Question

17£®ÈçͼËùʾ£¬×ã¹»´óµÄÓ«¹âÆÁON´¹Ö±xOy×ø±êÃ棬ÓëxÖá¼Ð½ÇΪ30¡ã£¬µ±yÖáÓëON¼äÓÐÑØ+y·½Ïò¡¢³¡Ç¿ÎªEµÄÔÈÇ¿µç³¡Ê±£¬Ò»ÖÊÁ¿Îªm¡¢µçºÉÁ¿Îª-qµÄÀë×Ó´ÓyÖáÉϵÄPµã£¬ÒÔËÙ¶Èv₀¡¢ÑØ+xÖá·½ÏòÉäÈëµç³¡£¬Ç¡ºÃ´¹Ö±´òµ½Ó«¹âÆÁÉϵÄMµã£¨Í¼ÖÐδ±ê³ö£©£®ÏÖ³·È¥µç³¡£¬ÔÚyÖáÓëON¼ä¼ÓÉÏ´¹Ö±×ø±êÃæÏòÀïµÄÔÈÇ¿´Å³¡£¬ÏàͬµÄÀë×ÓÈÔÒÔËÙ¶Èv₀´ÓyÖáÉϵÄQµãÑØ+xÖá·½ÏòÉäÈë´Å³¡£¬Ç¡ºÃÒ²´¹Ö±´òµ½Ó«¹âÆÁÉϵÄMµã£¬Àë×ÓµÄÖØÁ¦²»¼Æ£®Çó£º
£¨1£©Àë×ÓÔڵ糡ÖÐÔ˶¯µÄʱ¼ät₁£»
£¨2£©Pµã¾àOµãµÄ¾àÀëy₁ºÍÀë×ÓÔڴų¡ÖÐÔ˶¯µÄ¼ÓËٶȴóСa£»
£¨3£©ÈôÏàͬµÄÀë×Ó·Ö±ð´ÓyÖáÉϵIJ»Í¬Î»ÖÃÒÔËÙ¶Èv=ky£¨y£¾0£¬kΪ³£Êý£©¡¢ÑØ+xÖá·½ÏòÉäÈë´Å³¡£¬Àë×Ó¶¼ÄÜ´òµ½Ó«¹âÆÁÉÏ£¬kÓ¦Âú×ãµÄÌõ¼þ£®

Answer 1

·ÖÎö £¨1£©Àë×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬Ó¦ÓÃÀàƽÅ×Ô˶¯¹æÂÉ¿ÉÒÔÇó³öÀë×ÓµÄÔ˶¯Ê±¼ä£®
£¨2£©×÷³öÀë×ÓÔ˶¯¹ì¼££¬¸ù¾Ý¼¸ºÎ֪ʶÇó³ö¾àÀ룬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö¼ÓËٶȣ®
£¨3£©×÷³öÀë×ÓÔ˶¯¹ì¼££¬Ó¦ÓÃÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öÀë×ÓµÄÁÙ½ç¹ìµÀ°ë¾¶£¬È»ºó·ÖÎö´ðÌ⣮

½â´ð ½â£º£¨1£©ÉèÀë×Ó´¹Ö±´òµ½Ó«¹âÆÁÉϵÄMµãʱ£¬
ÑØy·½ÏòµÄ·ÖËٶȴóСΪv_y£¬Ôڵ糡ÖÐÔ˶¯µÄ¼ÓËÙ¶ÈΪa₁£¬
Ôò£º${v_y}=\frac{v_0}{{tan{{30}^o}}}$£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵãºqE=ma₁£¬
ÊúÖ±·ÖËٶȣºv_y=a₁t₁£¬½âµÃ£º${t_1}=\frac{{\sqrt{3}m{v_0}}}{qE}$£»
£¨2£©Óɼ¸ºÎ¹Øϵ¿ÉÖª£º${y_1}=\frac{1}{2}{a_1}t_1^2+{v_0}{t_1}tan{30^o}$£¬
½âµÃ£º${y_1}=\frac{5mv_0^2}{2qE}$£¬
ÉèÀë×ÓÔڴų¡ÖÐ×öÔ²ÖÜÔ˶¯°ë¾¶Îªy₂£¬Ôò£º${y_2}cos{30^o}={v_0}{t_1}$£¬
¶ø£º$a=\frac{v_0^2}{y_2}$£¬½âµÃ£º$a=\frac{qE}{2m}$£»
£¨3£©ÈçͼËùʾ£¬Éè´Ó×Ý×ø±êΪy´¦ÉäÈë´Å³¡µÄÀë×Ó£¬
Ç¡ºÃÄÜ´òµ½Ó«¹âÆÁÉÏ£¬¶ÔÓ¦µÄÔ²ÖÜÔ˶¯°ë¾¶Îªr₀£¬

Ó뼸ºÎ֪ʶµÃ£º${r_0}+\frac{r_0}{{cos{{30}^o}}}=y$£¬
´ËÀë×Ó½øÈë´Å³¡Ê±µÄËÙ¶Èv=ky£¬ÉèÔ˶¯°ë¾¶Îªr£¬
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵãº$qBv=m\frac{v^2}{r}$£¬
ΪʹÀë×ÓÄÜ´òµ½Ó«¹âÆÁÉÏÓ¦Âú×㣺r¡Ýr₀£¬
ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵãºqBv₀=ma£¬
½âµÃ£º$k¡Ý\frac{{£¨2\sqrt{3}-3£©qE}}{{2m{v_0}}}$£»
´ð£º£¨1£©Àë×ÓÔڵ糡ÖÐÔ˶¯µÄʱ¼ät₁Ϊ$\frac{\sqrt{3}m{v}_{0}}{qE}$£»
£¨2£©Pµã¾àOµãµÄ¾àÀëy₁Ϊ$\frac{5m{v}_{0}^{2}}{2qE}$£¬Àë×ÓÔڴų¡ÖÐÔ˶¯µÄ¼ÓËٶȴóСaΪ$\frac{qE}{2m}$£»
£¨3£©kÓ¦Âú×ãµÄÌõ¼þÊÇ£º$k¡Ý\frac{{£¨2\sqrt{3}-3£©qE}}{{2m{v_0}}}$£®

µãÆÀ ±¾Ì⿼²éÁËÁ£×ÓÔڵ糡Óë´Å³¡ÖеÄÔ˶¯£¬·ÖÎöÇå³þÀë×ÓÔ˶¯¹ý³Ì£¬×÷³öÁ£×ÓÔ˶¯¹ì¼££¬Ó¦ÓÃÀàƽÅ×Ô˶¯¹æÂÉ¡¢Å£¶ÙµÚ¶þ¶¨Âɼ´¿ÉÕýÈ·½âÌ⣬½âÌâʱҪעÒ⼸ºÎ֪ʶµÄÓ¦Óã®