Question

5£®ÈçͼËùʾ£¬Á½¶ÔÏ໥ƽÐеļ¸ºÎÐÎ×´ÍêÈ«ÏàͬµÄÕý¶ÔƽÐнðÊô°åa¡¢bÓëc¡¢d£¬ËÄ°å´¹Ö±ÓÚÖ½Ãæ·ÅÖã¬Ëİ峤¾ùΪL£¬ÏàÁÚÁ½°å¼äµÄ¾àÀëҲΪL£¬°åºñ¶È²»¼Æ£¬aÓëb¼äÓëcÓëd¼äÓÐÏàͬ´óСµÄÔÈÇ¿µç³¡£¨ÆäËüÇøÓòÎ޵糡£©£¬°åÓÒ²àÇøÓòIºÍ×ó²àÇøÓòII ¾ùÓд¹Ö±ÓÚÖ½ÃæµÄÔÈÇ¿´Å³¡£¨Í¼ÖÐδ»­³ö£©£®ÏÖÓÐÒ»ÖÊÁ¿Îªm¡¢µçÁ¿ÎªqµÄÕýÁ£×Ó´Óa¡¢b °å¼ä×ó²àÖеãOÑؼ«°åÖÐÖáÏßÒÔ³õËÙ¶Èv½øÈëƽÐнðÊô°åa¡¢b°å¼ä£¬Ç¡ºÃ´Óa°åÓÒ²à±ßÔµ£¨²»½Ó´¥£©·É³ö½øÈë´Å³¡ÇøÓòI£¬ËæºóÇ¡ÄÜ´Ód°åÓÒ²à±ßÔµ£¨²»½Ó´¥£©½øÈëc¡¢d¼ä²¢´Ó c¡¢d¼ä×ó²àÖеãO¡äÑؼ«°åÖÐÖáÏß½øÈë´Å³¡ÇøÓò¢ò£¬È»ºó¸ÕºÃ»Øµ½a¡¢b¼«°å¼äOµã×öÖÜÆÚÐÔÔ˶¯£®²»¼ÆÁ£×ÓÖØÁ¦£¬ÊÔÇó£º
£¨1£©ÔÈÇ¿µç³¡µç³¡Ç¿¶È´óСE£»
£¨2£©ÇøÓòIIµÄ´Å³¡¸ÐӦǿ¶È´óСB£»
£¨3£©Á£×Ó´ÓO¾­O¡ä»Øµ½O×öÖÜÆÚÐÔÔ˶¯µÄÖÜÆÚ£®

Answer 1

·ÖÎö £¨1£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬½«Á£×ÓµÄÔ˶¯·Ö½â£¬¼´¿ÉÇó³öÁ£×ÓÉä³öµç³¡Ê±µÄËٶȴóС£¬È»ºó½áºÏ¶¯Äܶ¨Àí¼´¿ÉÇó³öµç³¡Ç¿¶ÈµÄ´óС£»
£¨2£©Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬»­³öÁ£×ÓÔ˶¯µÄ¹ì¼££¬ÕÒ³öÁ£×ÓÔ˶¯µÄ°ë¾¶£¬½áºÏÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬¼´¿ÉÇó³ö´Å¸ÐӦǿ¶È£»
£¨3£©Á£×ÓÔ˶¯µÄÖÜÆÚµÈÓÚÁ£×Ó·Ö±ðÔڵ糡ÖÐÓë´Å³¡ÖÐÔ˶¯Ê±¼äµÄºÍ£¬½áºÏÔ˶¯µÄ¹ì¼££¬·Ö±ðÇó³ö¸÷¶Îʱ¼ä¼´¿É£®

½â´ð ½â£º£¨1£©Á£×ÓÔڵ糡ÖÐÑؼ«°åµÄ·½Ïò×öÔÈËÙÖ±ÏßÔ˶¯£¬ÉèÁ£×ÓÔÚa¡¢b°å¼äÔ˶¯Ê±¼äΪt₁£¬t₁=$\frac{L}{v}$£»
Ñص糡Ïߵķ½Ïò£º$\frac{1}{2}L=\frac{0+{v}_{y}}{2}•{t}_{1}$
ËùÒÔ£ºv_y=v
ÖªÁ£×ÓÇ¡ºÃ´Óa¡¢b°åÓÒ²à±ßÔµ£¨²»½Ó´¥£©·É³öʱËٶȴóСΪ£º$v¡ä=\sqrt{{v}^{2}+{v}_{y}^{2}}=\sqrt{2}v$
Á£×ÓÔڵ糡ÖÐÔ˶¯£¬µç³¡Á¦×ö¹¦£¬µÃ£ºqE$\frac{1}{2}$L=$\frac{1}{2}$m£¨$\sqrt{2}$v£©²-$\frac{1}{2}$mv²
ÁªÁ¢µÃ£ºE=$\frac{m{v}^{2}}{qL}$
£¨2£©ÓÉÌâ¿ÉÖª£¬Á£×ӻص½O¡äµãµÄËÙ¶ÈΪv£¬ÔÚ¼«°å×ó²à×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÓÉͼ¿ÉÖª£¬Á£×Ó´ÓO¡ä»Øµ½O×öÔÈËÙÔ²ÖÜÔ˶¯°ë¾¶R=L£¬ËÙÂÊΪv£¬Ôò£º
qvB=$\frac{m{v}^{2}}{L}$
µÃ£ºB=$\frac{mv}{qL}$
£¨3£©»­³öÁ£×ÓÔ˶¯µÄ¹ì¼£Èçͼ£º

ÉèÁ£×ÓÔÚ°åÓÒ²àÇøÓò¢ñÔ˶¯Ê±¼äΪt₂£¬ÔÚc¡¢d°å¼äÔ˶¯Ê±¼äΪt₃£¬ÔÚ°å×ó²àÇøÓò¢òÔ˶¯Ê±¼äΪt₄£¬ÓÉÔ˶¯¶Ô³ÆÐÔÖªt₃=t₁
Á£×Ó´ÓO¾­O'»Øµ½O×öÖÜÆÚÐÔÔ˶¯µÄÖÜÆÚT=2t₁+t₂+t₄
Á£×ÓÉä³öµç³¡Ê±Ëٶȵķ½ÏòÓëˮƽ·½ÏòÖ®¼äµÄ¼Ð½Ç£º$tan¦È=\frac{{v}_{y}}{v}=\frac{v}{v}=1$
ËùÒÔ£º¦È=45¡ãËùÒÔÓÉͼÖм¸ºÎ¹Øϵ¿ÉÖª£¬Á£×ÓÔÚ¼«°åÓÒ²àÔ˶¯µÄ°ë¾¶£º${r}_{1}=\frac{\frac{3}{2}L}{cos45¡ã}$=$\frac{{3\sqrt{2}L}}{2}$
Á£×ÓÔ˶¯µÄÊÇ£ºt₂=$\frac{\frac{3}{4}¡Á2¦Ð{r}_{1}}{\sqrt{2}v}=\frac{9¦ÐL}{4v}$
Á£×ÓÔÚ¼«°åµÄ×ó²àµÄÔ˶¯¹ì¼£ÊÇ°ë¸öÔ²ÖÜ£¬ËùÒÔ£ºt₄=$\frac{1}{2}•\frac{2¦Ð{r}_{2}}{v}=\frac{¦ÐL}{v}$
Á£×Ó´ÓO¾­O'»Øµ½O×öÖÜÆÚÐÔÔ˶¯µÄÖÜÆÚT=£¨2+$\frac{13¦Ð}{4}$£©$\frac{L}{v}$
´ð£º£¨1£©ÔÈÇ¿µç³¡µç³¡Ç¿¶È´óСÊÇ$\frac{m{v}^{2}}{qL}$£»
£¨2£©ÇøÓòIIµÄ´Å³¡¸ÐӦǿ¶È´óСÊÇ$\frac{mv}{qL}$£»
£¨3£©Á£×Ó´ÓO¾­O¡ä»Øµ½O×öÖÜÆÚÐÔÔ˶¯µÄÖÜÆÚÊÇ£¨2+$\frac{13¦Ð}{4}$£©$\frac{L}{v}$£®

µãÆÀ ¸ÃÌ⿼²éÁ£×ÓÔڵ糡ÖÐÓë´Å³¡ÖеÄÔ˶¯£¬°´Õչ淶»¯µÄ²½Ö裬×ö³öÁ£×ÓÔ˶¯µÄ¹ì¼££¬½áºÏ¼¸ºÎ¹Øϵ£¬ÕÒ³öÆäÖеij¤¶È¹ØϵÓë½Ç¶È¹Øϵ£¬¼´¿ÉÕýÈ·½â´ð£®