ÖÎöÇå³þÎïÌåµÄÊÜÁ¦Çé¿öºÍÔ˶¯Çé¿ö£¬ÄѶȽϴó£®