Question

9£®ÈçͼËùʾ£¬Ò»¸ö°ë¾¶ÎªR=1.5mµÄ½ðÊôÔ²»·ÊúÖ±¹Ì¶¨·ÅÖ㬻·ÉÏÌ×ÓÐÒ»¸öÖÊÁ¿ÎªmµÄСÇò£¬Ð¡Çò¿ÉÔÚ»·ÉÏ×ÔÓÉ»¬¶¯£¬Óë»·¼äµÄ¶¯Ä¦²ÁÒòÊýΪ0.75£®²»¼Æ¿ÕÆø×èÁ¦£¬ÖØÁ¦¼ÓËÙ¶Èg=10m/s²£®µ±Ð¡ÇòÏòÓÒ»¬¶¯¾­¹ý»·µÄ×î¸ßµãʱ£º£¨½á¹û¿ÉÓøùºÅ±íʾ£©
£¨1£©Èô´Ë¿Ì»·¶ÔСÇòµÄĦ²ÁÁ¦ÎªÁ㣬Çó´Ë¿ÌСÇòµÄËÙÂÊ£®
£¨2£©Èô´Ë¿Ì»·¶ÔСÇòµÄĦ²ÁÁ¦´óСΪ0.3mg£¬Çó´Ë¿Ì»·¶ÔСÇòµÄ×÷ÓÃÁ¦´óС£®
£¨3£©Èô´Ë¿Ì»·¶ÔСÇòµÄĦ²ÁÁ¦´óСΪ0.3mg£¬Çó´Ë¿ÌСÇòµÄËÙÂÊ£®

Answer 1

·ÖÎö £¨1£©Ä¦²ÁÁ¦ÎªÁ㣬ÖØÁ¦ÍêÈ«ÌṩÏòÐÄÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇóµÃËٶȣ»
£¨2£©¸ù¾Ýf=¦ÌF_NÇóµÃÏ໥×÷ÓÃÁ¦£»
£¨3£©¸ù¾ÝĦ²ÁÁ¦ÇóµÃ»·ÓëСÇò¼äµÄÏ໥×÷ÓÃÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇóµÃËÙÂÊ

½â´ð ½â£º£¨1£©Ä¦²ÁÁ¦f=0£¬Ôò»·¶ÔСÇòµÄµ¯Á¦N=0                    
¶ÔСÇòÊÜÁ¦·ÖÎöÓУº$mg=\frac{m{v}^{2}}{R}$                          
½âµÃСÇòËÙÂÊ $v=\sqrt{15}m/s$
£¨2£©»¬¶¯Ä¦²ÁÁ¦ f=¦ÌN£¬
½«f=0.3mg¡¢¦Ì=0.75´úÈë
½âµÃ»·¶ÔСÇòµÄµ¯Á¦N=$\frac{f}{¦Ì}=\frac{0.3mg}{0.75}$=0.4mg
Óɹ´¹É¶¨Àí£¬»·¶ÔСÇòµÄ×÷ÓÃÁ¦$F=\sqrt{{N}^{2}+{f}^{2}}=0.5mg$
£¨3£©ÓɵڶþСÌâ¿ÉÖª£¬»·¶ÔСÇòµÄµ¯Á¦N=0.4mg
µ±»·¶ÔСÇòµÄµ¯Á¦ÏòÉÏʱ£º$mg-N=\frac{{mv}_{1}^{2}}{R}$
½âµÃСÇòµÄËÙÂÊ v₁=3m/s
µ±»·¶ÔСÇòµÄµ¯Á¦ÏòÏÂʱ£º$mg+N=\frac{{mv}_{2}^{2}}{R}$
½âµÃСÇòµÄËÙÂÊ ${v}_{2}=\sqrt{21}m/s$
´ð£º£¨1£©Èô´Ë¿Ì»·¶ÔСÇòµÄĦ²ÁÁ¦ÎªÁ㣬´Ë¿ÌСÇòµÄËÙÂÊΪ$\sqrt{15}$m/s£®
£¨2£©Èô´Ë¿Ì»·¶ÔСÇòµÄĦ²ÁÁ¦´óСΪ0.3mg£¬´Ë¿Ì»·¶ÔСÇòµÄ×÷ÓÃÁ¦´óСΪ0.5mg£®
£¨3£©Èô´Ë¿Ì»·¶ÔСÇòµÄĦ²ÁÁ¦´óСΪ0.3mg£¬´Ë¿ÌСÇòµÄËÙÂÊΪ3m/s»òÕß$\sqrt{21}$m/s£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÖªµÀСÇò×öÔ²ÖÜÔ˶¯ÏòÐÄÁ¦µÄÀ´Ô´£¬½áºÏÅ£¶ÙµÚ¶þ¶¨ÂɽøÐÐÇó½â£¬×¢ÒâÔÚ×î¸ßµã£¬»·¶ÔÇòµÄµ¯Á¦¿ÉÄÜÏòÉÏ£¬¿ÉÄÜÏòÏ£®