Question

4£®ÈçͼËùʾ£¬Á½¿éƽÐнðÊô¼«°åMNˮƽ·ÅÖ㬰峤L=1m£®¼ä¾àd=$\frac{\sqrt{3}}{3}$m£¬Á½½ðÊô°å¼äµçѹU_MN=1¡Á10⁴ V£»ÔÚƽÐнðÊô°åÓÒ²àÒÀ´Î´æÔÚABCºÍFGHÁ½¸öÈ«µÈµÄÕýÈý½ÇÐÎÇøÓò£¬ÕýÈý½ÇÐÎABCÄÚ´æÔÚ´¹Ö±Ö½ÃæÏòÀïµÄÔÈÇ¿´Å³¡B₁£¬Èý½ÇÐεÄÉ϶¥µãAÓëÉϽðÊô°åMƽÆ룬BC±ßÓë½ðÊô°åƽÐУ¬AB±ßµÄÖеãPÇ¡ºÃÔÚϽðÊô°åNµÄÓҶ˵㣻ÕýÈý½ÇÐÎFGHÄÚ´æÔÚ´¹Ö±Ö½ÃæÏòÍâµÄÔÈÇ¿´Å³¡B₂£¬ÒÑÖªA¡¢F¡¢G´¦ÓÚͬһֱÏßÉÏ£®B¡¢C¡¢HÒ²´¦ÓÚͬһֱÏßÉÏ£®AFÁ½µã¾àÀëΪ$\frac{2}{3}$m£®ÏÖ´ÓƽÐнðÊô¼«°åMN×ó¶ËÑØÖÐÐÄÖáÏß·½ÏòÈëÉäÒ»¸öÖØÁ¦²»¼ÆµÄ´øµçÁ£×Ó£¬Á£×ÓÖÊÁ¿m=3¡Á10^-10 kg£¬´øµçÁ¿q=+1¡Á10^-4 C£¬³õËÙ¶Èv₀=1¡Á10⁵ m/s£®Çó£º
£¨1£©´øµçÁ£×Ӵӵ糡ÖÐÉä³öʱµÄËÙ¶ÈvµÄ´óСºÍ·½Ïò£¿
£¨2£©Èô´øµçÁ£×Ó½øÈëÈý½ÇÐÎÇøÓòABCºó´¹Ö±´òÔÚAC±ßÉÏ£¬Çó¸ÃÇøÓòµÄ´Å¸ÐӦǿ¶È£¿
£¨3£©½ÓµÚ£¨2£©ÎÊ£¬ÈôҪʹ´øµçÁ£×ÓÓÉFH±ß½ç½øÈëFGHÇøÓò²¢ÄÜÔٴλص½FH½çÃ棬ÇóB₂ÖÁÉÙӦΪ¶à´ó£¿

Answer 1

·ÖÎö £¨1£©´øµçÁ£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬¸ù¾ÝƽÅ×Ô˶¯µÄ»ù±¾¹æÂɼ´¿ÉÇó½â£»
£¨2£©Çó³ö´øµçÁ£×Ó³öµç³¡Ê±ÊúÖ±·½ÏòµÄƫתµÄλÒÆ£¬¸ù¾Ý¼¸ºÎ¹Øϵ¼°ÏòÐÄÁ¦¹«Ê½¼´¿ÉÇó½â´Å³¡Ç¿¶È£»
£¨3£©·ÖÎöÖªµ±¹ì¼£Óë±ß½çGHÏàÇÐʱ£¬¶ÔÓ¦´Å¸ÐӦǿ¶ÈB₂×î´ó£¬»­³öÁ£×ÓÔ˶¯¹ì¼£¸ù¾Ý¼¸ºÎ¹Øϵ¼°ÏòÐÄÁ¦¹«Ê½¼´¿ÉÇó½â´Å³¡Ç¿¶ÈÓ¦Âú×ãµÄÌõ¼þ£®

½â´ð ½â£º£¨1£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬
Á£×ӵļÓËٶȣºa=$\frac{qU}{md}$$\frac{\sqrt{3}}{3}$¡Á10¹⁰m/s²£®
ÓÉL=v₀t£¬½âµÃ£ºt=1¡Á10^-5s£®
ÊúÖ±·½ÏòËÙ¶ÈΪ£ºv_y=at=$\frac{\sqrt{3}}{3}$¡Á10⁵m/s£®
Éä³öʱËٶȣºv=$\sqrt{{v}_{0}^{2}+{v}_{y}^{2}}$=$\frac{2\sqrt{3}}{3}$¡Á10⁵m/s£¬
ËÙ¶ÈvÓëˮƽ·½Ïò¼Ð½ÇΪ¦È£¬tan¦È=$\frac{{v}_{y}}{{v}_{0}}$=$\frac{\sqrt{3}}{3}$£¬
½âµÃ£º¦È=30¡ã£¬¼´´¹Ö±ÓÚAB·½ÏòÉä³ö£®
£¨2£©´øµçÁ£×ÓÉä³öµç³¡Ê±ÊýÖµ·½ÏòÆ«ÒƵÄλÒÆ£º
y=$\frac{1}{2}$at²=$\frac{\sqrt{3}}{6}$m=$\frac{d}{2}$£¬¼´Á£×ÓÓÉPµã´¹Ö±ABÉäÈë´Å³¡£¬
Óɼ¸ºÎ¹Øϵ֪£¬Ôڴų¡ABCÇøÓòÄÚ×öÔÈËÙÔ²ÖÜÔ˶¯µÄ°ë¾¶£ºR₁=$\frac{d}{cos30¡ã}$=$\frac{2}{3}$m£®
ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵãºqvB₁=m$\frac{{v}^{2}}{{R}_{1}}$£¬½âµÃ£ºB₁=$\frac{3\sqrt{3}}{10}$T£®
£¨3£©µ±¹ì¼£Óë±ß½çGHÏàÇÐʱ£¬¶ÔÓ¦´Å¸ÐӦǿ¶ÈB₂×î´ó£¬Ô˶¯¹ì¼£ÈçͼËùʾ£®
Óɼ¸ºÎ¹Øϵ¿ÉÖª£ºR₂+$\frac{{R}_{2}}{sin60¡ã}$=1£®½âµÃ£ºR₂=£¨ 2$\sqrt{3}$-3£©m£®
ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵãºqvB₂=m$\frac{{v}^{2}}{{R}_{2}}$£¬½âµÃ£ºB₂=$\frac{2+\sqrt{3}}{5}$T£®
ËùÒÔB₂Ó¦Âú×ãµÄÌõ¼þΪ´óÓÚ£º$\frac{2+\sqrt{3}}{5}$T£®
´ð£º£¨1£©´øµçÁ£×Ӵӵ糡ÖÐÉä³öʱµÄËÙ¶ÈvµÄ´óСΪ£º$\frac{2\sqrt{3}}{3}$¡Á10⁵m/s£¬·½Ïò£º´¹Ö±ÓÚAB·½Ïò³öÉ䣮
£¨2£©Èô´øµçÁ£×Ó½øÈëÖмäÈý½ÇÐÎÇøÓòºó´¹Ö±´òÔÚAC±ßÉÏ£¬¸ÃÇøÓòµÄ´Å¸ÐӦǿ¶ÈB₁Ϊ$\frac{3\sqrt{3}}{10}$T£®
£¨3£©ÈôҪʹ´øµçÁ£×ÓÓÉFH±ß½ç½øÈëFGHÇøÓò²¢ÄÜÔٴλص½FH½çÃ棬B₂Ó¦Âú×ãµÄÌõ¼þÊÇ´óÓÚ$\frac{2+\sqrt{3}}{5}$T£®

µãÆÀ ±¾Ì⿼²éÁËÁ£×ÓÔڴų¡ÖеÄÔ˶¯£¬×öºÃ´ËÀàÌâÄ¿µÄ¹Ø¼üÊÇ׼ȷµÄ»­³öÁ£×ÓÔ˶¯µÄ¹ì¼£Í¼£¬ÀûÓü¸ºÎ֪ʶÇó³öÁ£×ÓÔ˶¯µÄ°ë¾¶£¬ÔÙ½áºÏ°ë¾¶¹«Ê½ºÍÖÜÆÚ¹«Ê½È¥·ÖÎö£¬ÄѶȽϴó£»
½â´øµçÁ£×ÓÔÚÓнç´Å³¡ÖÐÔ˶¯ÎÊÌâµÄÒ»°ã˼·£º
1¡¢¸ù¾ÝÌâÒâ×÷³öÁ£×ÓµÄÔ˶¯¹ì¼££»
2¡¢È·¶¨Á£×Ó×öÔ²ÖÜÔ˶¯µÄÔ²ÐÄ£¬Ó¦Óü¸ºÎ֪ʶÇó³öÁ£×ӵĹìµÀ°ë¾¶Óëת¹ýµÄÔ²ÐĽǣ»
3¡¢Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉÓëÁ£×ÓÖÜÆÚ¹«Ê½·ÖÎö´ðÌ⣮