Question

1£®ÈçͼËùʾΪʾ²¨¹Ü¹¤×÷Ô­ÀíµÄʾÒâͼ£¬µÆË¿ÉÏ·¢³öµÄµç×Ó£¨³õËÙΪ0£¬ÖÊÁ¿Îªm£¬µçºÉÁ¿Îªe£©¾­¼ÓËٵ糡U₁¼ÓËÙºóÑØ°åÖÐÑë½øÈëƫתµç³¡£¬Æ«×ªµç³¡Á½¼«°å³¤ÎªL£¬¼ä¾àΪd£¬Æ«×ªµçѹΪU₂£®Çó£º
£¨1£©µç×Ó½øÈëƫתµç³¡Ê±µÄËÙ¶Èv₀
£¨2£©Èôµç×ÓÄÜ´Óƫתµç³¡Éä³ö£¬µç×ÓÉä³öʱµÄ²àÒÆÁ¿ºÍƫת½Ç£®
£¨3£©Èôµç×Ó²»ÄÜ´Óƫתµç³¡Éä³ö£¬µç×Ó´òµ½¼«°åÉϵÄËٶȴóСv£®
£¨4£©ÎªÁËÌá¸ßʾ²¨¹ÜµÄÁéÃô¶È£¨Ã¿µ¥Î»µçѹÒýÆðµÄƫתÁ¿h/U₂£©¿ÉÒÔ²ÉÓÃʲô´ëÊ©£¿

Answer 1

·ÖÎö £¨1£©µç×ÓÔÚ¼ÓËٵ糡ÖмÓËÙ£¬Ó¦Óö¯Äܶ¨Àí¿ÉÒÔÇó³öµç×ÓµÄËٶȣ®
£¨2£©µç×ÓÔÚƫתµç³¡ÖÐ×öÀàƽÅ×Ô˶¯£¬Ó¦ÓÃÀàƽÅ×Ô˶¯¹æÂÉÇó³öµç×ÓµÄÆ«ÒÆÁ¿Óëƫת½Ç£®
£¨3£©µç×ÓÔÚƫתµç³¡ÖÐ×öÀàƽÅ×Ô˶¯£¬Ó¦Óö¯Äܶ¨ÀíÇó³öµç×ÓµÄËٶȣ®
£¨4£©µç×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬Ó¦ÓÃÀàƽÅ×Ô˶¯Çó³öÁéÃô¶È±í´ïʽ£¬È»ºó·ÖÎö´ðÌ⣮

½â´ð ½â£º£¨1£©ÔÚ¼ÓËٵ糡ÖУ¬Óɶ¯Äܶ¨ÀíµÃ£ºeU₁=$\frac{1}{2}$mv₀²-0£¬
½âµÃ£ºv₀=$\sqrt{\frac{2e{U}_{1}}{m}}$£»
£¨2£©µç×ÓÔÚƫתµç³¡ÖÐ×öÀàƽÅ×Ô˶¯£¬µç×ÓµÄÔ˶¯Ê±¼ä£ºt=$\frac{L}{{v}_{0}}$£¬
µç×ÓµÄÆ«ÒÆÁ¿£ºy=$\frac{1}{2}$at²=$\frac{1}{2}$$\frac{e{U}_{2}}{md}$$£¨\frac{L}{{v}_{0}}£©^{2}$=$\frac{{U}_{2}{L}^{2}}{4{U}_{1}d}$£¬
µç×Óƫת½Ç£ºtan¦Á=$\frac{{v}_{y}}{{v}_{0}}$=$\frac{at}{{v}_{0}}$=$\frac{\frac{e{U}_{2}}{md}¡Á\frac{L}{{v}_{0}}}{{v}_{0}}$=$\frac{e{U}_{2}L}{md{v}_{0}^{2}}$=$\frac{{U}_{2}L}{2{U}_{1}d}$£»
£¨3£©µç×ÓÓɼ«°åÖÐÑëÉäÈ룬×îÖÕ´òÔÚ¼«°åÉÏ£¬Óɶ¯Äܶ¨ÀíµÃ£º
e$\frac{{U}_{2}}{2}$=$\frac{1}{2}$mv²-$\frac{1}{2}$mv₀²£¬
½âµÃµç×ÓËٶȣºv=$\sqrt{\frac{e£¨2{U}_{1}+{U}_{2}£©}{m}}$£»
£¨4£©µç×ÓµÄÆ«ÒÆÁ¿£ºy=$\frac{{U}_{2}{L}^{2}}{4{U}_{1}d}$£¬
µç×ӹܵÄÁéÃô¶È£º$\frac{h}{{U}_{2}}$=$\frac{{L}^{2}}{4{U}_{1}d}$£¬
ÒªÌá¸ßµç×ӹܵÄÁéÃô¶È£¬¿ÉÒÔÔö¼ÓL¡¢»ò¼õСU₁¡¢»ò¼õСd£®
´ð£º£¨1£©µç×Ó½øÈëƫתµç³¡Ê±µÄËÙ¶Èv₀Ϊ$\sqrt{\frac{2e{U}_{1}}{m}}$£»
£¨2£©Èôµç×ÓÄÜ´Óƫתµç³¡Éä³ö£¬µç×ÓÉä³öʱµÄ²àÒÆÁ¿Îª£º$\frac{{U}_{2}{L}^{2}}{4{U}_{1}d}$£¬Æ«×ª½ÇΪ£ºarctan$\frac{{U}_{2}L}{2{U}_{1}d}$£®
£¨3£©Èôµç×Ó²»ÄÜ´Óƫתµç³¡Éä³ö£¬µç×Ó´òµ½¼«°åÉϵÄËٶȴóСvΪ$\sqrt{\frac{e£¨2{U}_{1}+{U}_{2}£©}{m}}$£®
£¨4£©ÎªÁËÌá¸ßʾ²¨¹ÜµÄÁéÃô¶È¿ÉÒÔ²ÉÓõĴëÊ©ÓУºÔö¼ÓL¡¢»ò¼õСU₁¡¢»ò¼õСd£®

µãÆÀ ±¾Ì⿼²éÁ˵ç×ÓÔÚ¼ÓËٵ糡Óëƫתµç³¡ÖеÄÔ˶¯£¬ÊìÁ·ÕÆÎÕÀàƽÅ×֪ʶ¡¢¶¯Äܶ¨Àí¿ÉÒÔ½âÌ⣬±¾ÌâÎÊÌâËäÈ»½Ï¶à£¬µ«ÄѶȲ»´ó£¬ÊÇÒ»µÀÖеµÌ⣮