Question

8£®ÈçͼËùʾ£¬xOyƽÃæÄÚ£¬xÖáÉÏ·½ÓÐ-y·½ÏòµÄÔÈÇ¿µç³¡£¬xÖáÏ·½Óд¹Ö±xOyƽÃæÏòÍâµÄÔÈÇ¿´Å³¡£¬µç³¡¡¢´Å³¡µÄ·¶Î§¶¼×ã¹»´ó£¬Ò»ÖÊÁ¿m¡¢µçºÉ+qµÄÁ£×Ó´ÓyÖáÉÏ×ø±êΪ£¨0£¬h£©µÄPµãÑØ+x·½ÏòÉä³ö£¬ËٶȴóСΪv₀£¬²»¼ÆÁ£×ÓµÄÖØÁ¦£¬Á£×ÓµÚÒ»´Î¹ýxÖáʱλÖÃΪQµã£¬Ëٶȷ½ÏòÓë+x·½Ïò¼Ð½ÇΪ45¡ã£®
£¨1£©Èô¹ýQµãºó£¬Á£×Ó¾­´Å³¡Ö±½Óµ½´ïÔ­µãO£¬Çóµç³¡Ç¿¶ÈEÓë´Å¸ÐӦǿ¶ÈBµÄ±ÈÖµ$\frac{E}{B}$£»
£¨2£©ÈôÁ£×ÓÔÚµç´Å³¡ÖÐÔ˶¯Ê±Äܾ­¹ýxÖáÉÏQµãÓÒ²àµÄMµã£¨Î´±ê³ö£©£¬Çó´Å¸ÐӦǿ¶ÈBÓ¦¸ÃÂú×ãµÄÌõ¼þ£»
£¨3£©ÈôÁ£×ÓÔÚµç´Å³¡ÖÐÔ˶¯Ê±Äܾ­¹ýxÖáÉÏx_N=-3hµÄNµã£¨Î´±ê³ö£©£¬Çó³öÁ£×Ó´ÓPµã³ö·¢µ½´ïNµã¿ÉÄܾ­ÀúµÄʱ¼ät£®

Answer 1

·ÖÎö £¨1£©Á£×ÓÔڵ糡ÖÐ×öÀàËÆƽÅ×Ô˶¯£¬¸ù¾Ý·ÖλÒƹ«Ê½ÁÐʽ·ÖÎö£»Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÂåÂØ×ÈÁ¦ÌṩÏòÐÄÁ¦£¬»­³ö¹ì¼££¬µÃµ½¹ìµÀ°ë¾¶£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽ£»×îºóÁªÁ¢Çó½âµÃµ½µç³¡Ç¿¶ÈEÓë´Å¸ÐӦǿ¶ÈBµÄ±ÈÖµ$\frac{E}{B}$£»
£¨2£©ÔÚµÚÒ»ÎÊ·ÖÎöµÄ»ù´¡ÉÏ£¬½«Á£×ÓÖØлص½µç³¡µÄ¹ì¼£»­³ö£¬µÃµ½Ôٴε½´ïxÖáʱÏòÓÒÒƶ¯µÄ¾àÀëÓë¹ì¼£Ô²°ë¾¶RµÄ¹Øϵ£¬¾Ý´Ë·ÖÎöµÃµ½¹ì¼£Ô²°ë¾¶µÄ·¶Î§£¬ÔÙ¸ù¾ÝÂåÂØ×ÈÁ¦µÈÓÚÏòÐÄÁ¦ÁÐʽ·ÖÎöµÃµ½´Å¸ÐӦǿ¶ÈµÄ´óС·¶Î§£»
£¨3£©µ±´Å¸ÐӦǿ¶ÈСÓÚµÚ£¨2£©ÎÊÖÐ×îСֵʱ£¬Á£×ÓÔٴνøÈë´Å³¡µÄµãµÄ×ø±ê²»¶ÏµÄÏò×óÆ«ÒÆ£»ÏȽáºÏ¼¸ºÎ¹ØϵÁÐʽ£¬ÔÙ±íʾ³öʱ¼ä£¬ÁªÁ¢Çó½â£¬×¢Òâ¶à½â£®

½â´ð ½â£º£¨1£©Á£×ӵĹ켣ÈçͼËùʾ£º

Ôڵ糡ÖУ¬¸ù¾Ý·ÖÔ˶¯¹«Ê½£¬ÓУº
ˮƽ·ÖλÒÆx=v₀t₀£¬ÊúÖ±·ÖλÒÆh=$\frac{1}{2}•\frac{qE}{m}•{t}_{0}^{2}$£¬
ˮƽ·ÖËÙ¶Èv_x=v₀£¬ÊúÖ±·ÖËÙ¶È${v}_{y}=\frac{qE}{m}•{t}_{0}$£¬ºÏËÙ¶Èv=$\sqrt{{v}_{x}^{2}+{v}_{y}^{2}}$£¬
ËÙ¶Èƫת½ÇÕýÇÐÖµtan45¡ã=$\frac{{v}_{y}}{{v}_{x}}$£¬
ÁªÁ¢½âµÃ£ºx=2h£¬v=$\sqrt{2}$v₀£»
Óɹ켣ͼºÍ¼¸ºÎ֪ʶ¿ÉÖª£º
Ôڴų¡ÖÐÔ²ÖÜÔ˶¯µÄ°ë¾¶R=$\sqrt{2}h=\frac{mv}{qB}$=$\frac{m•\sqrt{2}{v}_{0}}{qB}$£¨1£©
Ôڵ糡ÖÐ×öÀàƽÅ×Ô˶¯ÓУº${v}_{y}={v}_{0}=\frac{qE}{m}•\frac{2h}{{v}_{0}}$£¨2£©
ÓÉ£¨1£©ºÍ£¨2£©Ê½½âµÃ$\frac{E}{B}$=$\frac{{v}_{0}}{2}$
£¨2£©Á£×ӻص½´Å³¡ºó£¬×öÔÈËÙÔ²ÖÜÔ˶¯£¬¶ÔÓÚÖ±Ï߽߱磬Á£×ÓÉäÈëʱËÙ¶ÈÓë±ß½çµÄ¼Ð½ÇµÈÓÚÉä³öʱÓë±ß½çµÄ¼Ð½Ç£¬¹ÊÉäÈëËÙ¶ÈÓë+x·½Ïò³É45½Ç£¬»­³öµÚÒ»ÎÊÖÐÁ£×Ó·µ»Øµç³¡ºóµÄÔ˶¯¹ì¼££¬ÈçͼËùʾ£º

ÓÉÓÚˮƽ·ÖÔ˶¯ÊÇÔÈËÙÖ±ÏßÔ˶¯£¬ÊúÖ±·ÖÔ˶¯ÊÇÀàËÆÊúÖ±ÉÏÅ×Ô˶¯£¬½áºÏ¶Ô³ÆÐÔ¿É֪ˮƽ·ÖλÒÆΪ4h£¬¶øÔڴų¡ÖеÄÏò×óµÄλÒÆΪ$\sqrt{2}R$£¬Ö»ÒªÂú×ã4h$£¾\sqrt{2}R$£¬
¼´R$£¼2\sqrt{2}h$£¬Á£×Ӿͻá´òÔÚQµãµÄÓҲࣻ
Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯Ê±£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ£¬ÓУº
qvB=m$\frac{{v}^{2}}{R}$£¬
ÆäÖÐv=$\sqrt{2}$v₀£¬
½âµÃ£ºB£¾$\frac{m{v}_{0}}{2qh}$£»
£¨3£©µ±´Å¸ÐӦǿ¶ÈµÈÓÚ$\frac{m{v}_{0}}{2qh}$ʱ£¬¹ì¼£ÈçͼËùʾ£º

µ±´Å¸ÐӦǿ¶ÈСÓÚ$\frac{m{v}_{0}}{2qh}$ʱ£¬Á£×ÓÔÚµç´Å³¡ÖÐÖÜÆÚÐÔÔ˶¯µÄ¹ì¼£²»¶ÏµÄÏò×óƽÒÆ£¬Ò»¸öÖÜÆÚÄÚƽÒÆ$¡÷x=\sqrt{2}R-4h$£¬
¢ÙÈç¹û´Ó´Å³¡½øÈëµç³¡Ê±Í¨¹ýx_N=-3hµÄNµã£¬Ôò£º
-3h=2h-$\sqrt{2}R$-k¡÷x£¬k=0¡¢1¡¢2¡¢¡­
½âµÃ£ºB=$\frac{2£¨k+1£©m{v}_{0}}{£¨4k+5£©qh}$£¬k=0¡¢1¡¢2¡¢¡­£»
×Üʱ¼ä£ºt_×Ü=£¨k+1£©•$\frac{3}{4}$T+£¨2k+1£©t₀£¬
ÆäÖÐT=$\frac{2¦Ðm}{qB}$£¬t₀=$\frac{2h}{{v}_{0}}$£¬
½âµÃ£ºt_×Ü=$\frac{3¦Ð£¨4k+5£©h}{{4{v_0}}}+\frac{2£¨2k+1£©h}{v_0}$£¬k=0¡¢1¡¢2¡¢¡­£»
¢ÚÈç¹û´Óµç³¡½øÈë´Å³¡Ê±Í¨¹ýx_N=-3hµÄNµã£¬Ôò£º
-3h=2h-k¡÷x£¬k=0¡¢1¡¢2¡¢¡­
½âµÃ£ºB=$\frac{2km{v}_{0}}{£¨4k+5£©qh}$£¬k=0¡¢1¡¢2¡¢¡­£»
×Üʱ¼ä£ºt_×Ü=k•$\frac{3}{4}$T+£¨2k+1£©t₀£¬
ÆäÖÐT=$\frac{2¦Ðm}{qB}$£¬t₀=$\frac{2h}{{v}_{0}}$£¬
½âµÃ£ºt_×Ü=$\frac{3¦Ð£¨4k+1£©h}{{4{v_0}}}+\frac{2£¨2k+1£©h}{v_0}$£¬k=0¡¢1¡¢2¡¢¡­£»
´ð£º£¨1£©Èô¹ýQµãºó£¬Á£×Ó¾­´Å³¡Ö±½Óµ½´ïÔ­µãO£¬µç³¡Ç¿¶ÈEÓë´Å¸ÐӦǿ¶ÈBµÄ±ÈÖµ$\frac{E}{B}$Ϊ$\frac{{v}_{0}}{2}$£»
£¨2£©ÈôÁ£×ÓÔÚµç´Å³¡ÖÐÔ˶¯Ê±Äܾ­¹ýxÖáÉÏQµãÓÒ²àµÄMµã£¨Î´±ê³ö£©£¬´Å¸ÐӦǿ¶ÈBÓ¦¸ÃÂú×ãµÄÌõ¼þΪB£¾$\frac{m{v}_{0}}{2qh}$£»
£¨3£©ÈôÁ£×ÓÔÚµç´Å³¡ÖÐÔ˶¯Ê±Äܾ­¹ýxÖáÉÏx_N=-3hµÄNµã£¨Î´±ê³ö£©£¬Á£×Ó´ÓPµã³ö·¢µ½´ïNµã¿ÉÄܾ­ÀúµÄʱ¼ätΪ$\frac{3¦Ð£¨4k+5£©h}{{4{v_0}}}+\frac{2£¨2k+1£©h}{v_0}$»ò$\frac{3¦Ð£¨4k+1£©h}{{4{v_0}}}+\frac{2£¨2k+1£©h}{v_0}$£¬k=0¡¢1¡¢2¡¢¡­£®

µãÆÀ ±¾Ìâ¹Ø¼üÊÇÃ÷È·Á£×ÓÔÚµç´Å³¡ÖеÄÔ˶¯¹æÂÉ£¬Òª»­³öÔ˶¯¹ì¼££¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂɺÍÀàƽÅ×Ô˶¯¹ì¼£²¢½áºÏ¼¸ºÎ¹Øϵ·ÖÎö£¬µÚ2Îʺ͵Ú3ÎÊÊǶà½âÎÊÌ⣬ҪÔì³ÉÖÜÆÚÐÔ£¬ÄѶȽϴó£®