Question

4£®Ä³Í¬Ñ§ÓÃÈçͼװÖòâÁ¿Ä¾¿éÓëƽ°å¼äµÄĦ²ÁÒòÊý£®G₁ºÍG₂ΪÁ½¸ö¹âµçÃÅ£¬·Ö±ðÓë¼ÆʱÆ÷Á¬½Ó£¬ÓÃÌìƽ·Ö±ð²â³öÇ£ÒýíÀÂëµÄÖÊÁ¿mºÍľ¿é¼°ÉÏÃæµÄµµ¹âխƬµÄ×ÜÖÊÁ¿M£¬mÓëMµÄ¹ØϵÊÇÈÎÒâµÄ£¬ÊÍ·ÅÇ£ÒýíÀÂ롢ľ¿éÑØˮƽƽ°å»¬¶¯£¬·Ö±ð²â³öÁËľ¿éÉÏխƬͨ¹ýÁ½¸ö¹âµçÃŵÄʱ¼ät₁ºÍt₂£¬¶øºóÓÖÓÃÓα꿨³ß²â³öխƬ¿í¶Èd£¬Ôò£º

£¨1£©¸Ãͬѧ»¹ÐèÒª²âÁ¿µÄÎïÀíÁ¿ÊÇÁ½¹âµçÃżä¾àÀëL
£¨2£©¶¯Ä¦²ÁÒòÊýµÄ±í´ïʽΪ$\frac{m}{M}$-$\frac{£¨M+m£©{d}^{2}£¨{t}_{1}^{2}-{t}_{2}^{2}£©}{2MgL{t}_{1}^{2}{t}_{2}^{2}}$£¨ÓÃÌâÖиø³öµÄ×ÖĸºÍ²âÁ¿µÄÎïÀíÁ¿±íʾ£©

Answer 1

·ÖÎö ÏÈÀûÓü«¶Ìʱ¼äµÄƽ¾ùËٶȱíʾ˲ʱËٶȣ¬È»ºó¶Ô»¬¿éµÄ¼ÓËÙ¹ý³ÌÔËÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÇó½â³ö¶¯Ä¦²ÁÒòËصıí´ïʽ¼´¿É£®

½â´ð ½â£º¶ÔÕûÌåÊÜÁ¦·ÖÎö£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵãº
mg-Mg=£¨M+m£©a
Óü«¶Ìʱ¼äµÄƽ¾ùËٶȱíʾ˲ʱËٶȣ¬¹Êͨ¹ýÁ½¸ö¹âµçÃŵÄ˲ʱËٶȷֱðΪ£º
${v}_{1}=\frac{d}{{t}_{1}}$
${v}_{2}=\frac{d}{{t}_{2}}$ 
ÉèÁ½¹âµçÃżä¾àÀëL£¬¸ù¾ÝËÙ¶ÈλÒƹ«Ê½£¬ÓУº
${v}_{2}^{2}-{v}_{1}^{2}=2aL$ 
ÁªÁ¢½âµÃ£º
¦Ì=$\frac{m}{M}$-$\frac{£¨M+m£©{d}^{2}£¨{t}_{1}^{2}-{t}_{2}^{2}£©}{2MgL{t}_{1}^{2}{t}_{2}^{2}}$
¹Ê»¹ÐèÒª²âÁ¿µÄÎïÀíÁ¿ÊÇÁ½¹âµçÃżä¾àÀëL£»
¹Ê´ð°¸Îª£º£¨1£©Á½¹âµçÃżä¾àÀëL£»£¨2£©$\frac{m}{M}$-$\frac{£¨M+m£©{d}^{2}£¨{t}_{1}^{2}-{t}_{2}^{2}£©}{2MgL{t}_{1}^{2}{t}_{2}^{2}}$£®

µãÆÀ ±¾Ìâ¹Ø¼üÊÇÃ÷È·»¬¿éºÍÎïÌåµÄÊÜÁ¦Çé¿öºÍÔ˶¯Çé¿ö£¬È»ºó¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ¡¢Ô˶¯Ñ§¹«Ê½ÁÐʽÇó½â£¬×¢ÒâÓü«¶Ìʱ¼äÄÚµÄƽ¾ùËٶȱíʾ˲ʱËٶȣ¬»ù´¡ÌâÄ¿£®