Question

6£®Èçͼ¼×Ëùʾ£¬Æ½ÐнðÊô°åAºÍB¼äµÄ¾àÀëΪd£¬ÏÖÔÚA¡¢B°åÉϼÓÉÏÈçͼÒÒËùʾµÄ·½²¨µçѹ£¬t=0ʱA°å±ÈB°åµÄµçÊƸߣ®µçѹµÄÕýÏòֵΪU₀£¬·´ÏòֵҲΪU₀£¬ÏÖÓÐÖÊÁ¿ÎªmµçÁ¿Îª+qµÄÁ£×Ó×é³ÉµÄÁ£×ÓÊø£¬´ÓABµÄÖеãOÑؽðÊô°åÖÐÖáÏßOO¡äÒÔËÙ¶Èv₀=$\frac{{q{U_0}T}}{3md}$²»¶ÏÉäÈ룬ËùÓÐÁ£×ÓÔÚAB¼äµÄ·ÉÐÐʱ¼ä¾ùΪT£¬²»¼ÆÖØÁ¦Ó°Ï죮ÊÔÇó£º
£¨1£©t=0ʱÉäÈëµÄ´øµçÁ£×ÓÔÚÁ½°å¼äµÄƫת¾àÀ룻
£¨2£©Á£×ÓÉä³öµç³¡Ê±µÄËٶȣ»
£¨3£©ÈôҪʹÉä³öµç³¡µÄÁ£×Ó¾­Ä³Ò»´¹Ö±Ö½ÃæµÄÔ²ÐÎÓнçÔÈÇ¿´Å³¡Æ«×ªºó£¬¶¼ÄÜ´ÓÔ²ÐÎÓнç´Å³¡±ß½çÉϵÄͬһ¸öµãÉä³ö£¬´Ó¶øÄܱãÓÚÔÙÊÕ¼¯£¬Ôò´Å³¡ÇøÓòµÄ×îС°ë¾¶ºÍÏàÓ¦µÄ´Å¸ÐÇ¿¶ÈÊǶà´ó£¿

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ£¬½áºÏÔ˶¯Ñ§¹«Ê½Çó³öt=0ʱÉäÈëµÄ´øµçÁ£×ÓÔÚÁ½°å¼äµÄƫת¾àÀ룻
£¨2£©Á£×ÓÔÚ´ò³öÁ£×ÓµÄËٶȶ¼ÊÇÏàͬµÄ£¬ÓÉËٶȺϳɷ¨Çó½â£»
£¨3£©ÒªÊ¹Æ½ÐÐÁ£×ÓÄܹ»½»ÓÚÔ²Ðδų¡ÇøÓò±ß½çÇÒÓÐ×îСÇøÓòʱ£¬´Å³¡Ö±¾¶×îСֵÓëÁ£×Ó¿í¶ÈÏàµÈ£¬¼´¿ÉµÃµ½´Å³¡ÇøÓòµÄ×îС°ë¾¶£®Á£×Ó½øÈëÔÈÇ¿´Å³¡ÖУ¬ÓÉÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬¿ÉÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öÏàÓ¦µÄ´Å¸ÐÇ¿¶È£®

½â´ð ½â£º£¨1£©µ±Á£×ÓÓÉt=0ʱ¿Ì½øÈëµç³¡£¬ÏòÏÂƫת¾àÀëΪ£º
${s_1}=\frac{1}{2}a{£¨\frac{2T}{3}£©^2}+a£¨{\frac{2T}{3}}£©•\frac{T}{3}-\frac{1}{2}a{£¨\frac{T}{3}£©^2}$$a=\frac{{q{U_0}}}{md}$
½âµÃ£º${s_1}=\frac{{7q{U_0}{T^2}}}{18md}$
£¨2£©´ò³öÁ£×ÓµÄËٶȶ¼ÊÇÏàͬµÄ£¬ÔÚÑص糡Ïß·½ÏòËٶȴóСΪ£º${v_y}=a•\frac{T}{3}$
ËùÒÔ´ò³öËٶȴóСΪ£º$v=\sqrt{v_0^2+v_y^2}$
½âµÃ£º$v=\frac{{\sqrt{2}q{U_0}T}}{3md}$
ÉèËٶȷ½ÏòÓëv₀µÄ¼Ð½ÇΪ¦È£¬ÔòÓУº$tan¦È=\frac{{v}_{y}}{{v}_{0}}=1$£¬
½âµÃ£º¦È=45¡ã
£¨3£©µ±Á£×ÓÔÚt=nTʱ¿Ì½øÈëµç³¡£¬ÏòÏÂƫת¾àÀë×î´óΪ£º${s_1}=\frac{{7q{U_0}{T^2}}}{18md}$£¬
µ±Á£×ÓÓÉ$t=nT+\frac{2T}{3}$ʱ¿Ì½øÈëµç³¡£¬ÏòÉÏƫת¾àÀë×î´óΪ£º${s_2}=\frac{{q{U_0}{T^2}}}{18md}$£¬
ËùÒÔ£¬ÔÚ¾àÀëO¡äÖеãÏ·½$\frac{{7q{U_0}{T^2}}}{18md}$ÖÁÉÏ·½$\frac{{q{U_0}{T^2}}}{18md}$·¶Î§ÄÚÓÐÁ£×Ó´ò³ö£®
ËùÓÐÁ£×ÓÉä³öµç³¡Ê±µÄËٶȷ½Ïò±Ë´ËƽÐУ¬ÒªÊ¹Æ½ÐÐÁ£×ÓÄܹ»½»ÓÚÔ²Ðδų¡ÇøÓò±ß½çÇÒÓÐ×îСÇøÓòʱ£¬´Å³¡Ö±¾¶×îСֵÓëÁ£×Ó¿í¶ÈÏàµÈ£¬
Á£×Ó¿í¶ÈΪ£ºD=£¨s₁+s₂£©cos45¡ã
¹Ê´Å³¡ÇøÓòµÄ×îС°ë¾¶Îª£º$r=\frac{D}{2}=\frac{{\sqrt{2}q{U_0}{T^2}}}{9md}$
Á£×ÓÔڴų¡ÖÐ×÷Ô²ÖÜÔ˶¯£¬ÓУº$qvB=m\frac{v^2}{r}$
½âµÃ£º$B=\frac{3m}{qT}$£®
´ð£º£¨1£©t=0ʱÉäÈëµÄ´øµçÁ£×ÓÔÚÁ½°å¼äµÄƫת¾àÀëΪ$\frac{7q{U}_{0}{T}^{2}}{18md}$£»
£¨2£©Á£×ÓÉä³öµç³¡Ê±µÄËÙ¶ÈΪ$\frac{\sqrt{2}q{U}_{0}T}{3md}$£»
£¨3£©´Å³¡ÇøÓòµÄ×îС°ë¾¶Îª$\frac{\sqrt{2}q{U}_{0}{T}^{2}}{9md}$£¬ÏàÓ¦µÄ´Å¸ÐÇ¿¶ÈÊÇ$\frac{3m}{qT}$£®

µãÆÀ ±¾Ì⿼²éÁË´øµçÁ£×ÓÔڵ糡ºÍ´Å³¡ÖеÄÔ˶¯£¬ÕÆÎÕ´¦ÀíÀàƽÅ×Ô˶¯µÄ·½·¨£¬ÒÔ¼°ÖªµÀÁ£×Ó½øÈë´Å³¡ºó×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÔËÓü¸ºÎ֪ʶÇó³ö°ë¾¶£®