Question

19£®ÈçͼËùʾ£¬ÔÚ¾ØÐÎÇøÓòabcdÄÚ³äÂú´¹Ö±Ö½ÃæÏòÀïµÄÔÈÇ¿´Å³¡£¬´Å¸ÐӦǿ¶ÈΪB£®ÔÚad±ßÖеãOµÄÁ£×ÓÔ´£¬ÔÚt=0ʱ¿Ì´¹Ö±Óڴų¡·¢Éä³ö´óÁ¿µÄͬÖÖ´øµçÁ£×Ó£¬ËùÓÐÁ£×ӵijõËٶȴóСÏàͬ£¬·½ÏòÓëOdµÄ¼Ð½Ç·Ö²¼ÔÚ0¡«180¡ã·¶Î§ÄÚ£®ÒÑÖªÑØOd·½Ïò·¢ÉäµÄÁ£×ÓÔÚt=t₀ʱ¿Ì¸ÕºÃ´Ó´Å³¡±ß½çcdÉϵÄpµãÀ뿪´Å³¡£¬ab=1.5L£¬bc=$\sqrt{3}$L£¬Á£×ÓÔڴų¡ÖÐ×öÔ²ÖÜÔ˶¯µÄ°ë¾¶R=L£¬²»¼ÆÁ£×ÓµÄÖØÁ¦ºÍÁ£×Ó¼äµÄÏ໥×÷Óã¬Çó£º
£¨1£©Á£×Ó´øµçµÄµçÐÔºÍÁ£×ÓÔڴų¡ÖеÄÔ˶¯ÖÜÆÚT£»
£¨2£©Á£×ӵıȺɣ»
£¨3£©Á£×ÓÔڴų¡ÖÐÔ˶¯µÄ×ʱ¼ä£®

Answer 1

·ÖÎö £¨1£©ÓÉÁ£×ÓÑØOd·½Ïò·¢Éä´Ó´Å³¡±ß½çcdÉϵÄpµãÀ뿪´Å³¡£¬ËµÃ÷Á£×ÓÊÜÏòÓÒµÄÂåÂ××ÈÁ¦ÏòÓÒÆ«£¬ÓÉ×óÊÖ¶¨ÔòÖªÁ£×Ó´øÕýµçºÉ£¬»­³öÔ˶¯¹ì¼££¬¸ù¾Ý¼¸ºÎ֪ʶÇó½âƫת½Ç£¬¸ù¾Ý½Ç¶ÈºÍʱ¼ä¹ØϵÇó½âÖÜÆÚ£»
£¨2£©Á£×Ó×öÔ²ÖÜÔ˶¯µÄÏòÐÄÁ¦ÓÉÂåÂØ×ÈÁ¦Ìṩ£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵãº$q{v_0}B=m\frac{{{v_0}^2}}{r}$ºÍT=$\frac{2¦ÐR}{{v}_{0}}$Öª±ÈºÉ£»
£¨3£©»­³öÔ˶¯¹ì¼££¬ÏÒ×Ϊ2L£¬ÕÒµ½¶ÔÓ¦µÄ×î´óÔ²ÐĽǣ¬´Ó¶øÖª×ʱ¼ä£®

½â´ð ½â£º£¨1£©ÓÉÁ£×ÓÑØOd·½Ïò·¢Éä´Ó´Å³¡±ß½çcdÉϵÄpµãÀ뿪´Å³¡£¬ËµÃ÷Á£×ÓÊÜÏòÓÒµÄÂåÂ××ÈÁ¦ÏòÓÒÆ«£¬ÓÉ×óÊÖ¶¨ÔòÖªÁ£×Ó´øÕýµçºÉ       
³õËÙ¶ÈÑØOd·½Ïò·¢ÉäµÄÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ¹ì¼£Èçͼ1£¬ÆäÔ²ÐÄΪ¦È£¬
Óɼ¸ºÎ¹ØϵÓУºsin¦È=$\frac{\sqrt{3}}{2}$
ËùÒÔ£º¦È=60¡ã
$\frac{{t}_{0}}{T}$=$\frac{¦È}{360¡ã}$
½âµÃ£ºT=6t₀                                 
£¨2£©Á£×Ó×öÔ²ÖÜÔ˶¯µÄÏòÐÄÁ¦ÓÉÂåÂØ×ÈÁ¦Ìṩ£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵãº
$q{v_0}B=m\frac{{{v_0}^2}}{r}$

T=$\frac{2¦ÐR}{{v}_{0}}$
´øµç΢Á£Ôڴų¡ÖÐ×öÔ²ÖÜÔ˶¯µÄÖÜÆÚΪ$T=\frac{2¦Ðm}{qB}$
ÁªÁ¢ÒÔÉÏʽ×Ó½âµÃ$\frac{q}{m}$=$\frac{¦Ð}{3{B}_{0}{t}_{0}}$
£¨3£©Èçͼ2Ëùʾ£¬Ôڴų¡ÖÐÔ˶¯Ê±¼ä×µÄÁ£×ӵĹ켣µÄÏÒOb=$\sqrt{3}$L£¬Ô²¹ì¼£µÄÖ±¾¶Îª2L£¬ËùÒÔ£ºObÏÒ¶ÔÓ¦µÄÔ²ÐĽÇΪ120¡ã£¬Á£×ÓÔڴų¡ÖÐÔ˶¯µÄ×ʱ¼ä  t_max=$\frac{T}{3}$=2t₀          
´ð£º£¨1£©Á£×ÓÔڴų¡ÖеÄÔ˶¯ÖÜÆÚTΪ6t₀£»
£¨2£©Á£×ӵıȺÉΪ$\frac{¦Ð}{3B{t}_{0}}$£»
£¨3£©Á£×ÓÔڴų¡ÖÐÔ˶¯µÄ×ʱ¼äΪ2t₀£®

µãÆÀ ±¾Ì⿼²é·ÖÎöºÍ´¦ÀíÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ¹ì¼£ÎÊÌ⣬ÄѵãÔÚÓÚ·ÖÎöʱ¼äµÄ×î´óÖµ£¬Ò²¿ÉÒÔÔËÓü«ÏÞ·ÖÎö·¨·ÖÎö£®