Question

2£®ÌìÎÄѧ¼Ò¹Û²âºÓÍâÐÇϵ´óÂóÕÜÂ×ÔÆʱ£¬·¢ÏÖÁËLMCX-3Ë«ÐÇϵͳ£¬ËüÓɿɼûÐÇAºÍ²»¿É¼ûµÄ°µÐÇB¹¹³É£®Á½ÐÇÊÓΪÖʵ㣬²»¿¼ÂÇÆäËûÌìÌåµÄÓ°Ï죬A¡¢BΧÈÆÁ½ÕßÁ¬ÏßÉϵÄOµã×öÔÈËÙÔ²ÖÜÔ˶¯£¬ËüÃÇÖ®¼äµÄ¾àÀë±£³Ö²»±ä£¬ÈçͼËùʾ£®ÒýÁ¦³£Á¿ÎªG£¬Óɹ۲âÄܹ»µÃµ½¿É¼ûÐÇAµÄËÙÂÊvºÍÔËÐÐÖÜÆÚT£®
£¨1£©¿É¼ûÐÇAËùÊÜ°µÐÇBµÄÒýÁ¦F_A¿ÉµÈЧΪλÓÚOµã´¦ÖÊÁ¿Îªm¡äµÄÐÇÌ壨ÊÓΪÖʵ㣩¶ÔËüµÄÒýÁ¦£¬ÉèAºÍBµÄÖÊÁ¿·Ö±ðΪm₁¡¢m₂£¬Çóm¡ä£¨ÓÃm₁¡¢m₂±íʾ£©£»
£¨2£©Çó°µÐÇBµÄÖÊÁ¿m₂Óë¿É¼ûÐÇAµÄËÙÂÊv¡¢ÔËÐÐÖÜÆÚTºÍÖÊÁ¿m₁Ö®¼äµÄ¹Øϵʽ£®

Answer 1

·ÖÎö £¨1£©×¥×¡A¡¢B×öÔ²ÖÜÔ˶¯µÄÏòÐÄÁ¦ÏàµÈ£¬½ÇËÙ¶ÈÏàµÈ£¬Çó³öA¡¢B¹ìµÀ°ë¾¶µÄ¹Øϵ£¬´Ó¶øµÃÖªA¡¢B¾àÀëΪAÎÀÐǵĹìµÀ°ë¾¶¹Øϵ£¬¿É¼ûÐÇAËùÊÜ°µÐÇBµÄÒýÁ¦F_A¿ÉµÈЧΪλÓÚOµã´¦ÖÊÁ¿Îªm¡äµÄÐÇÌ壨ÊÓΪÖʵ㣩¶ÔËüµÄÒýÁ¦£¬¸ù¾ÝÍòÓÐÒýÁ¦¶¨Âɹ«Ê½Çó³öÖÊÁ¿m¡ä£®
£¨2£©¸ù¾ÝÍòÓÐÒýÁ¦ÌṩÏòÐÄÁ¦Çó³ö°µÐÇBµÄÖÊÁ¿m₂Óë¿É¼ûÐÇAµÄËÙÂÊv¡¢ÔËÐÐÖÜÆÚTºÍÖÊÁ¿m₁Ö®¼äµÄ¹Øϵʽ£®

½â´ð ½â£º£¨1£©ÉèA¡¢BµÄÔ²¹ìµÀ°ë¾¶·Ö±ðΪr₁¡¢r₂£¬½ÇËٶȾùΪ¦Ø£¬
ÓÉË«ÐÇËùÊÜÏòÐÄÁ¦´óСÏàͬ£¬¿ÉµÃm₁¦Ø²r₁=m₂¦Ø²r₂
ÉèA¡¢BÖ®¼äµÄ¾àÀëΪL£¬ÓÖL=r₁+r₂ÓÉÉÏÊö¸÷ʽµÃ£ºL=$\frac{{m}_{1}+{m}_{2}}{{m}_{2}}$r₁¡­¢Ù
ÓÉÍòÓÐÒýÁ¦¶¨Âɵã¬Ë«ÐǼäµÄÒýÁ¦Îª£ºF=G$\frac{{m}_{1}{m}_{2}}{{L}^{2}}$
½«¢Ùʽ´úÈëÉÏʽµÃ£ºF=$G\frac{{m}_{1}{{m}_{2}}^{3}}{£¨{m}_{1}+{m}_{2}£©^{2}{{r}_{1}}^{2}}$¡­¢Ú
ÓÉÌâÒ⣬½«´ËÒýÁ¦ÊÓΪOµã´¦ÖÊÁ¿Îªm¡äµÄÐÇÌå¶Ô¿É¼ûÐÇAµÄÒýÁ¦£¬ÔòÓУºF=G$\frac{{m}_{1}m¡ä}{{{r}_{1}}^{2}}$¡­¢Û
±È½Ï¢Ú¢Û¿ÉµÃ£ºm¡ä=$\frac{{{m}_{2}}^{3}}{{£¨{m}_{1}+{m}_{2}£©}^{2}}$¡­¢Ü
£¨2£©¶Ô¿É¼ûÐÇA£¬ÓУºG$\frac{{m}_{1}m¡ä}{{{r}_{1}}^{2}}={m}_{1}\frac{{v}^{2}}{{r}_{1}}$¡­¢Ý
¿É¼ûÐÇAµÄ¹ìµÀ°ë¾¶Îª£ºr₁=$\frac{vT}{2¦Ð}$¡­¢Þ
ÓɢܢݢÞʽ½âµÃ£º$\frac{{{m}_{2}}^{3}}{{£¨{m}_{1}+{m}_{2}£©}^{2}}$=$\frac{v3T}{2¦ÐG}$£®
´ð£º£¨1£©m¡ä=$\frac{{{m}_{2}}^{3}}{{£¨{m}_{1}+{m}_{2}£©}^{2}}$£»
£¨2£©°µÐÇBµÄÖÊÁ¿m₂Óë¿É¼ûÐÇAµÄËÙÂÊv¡¢ÔËÐÐÖÜÆÚTºÍÖÊÁ¿m₁Ö®¼äµÄ¹ØϵʽΪ$\frac{{{m}_{2}}^{3}}{{£¨{m}_{1}+{m}_{2}£©}^{2}}$=$\frac{v3T}{2¦ÐG}$£®

µãÆÀ ¶ÔÓÚÌìÌåÔ˶¯ÎÊÌâ¹Ø¼üÒª½¨Á¢ÎïÀíÄ£ÐÍ£®Ë«ÐÇÎÊÌâÓëÈËÔìµØÇòÎÀÐǵÄÔ˶¯Ä£ÐͲ»Í¬£¬Á½ÐǶ¼ÈÆ×ÅËüÃÇÖ®¼äÁ¬ÏßÉϵÄÒ»µãΪԲÐÄ×öÔÈËÙÔ²ÖÜÔ˶¯£¬Ë«ÐÇ¡¢Ô²ÐÄʼÖÕ¡°Èýµã¡±Ò»Ïߣ®