Question

16£®Èçͼ¼×Ëùʾ£¬´óÁ¿µç×ÓÓɾ²Ö¹¿ªÊ¼£¬¾­¼ÓËٵ糡¼ÓËÙºó£¬Á¬Ðø²»¶ÏµØÑØˮƽ·½Ïò´Óƫתµç³¡µÄÏà¾àΪdµÄÁ½°åÕýÖмäOO¡äÉäÈëƫתµç³¡£®µ±Æ«×ªµç³¡µÄÁ½°å²»´øµçʱ£¬ÕâЩµç×Óͨ¹ýÁ½°åÖ®¼äµÄʱ¼äΪ2t₀£»µ±ÔÚÁ½°åÉϼÓÈçͼÒÒËùʾµÄµçѹʱ£¨U₀ΪÒÑÖª£©£¬ËùÓеç×Ó¾ùÄÜ´ÓÁ½°å¼äͨ¹ý£¬È»ºó½øÈë´¹Ö±Ö½ÃæÏòÁ¿¡¢´Å³¡Ó¦Ç¿¶ÈΪBµÄÔÈÇ¿´Å³¡ÖУ¬×îºó¶¼´¹Ö±´òÔÚÊúÖ±·ÅÖõÄÓ«¹âÆÁÉÏ£®ÒÑÖªµç×ÓµÄÖÊÁ¿Îªm¡¢µçºÉÁ¿Îªe£¬ÆäÖØÁ¦²»¼Æ£®Çó£º

£¨1£©´Ó$\frac{{t}_{0}}{2}$ʱ¿Ì½øÈëƫתµç³¡µÄµç×ÓÀ뿪ƫתµç³¡Ê±µÄλÖõ½OO¡äµÄ¾àÀ룻
£¨2£©Æ«×ª´Å³¡ÇøÓòµÄˮƽ¿í¶ÈL£»
£¨3£©Æ«×ª´Å³¡ÇøÓòµÄ×îСÃæ»ýS£®

Answer 1

·ÖÎö £¨1£©µç×ÓÔÚƫתµç³¡ÖÐ×öÀàƽÅ×Ô˶¯ÓëÔÈËÙÖ±ÏßÔ˶¯£¬Ó¦ÓÃÀàƽÅ×Ô˶¯¹æÂÉ¡¢ÔÈËÙÖ±ÏßÔ˶¯¹æÂÉÇó³öÆ«ÒÆÁ¿£®
£¨2£©µç×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬µç×Ó´¹Ö±´òÔÚÓ«¹âÆÁÉÏ£¬¸ù¾ÝËٶȵĺϳÉÓë·Ö½â¡¢¼¸ºÎ֪ʶÇó³ö´Å³¡µÄ¿í¶È£®
£¨3£©Çó³öµç×ÓÀ뿪ƫתµç³¡Ê±µÄ×î´óÓë×îСƫÒÆÁ¿£¬È»ºóÇó³ö´Å³¡µÄ×îСÃæ»ý£®

½â´ð ½â£º£¨1£©µç×ÓÔÚƫתµç³¡ÖеļÓËٶȣºa=$\frac{eE}{m}$=$\frac{e{U}_{0}}{md}$£¬
µç×ÓµÄÆ«ÒÆÁ¿£ºy=$\frac{1}{2}$at₀²+a¡Á$\frac{{t}_{0}}{2}$¡Át₀£¬
½âµÃ£¬µç×ÓÀ뿪ƫתµç³¡Ê±µÄλÖõ½OO¡äµÄ¾àÀ룺y=$\frac{e{U}_{0}{t}_{0}^{2}}{md}$£»
£¨2£©µç×ÓÀ뿪ƫתµç³¡Ê±µÄËÙ¶ÈÆ«½ÇΪ¦È£¬µç×Ó´¹Ö±´òÔÚÓ«¹âÆÁÉÏ£¬µç×ÓÔڴų¡ÖеĹìµÀ°ë¾¶£ºR=$\frac{L}{sin¦È}$£¬
µç×ÓÀ뿪ƫתµç³¡Ê±µÄËÙ¶ÈΪv£¬´¹Ö±ÓÚƫת¼«°åµÄ·ÖËÙ¶ÈΪv_y£¬
µç×ÓÀ뿪ƫתµç³¡Ê±£ºsin¦È=$\frac{{v}_{y}}{v}$£¬v_y=$\frac{e{U}_{0}{t}_{0}}{md}$£¬ÒÑÖª£ºR=$\frac{mv}{eB}$£¬
½âµÃ£ºL=$\frac{{U}_{0}{t}_{0}}{dB}$£»
£¨3£©ÓÉÌâÒâ¿ÉÖª£¬´Ót₀¡¢3t₀¡¢¡­µÈʱ¿Ì½øÈëƫתµç³¡µÄµç×ÓÀ뿪ƫתµç³¡Ê±µÄλÖõ½OO¡ä¾àÀë×îС£¬
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãºa=$\frac{eE}{m}$=$\frac{e{U}_{0}}{md}$£¬y_min=$\frac{1}{2}$at₀²£¬
½âµÃ£ºy_min=$\frac{e{U}_{0}{t}_{0}^{2}}{2md}$£¬
´Ó0¡¢2t₀¡¢4t₀¡¢¡­µÈʱ¿Ì½øÈëƫתµç³¡µÄµç×ÓÀ뿪ƫתµç³¡Ê±µÄλÖõ½OO¡ä¾àÀë×î´ó£¬
y_max¡ä=v_yt₀+$\frac{1}{2}$at₀²£¬v_y=at₀£¬
½âµÃ£ºy_max¡ä=$\frac{3e{U}_{0}{t}_{0}^{2}}{2md}$£¬
ÓÉÓÚ¸÷¸öʱ¿Ì´Óƫתµç³¡ÖÐÉä³öµÄµç×ÓµÄËٶȴóСÏàµÈ£¬·½ÏòÏàͬ£¬Òò´Ëµç×Ó½øÈë´Å³¡ºó×öÔ²ÖÜÔ˶¯µÄ¹ìµÀ°ë¾¶Ïàͬ£¬¶¼ÄÜ´¹Ö±´òÔÚÓ«¹âÆÁÉÏ£¬µç×ÓÀ뿪ƫתµç³¡Ê±µÄλÖõ½OO¡äµÄ×î´ó¾àÀëÓë×îС¾àÀëµÄ²îֵΪ£º
¡÷y₁=y_max-y_min=$\frac{e{U}_{0}{t}_{0}^{2}}{md}$£¬
´¹Ö±´òÔÚÓ«¹âÆÁÉϵĵç×ÓÊøµÄ¿í¶È£º¡÷y=¡÷y₁=$\frac{e{U}_{0}{t}_{0}^{2}}{md}$£¬
ÔÈÇ¿´Å³¡µÄ×îСÃæ»ý£ºS=¡÷y¡ÁL=$\frac{e{U}_{0}^{2}{t}_{0}^{2}}{mB{d}^{2}}$£»
´ð£º£¨1£©´Ó$\frac{{t}_{0}}{2}$ʱ¿Ì½øÈëƫתµç³¡µÄµç×ÓÀ뿪ƫתµç³¡Ê±µÄλÖõ½OO¡äµÄ¾àÀëΪ$\frac{e{U}_{0}{t}_{0}^{2}}{md}$£»
£¨2£©Æ«×ª´Å³¡ÇøÓòµÄˮƽ¿í¶ÈLΪ$\frac{{U}_{0}{t}_{0}}{dB}$£»
£¨3£©Æ«×ª´Å³¡ÇøÓòµÄ×îСÃæ»ýSΪ$\frac{e{U}_{0}^{2}{t}_{0}^{2}}{mB{d}^{2}}$£®

µãÆÀ ±¾Ì⿼²éÁ˵ç×ÓÔڵ糡¡¢´Å³¡ÖеÄÔ˶¯£¬µç×ÓÔÚƫתµç³¡ÖÐƫת¡¢ÔÚÔÈÇ¿´Å³¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬·ÖÎöÇå³þµç×ÓµÄÔ˶¯¹ý³ÌÊÇÕýÈ·½âÌâµÄ¹Ø¼ü£¬Ó¦ÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄÔ˶¯¹æÂÉ¿ÉÒÔ½âÌ⣮