Question

19£®ÈçͼËùʾ£¬¿Õ¼ä´æÔÚÁ½¶ÔƽÐа壬ƽÐаå¼ä´æÔÚ´¹Ö±Ö½ÃæÏòÄÚµÄÔÈÇ¿´Å³¡£¬°å¼ä¾àd=5cm£¬MN¡¢PQΪ´Å³¡µÄ±ß½ç£¬MN¡¢PQÖ®¼ä´æÔÚˮƽÏòÓÒµÄÔÈÇ¿µç³¡£¬OO¡äΪ¸ÃÇøÓòµÄ¶Ô³ÆÖᣬMNÓëPQÖ®¼äµÄ¾àÀëL=2cm£®Á½¸öÖÊÁ¿¾ùΪm¡¢µçºÉÁ¿·Ö±ðΪ+qºÍ-qµÄÁ£×ÓÒÔÏàͬËٶȴóСv₀=2¡Á10⁵m/s´¹Ö±µç³¡Ïß½øÈëµç³¡£¬¶øºóÒÔv=2$\sqrt{2}$¡Á10⁵m/s´óСµÄËٶȽøÈë´Å³¡£¬Á£×ÓÖØÁ¦²»¼Æ£®
£¨1£©ÈôÁ½¸öÁ£×Ó¶¼´ÓOµãÑØOO¡äÖ±ÏßÈëÉ䣬ÊÔÅжÏÁ½Á£×ӵĹ켣ÊÇ·ñ¹ØÓÚOO¡äÖ±Ï߶Գƣ¿
£¨2£©Èô+qÁ£×Ó´ÓOµãÑØOO¡äÖ±ÏßÈëÉ䣬-qÁ£×ÓÓÉO¡äÑØO¡äOÖ±ÏßÈëÉ䣨δ»­³ö£©£¬ÇÒÒÑÖªÁ½Á£×ÓÔڴų¡ÖÐÔ˶¯µÄÖÜÆÚΪ$\frac{\sqrt{2}}{2}$¦Ð¡Á10^-7s£¬ÊÔÅжÏÁ½Á£×ÓÊÇ·ñ»á´òµ½°åÉÏ£¬Èô´òµ½°åÉÏ£¬Çó³ö´òÔÚ°åÉϵÄλÖã»Èô²»ÄÜ´òÔÚµ½ÉÏ£¬ÔòÇó³öÁ½Á£×Ó·Ö±ð´ÓO¡¢O¡ä½øÈëµ½µÚÒ»´ÎÀ뿪´Å³¡¸÷×ÔËùÓõÄʱ¼ä£®
£¨3£©Èô+qÁ£×ÓÈÔ´ÓOÑØOO¡äÖ±ÏßÈëÉ䣬-qÁ£×Ó´ÓO¡äÑØO¡äOÖ±ÏßÈëÉ䣬ÇÒÒÑÖªÁ½Á£×ӵıȺÉ$\frac{q}{m}$=5¡Á10⁷C/kg£¬ÈôҪʹÁ£×Ó½ø³ö´Å³¡Ò»´Îºó£¬´ÓMP»òNQÖ®¼äÀ뿪µç³¡£¬Çó´Å¸ÐӦǿ¶ÈBµÄÈ¡Öµ·¶Î§£®

Answer 1

·ÖÎö £¨1£©Á½¸öÁ£×ÓÉäÈëµç³¡ºó¶¼ÀàƽÅ×Ô˶¯£¬¸ù¾Ý³õËٶȡ¢ÊÜÁ¦Çé¿ö·ÖÎö¹ì¼£ÊÇ·ñ¶Ô³Æ£®
£¨2£©Á½¸öÁ£×ÓÏÈ×öÀàƽÅ×Ô˶¯£¬ºóÔڴų¡ÖÐ×öÔÈËÙÔ²ÖÜÔ˶¯£®Ïȸù¾ÝÀàƽÅ×Ô˶¯µÄ¹æÂÉÇó³öÔڵ糡ÖÐÔ˶¯Ê±¼äºÍÊúÖ±·ÖλÒÆ£®ÓÉT=$\frac{2¦Ðr}{v}$ÇóÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ¹ì¼£°ë¾¶£¬Óɼ¸ºÎ¹Øϵ·ÖÎöÁ£×ÓÄÜ·ñ´òÔÚ°åÉÏ£®
£¨3£©¶ÔÓÚÕýÁ£×Ó£¬Ç¡µ½QµãÁٽ磬°ë¾¶Ó¦Ð¡ÓÚ´ËÁÙ½çÖµ£®¶ÔÓÚ¸ºÁ£×Ó£¬Ç¡µ½MµãÁٽ磬°ë¾¶Ó¦Ð¡ÓÚ´ËÁÙ½çÖµ£®Óɼ¸ºÎ֪ʶºÍ°ë¾¶¹«Ê½½áºÏÇó½â£®

½â´ð ½â£º£¨1£©Õý¸ºÁ£×Ó½øÈëµç³¡Ê±³õËٶȴóСÏàµÈ¡¢·½ÏòÏà·´£®ËùÊܵĵ糡Á¦´óСÏàµÈ¡¢·½ÏòÏà·´£¬Ôò¼ÓËٶȴóСÏàµÈ¡¢·½ÏòÏà·´£¬ËùÒÔÁ½Á£×ӵĹ켣¹ØÓÚOO¡äÖ±Ï߶Գƣ®
£¨2£©Á£×ÓÔڵ糡ÖÐ×öÀàƽÅ×Ô˶¯£¬Æ½ÐÐÓڵ糡·½ÏòÓУºv_x=$\frac{\sqrt{2}}{2}$v=2¡Á10⁵m/s£¬
$\frac{{v}_{x}{t}_{0}}{2}$=$\frac{d}{2}$£¬
t₀=10^-7s
´¹Ö±Óڵ糡·½ÏòÓУºx=v₀t₀=2cm
Á£×ÓÔڴų¡ÖÐÔ˶¯ÖÜÆÚ T=$\frac{2¦Ðr}{v}$£¬Ôò¹ì¼£°ë¾¶ r=$\frac{Tv}{2¦Ð}$=1cm
ÕýÁ£×Ó£ºr+rcos45¡ã=$\frac{2+\sqrt{2}}{2}$cm£¼2cm£¬Ôò²»»á´òµ½°åÉÏ£®Ô˶¯Ê±¼ä t=t₀+$\frac{3}{4}$T=£¨1+$\frac{3\sqrt{2}¦Ð}{8}$£©¡Á10^-7s
¸ºÁ£×Ó£ºx+2rcos45¡ã=4cm£¼5cm£¬²»»á´òµ½°åÉÏ£¬Ô˶¯Ê±¼ä t¡ä=t₀+$\frac{1}{4}$T=£¨1+$\frac{\sqrt{2}¦Ð}{8}$£©¡Á10^-7s
£¨2£©ÕýÁ£×Ó£ºÇ¡µ½QµãÁٽ磬°ë¾¶Ó¦Ð¡ÓÚ´ËÁÙ½çÖµ£¬¶ÔÓ¦µÄ´Å¸ÐӦǿ¶ÈÉèΪB₁£®
¿ÉµÃÏÒ³¤Îª $\sqrt{2}{r}_{1}$=4-3=1cm
¹ì¼£°ë¾¶ r₁=$\frac{\sqrt{2}}{2}$cm
ÓÉr=$\frac{mv}{qB}$£¬µÃ B=$\frac{mv}{qr}$
½«r₁´úÈëµÃ B₁=0.8T
´Ëʱr₁ÒÑСÓÚµÚ£¨2£©ÎÊÖеÄr£¬¹Ê´ËʱµÄ´Å¸ÐӦǿ¶È±ÈB₁´ó£®
¸ºÁ£×Ó£ºÇ¡µ½MµãÁٽ磬°ë¾¶Ó¦Ð¡ÓÚ´ËÁÙ½çÖµ£¬¶ÔÓ¦µÄ´Å¸ÐӦǿ¶ÈÉèΪB₂£®
¿ÉµÃÏÒ³¤Îª $\sqrt{2}{r}_{2}$=5-2=3cm
¹ì¼£°ë¾¶ r₂=$\frac{3\sqrt{2}}{2}$cm
´Ëʱr₂£¾r₁£¬¶ÔÓ¦µÄB₂£¼B₁£®
×ۺϷÖÎöµÃ£º´Å¸ÐӦǿ¶ÈÖ»Òª´óÓÚB₁£¬ÕýÁ£×ӼȲ»»áÔٴνøÈë´Å³¡Ò²²»»á´òµ½°åÉÏ£¬¸ºÁ£×ÓÒ²²»»á´òµ½°åÉÏ£¬¼´ B£¾0.8T£®
´ð£º
£¨1£©Á½Á£×ӵĹ켣¹ØÓÚOO¡äÖ±Ï߶Գƣ®
£¨2£©ÕýÁ£×Ó²»»á´òµ½°åÉÏ£®Ô˶¯Ê±¼äΪ£¨1+$\frac{3\sqrt{2}¦Ð}{8}$£©¡Á10^-7s
¸ºÁ£×Ó²»»á´òµ½°åÉÏ£¬Ô˶¯Ê±¼äΪ£¨1+$\frac{\sqrt{2}¦Ð}{8}$£©¡Á10^-7s£®
£¨3£©´Å¸ÐӦǿ¶ÈBµÄÈ¡Öµ·¶Î§ÊÇB£¾0.8T£®

µãÆÀ Á£×ÓÔÚÂåÂ××ÈÁ¦×÷ÓÃÏÂ×öÔÈËÙÔ²ÖÜÔ˶¯£¬Ôڵ糡Á¦×÷ÓÃÏÂ×öÀàƽÅ×Ô˶¯£¬ÕÆÎÕÁ½ÖÖÔ˶¯µÄ´¦Àí¹æÂÉ£¬Ñ§»áÔ˶¯µÄ·Ö½âÓ뼸ºÎ¹ØϵµÄÓ¦Óã®