Question

1£®ÈçͼËùʾ£¬Æ½ÐаåµçÈÝÆ÷°å³¤ºÍ°å¾à¾ùΪ2L£¬µçÈÝÆ÷ÓÒ²à´æÔÚÓÐÊúÖ±±ß½çÇÒ´¹Ö±Ö½ÃæµÄÁ½¸öÓнçµÄÔÈÇ¿´Å³¡£¬´¹Ö±Ö½ÃæÏòÍâµÄΪÔÈÇ¿´Å³¡I£¬´¹Ö±Ö½ÃæÏòÀïµÄΪÔÈÇ¿´Å³¡¢ò£¬OQÁ¬ÏßµÄÑÓ³¤Ïßµ½Á½¼«°å¾àÀëÏàµÈ£¬ÆäÖÐ0M=MP=L£®Ò»ÖÊÁ¿Îªm¡¢´øµçºÉÁ¿Îª-qµÄ´øµçÁ£×Ó´ÓÉϼ«°å±ßÔµ´¦ÒÔËÙ¶Èv₀ÑØˮƽ·½ÏòÉäÈ룬ǡºÃ¾­¹ýO´¦ÉäÈëÇøÓò¢ñ£¬ÓÖ´ÓMµãÉä³öÇøÓò¢ñ£¨Á£×ÓµÄÖØÁ¦²»¼Æ£©£®
£¨1£©ÇóÁ½¼«°å¼äÔÈÇ¿µç³¡³¡Ç¿EµÄ´óС£»
£¨2£©ÇóÇø³Ç¢ñÄÚÔÈÇ¿´Å³¡´Å¸ÐӦǿ¶ÈBµÄ´óС£»
£¨3£©Èô´øµçÁ£×ÓÄÜÔٴλص½Ô­µãO£¬ÎÊÇøÓò¢òÄڴų¡µÄ¿í¶ÈdÖÁÉÙΪ¶àÉÙ£¿Á£×ÓÁ½´Î¾­¹ýÔ­µãOµÄʱ¼ä¼ä¸ôΪ¶àÉÙ£¿

Answer 1

·ÖÎö £¨1£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬Ó¦ÓÃÀàƽÅ×Ô˶¯¹æÂÉ¿ÉÒÔÇó³öµç³¡Ç¿¶È£®
£¨2£©Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÒÔÇó³ö´Å¸ÐӦǿ¶È´óС£®
£¨3£©Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬×÷³öÁ£×ÓÔ˶¯¹ì¼££¬Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö´Å³¡µÄ¿í¶È£¬¸ù¾ÝÁ£×ÓÔڴų¡ÖÐ×öÔ²ÖÜÔ˶¯µÄÖÜÆÚ£¬È»ºó¸ù¾ÝÁ£×ÓÔ˶¯¹ý³ÌÇó³öÁ£×ÓµÄÔ˶¯Ê±¼ä£®

½â´ð ½â£º£¨1£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬
ˮƽ·½Ïò£º2L=v₀t£¬
ÊúÖ±·½Ïò£ºL=$\frac{1}{2}$at²=$\frac{1}{2}$$\frac{qE}{m}$t²£¬
½âµÃ£ºE=$\frac{m{v}_{0}^{2}}{2qL}$£»
£¨2£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬
ˮƽ·½Ïò£º2L=v₀t£¬
À뿪µç³¡Ê±£ºv_y=at=$\frac{qE}{m}$t=v₀£¬
Á£×ÓÀ뿪µç³¡Ê±£ºv=$\sqrt{{v}_{0}^{2}+{v}_{y}^{2}}$=$\sqrt{2}$v₀£¬·½Ïò£ºÓëˮƽ·½Ïò³É45¡ã½Ç£¬
Á£×ÓÔڴų¡¢ñÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬Á£×ÓÔ˶¯¹ì¼£ÈçͼËùʾ£º

Óɼ¸ºÎ֪ʶ¿ÉÖª£ºL²=r²+r²£¬Á£×Ó¹ìµÀ°ë¾¶£ºr=$\frac{\sqrt{2}}{2}$L£¬
Á£×ÓÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵãºqvB=m$\frac{{v}^{2}}{r}$£¬
½âµÃ£ºB=$\frac{2m{v}_{0}}{qL}$£»
£¨3£©¢ÙÁ£×ÓÀ뿪´Å³¡¢ñºó×öÔÈËÙÖ±ÏßÔ˶¯£¬È»ºó½øÈë´Å³¡¢ò×öÔÈËÙÔ²ÖÜÔ˶¯£¬
´øµçÁ£×ÓÄÜÔٴλص½Ô­µãO£¬Á£×ÓÔ˶¯¹ì¼£ÈçͼËùʾ£º

Óɼ¸ºÎ֪ʶµÃ£ºR=$\frac{L}{sin45¡ã}$=$\sqrt{2}$L£¬
´Å³¡¢òµÄ×îС¿í¶ÈΪd£¬Ôò£ºd=R+Rsin45¡ã£¬
½âµÃ£ºd=£¨1+$\sqrt{2}$£©L£»
¢ÚÁ£×ÓÔڴų¡¢ñÖÐ×öÔ²ÖÜÔ˶¯×ª¹ýµÄÔ²ÐĽǣº¦Á=90¡ã£¬
Á£×ÓÔڴų¡¢òÖÐ×öÔ²ÖÜÔ˶¯×ª¹ýµÄÔ²ÐĽǣº¦Â=270¡ã£¬
Á£×ÓÔڴų¡¢ñÖÐ×öÔ²ÖÜÔ˶¯µÄÖÜÆÚ£ºT₁=$\frac{2¦Ðr}{v}$=$\frac{¦ÐL}{{v}_{0}}$£¬
Á£×ÓÔڴų¡¢òÖÐ×öÔ²ÖÜÔ˶¯µÄÖÜÆÚ£ºT₂=$\frac{2¦ÐR}{v}$=$\frac{2¦ÐL}{{v}_{0}}$£¬
Á£×ÓÔÚÁ½´Å³¡¼ä×öÔÈËÙÖ±ÏßÔ˶¯£¬À뿪¢ñ½øÈë¢ò¹ý³ÌµÄÔ˶¯Ê±¼ä£ºt¡ä=$\frac{s}{v}$=$\frac{\frac{L}{sin45¡ã}}{\sqrt{2}{v}_{0}}$=$\frac{L}{{v}_{0}}$£¬
Á£×ÓÁ½´Î¾­¹ýÔ­µãOµÄʱ¼ä¼ä¸ôΪ£ºt=2t₁+2t¡ä+t₂=2¡Á$\frac{¦Á}{360¡ã}$T₁+2t¡ä+$\frac{¦Â}{360¡ã}$T₂=$\frac{2¦ÐL+2L}{{v}_{0}}$£»
´ð£º£¨1£©Á½¼«°å¼äÔÈÇ¿µç³¡³¡Ç¿EµÄ´óСΪ$\frac{m{v}_{0}^{2}}{2qL}$£»
£¨2£©Çø³Ç¢ñÄÚÔÈÇ¿´Å³¡´Å¸ÐӦǿ¶ÈBµÄ´óСΪ$\frac{2m{v}_{0}}{qL}$£»
£¨3£©Èô´øµçÁ£×ÓÄÜÔٴλص½Ô­µãO£¬ÇøÓò¢òÄڴų¡µÄ¿í¶ÈdÖÁÉÙΪ£¨1+$\sqrt{2}$£©L£¬Á£×ÓÁ½´Î¾­¹ýÔ­µãOµÄʱ¼ä¼ä¸ôΪ$\frac{2¦ÐL+2L}{{v}_{0}}$£®

µãÆÀ ±¾Ì⿼²éÁËÁ£×ÓÔڵ糡Óë´Å³¡ÖеÄÔ˶¯£¬·ÖÎöÇå³þÁ£×ÓÔ˶¯¹ý³Ì¡¢×÷³öÁ£×ÓÔ˶¯¹ì¼£ÊǽâÌâµÄ¹Ø¼ü£¬Ó¦ÓÃÀàƽÅ×Ô˶¯¹æÂÉ¡¢Å£¶ÙµÚ¶þ¶¨ÂÉ¡¢Á£×ÓÔڴų¡×ö×öÔ²ÖÜÔ˶¯µÄÖÜÆÚ¹«Ê½¿ÉÒÔ½âÌ⣮