Question

12£®ÓîÖæÖдæÔÚһЩÀëÆäËûºãÐǽÏÔ¶µÄ¡¢ÓÉÖÊÁ¿ÏàµÈµÄÈý¿ÅÐÇ×é³ÉµÄËùν¡°ÈýÐÇϵͳ¡±£¬Í¨³£¿ÉºöÂÔÆäËûÐÇÌå¶ÔËüÃǵÄÒýÁ¦×÷Óã®Òѹ۲⵽Îȶ¨µÄÈýÐÇϵͳ´æÔÚÒ»ÖÖÐÎʽÊÇÈý¿ÅÐÇλÓڵȱßÈý½ÇÐεÄÈý¸ö¶¥µãÉÏ£¬²¢ÑØÍâ½ÓÓڵȱßÈý½ÇÐεÄÔ²¹ìµÀÔËÐУ®ÈçͼËùʾ£¬¼ÙÉèÿ¸öÐÇÌåµÄÖÊÁ¿¾ùΪM£¬ÏàÁÚµÄÁ½¿ÅÐÇÖ®¼äµÄ¾àÀëΪL£¬²¢ÇÒÒýÁ¦³£Á¿ÎªG£®ÊÔÇó£º
£¨1£©ÆäÖÐÈÎÒâÁ½¸öÐÇÌå¼äµÄÒýÁ¦´óС£»
£¨2£©Ã¿¸öÐÇÌåµÄ¼ÓËٶȴóС£»
£¨3£©Ã¿¸öÐÇÌåµÄÖÜÆÚºÍÏßËٶȴóС£®

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÍòÓÐÒýÁ¦¶¨ÂÉÁÐʽÇó½âÈÎÒâÁ½¸öÐÇÌå¼äµÄÒýÁ¦´óС£»
£¨2£©Ïȸù¾ÝƽÐÐËıßÐζ¨ÔòÇó½âºÏÁ¦£¬ÔÙ¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÇó½â¼ÓËٶȴóС£»
£¨3£©ºÏÁ¦ÌṩÏòÐÄÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÇó½âÖÜÆÚºÍÏßËٶȴóС£®

½â´ð ½â£º£¨1£©¸ù¾ÝÍòÓÐÒýÁ¦¶¨ÂÉ£¬ÈÎÒâÁ½¸öÐÇÌå¼äµÄÒýÁ¦´óСΪ£ºF=G$\frac{{M}^{2}}{{L}^{2}}$
£¨2£©Ã¿¸öÐÇÌåµÄºÏÁ¦£ºF_ºÏ=2Fcos30¡ã=$\frac{\sqrt{3}G{M}^{2}}{{L}^{2}}$
¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ£¬ÓУºa=$\frac{{F}_{ºÏ}}{M}$=$\frac{\sqrt{3}G{M}^{\;}}{{L}^{2}}$
£¨3£©ÐÇÇò×öÔÈËÙÔ²ÖÜÔ˶¯£¬ºÏÁ¦Ìá¸ßÏòÐÄÁ¦£¬¹Ê£º
F_ºÏ=m$\frac{4{¦Ð}^{2}}{{T}^{2}}r$=m$\frac{{v}^{2}}{r}$
ÆäÖУºr=$\frac{\sqrt{3}}{3}L$
½âµÃ£º
v=$\sqrt{\frac{GM}{L}}$
T=$\frac{2\sqrt{3}}{3}¦Ð\sqrt{\frac{{L}^{3}}{GM}}$
´ð£º£¨1£©ÆäÖÐÈÎÒâÁ½¸öÐÇÌå¼äµÄÒýÁ¦´óСΪG$\frac{{M}^{2}}{{L}^{2}}$£»
£¨2£©Ã¿¸öÐÇÌåµÄ¼ÓËٶȴóСΪ$\frac{\sqrt{3}G{M}^{\;}}{{L}^{2}}$£»
£¨3£©Ã¿¸öÐÇÌåµÄÖÜÆÚΪ$\frac{2\sqrt{3}}{3}¦Ð\sqrt{\frac{{L}^{3}}{GM}}$£¬ÏßËٶȴóСΪ$\sqrt{\frac{GM}{L}}$£®

µãÆÀ ±¾ÌâÊÇÈýÐÇÎÊÌ⣬¹Ø¼üÊÇÖªµÀÿ¸öÐÇÇò¾ù×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÖªµÀºÏÁ¦ÌṩÏòÐÄÁ¦£¬Äܸù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÇó½â£®