Question

7£®ÈçͼËùʾ£¬ABΪ¹â»¬Ë®Æ½×ÀÃ棬ÔÚABÓҶ˹̶¨ÊúֱƽÃæÄڰ뾶ΪR=1mµÄ°ëÔ²´Ö²ÚÔ²»¡¹ìµÀBQC£¬QµãÓëÔ²ÐÄOµÈ¸ß£®ÔÚˮƽ×ÀÃæÉÏ·ÅÒ»¿é³¤ÎªL=1mµÄľ°å£¬ÆäÖÊÁ¿ÎªM=2kg£¬Ä¾°åÓÒ¶ËÉϱíÃæÓëÔ²»¡¹ìµÀÏàÇÐÓÚBµã£®ÖÊÁ¿Îªm=1kgµÄ´øÕýµçСÎï¿é£¨¿ÉÊÓΪÖʵ㣩£¬µçÁ¿Îªq=10^-4C£®ÒÔ³õËÙ¶Èv₀=2m/s´Ó×ó¶Ë»¬ÉÏľ°å£®Õû¸ö¿Õ¼ä¼ÓÒ»µç³¡Ç¿¶ÈE=10⁵N/C£¬·½ÏòÓëˮƽ·½Ïò³É37¡ãбÏòϵÄÔÈÇ¿µç³¡£®Ð¡Îï¿éÓëľ°åÖ®¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì=0.25£¬ÉèСÎï¿éÓëľ°å¼äµÄ×î´ó¾²Ä¦²ÁÁ¦µÈÓÚ»¬¶¯Ä¦²ÁÁ¦£®ÖØÁ¦¼ÓËÙ¶Èg=10m/s²£®sin37¡ã=0.6£¬cos37¡ã=0.8£®Çó£º
£¨1£©ÇóСÎï¿éÔÚľ°åÉÏÏòÓÒ»¬ÐеļÓËٶȴóС£»
£¨2£©Ð¡Îï¿éµÚÒ»´Îµ½´ïBµãʱ£¬¶ÔÔ²»¡¹ìµÀBµãµÄѹÁ¦£®
£¨3£©Ð¡Îï¿é´Ó×ó¶Ë»¬ÉÏľ¿é¿ªÊ¼µ½µÚÒ»´Î·µ»Øµ½B£¬ÔÙ»¬ÉÏľ¿éÏò×óÔ˶¯£¬ÔÚ¾àÀëľ°åÓÒ¶Ë0.2m´¦¾ßÓÐÏàͬµÄËٶȣ¬ÔòСÎï¿éÔÚ´Ö²ÚÔ²»¡¹ìµÀÉÏÔ˶¯¿Ë·þĦ²ÁÁ¦×öµÄ¹¦ÊǶàÉÙ£®

Answer 1

·ÖÎö £¨1£©½«µç³¡Á¦·Ö½â³Éˮƽ·½ÏòÓëÊúÖ±·½Ïò£¬ÔÙ¸ù¾Ý»¬¶¯Ä¦²ÁÁ¦£¬À´È·¶¨×î´ó¾²Ä¦²ÁÁ¦£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉ¿ÉÇóµÃ¼ÓËٶȣ»
£¨2£©¸ù¾ÝÔ˶¯Ñ§¹«Ê½¿ÉÇóµÃÎïÌåBµãµÄËٶȣ»ÔÙÓÉÏòÐÄÁ¦¹«Ê½¿ÉÇóµÃ×÷ÓÃÁ¦£»
£¨3£©Ð¡Îï¿é´ÓBµã»¬ÉÏÔ²»¡¹ìµÀºóÔÙ·µ»ØBµã¹ý³Ì£¬ÔËÓö¯Äܶ¨Àí£¬ÔÙ¸ù¾ÝÔ˶¯Ñ§¹«Ê½£¬ÇóµÃÓëÏà¶ÔλÒƵĹØϵ£¬´Ó¶øÇóµÃ¿Ë·þĦ²ÁÁ¦×öµÄ¹¦£®

½â´ð ½â£º£¨1£©Ð¡ÎïÌåÊÜÖØÁ¦¡¢µç³¡Á¦¡¢Ö§³ÖÁ¦¼°Ä¦²ÁÁ¦µÄ×÷Óã»
µç³¡Á¦ÔÚˮƽ·½ÏòµÄ·ÖÁ¦Îª£ºqEcos37¡ã=10^-4¡Á10⁵¡Á0.8=8N
µç³¡Á¦ÔÚÊúÖ±·½ÏòµÄ·ÖÁ¦Îª£ºqEsin37¡ã=10^-4¡Á10⁵¡Á0.6=6N
СÎï¿éÓëľ°å¼äµÄ×î´ó¾²Ä¦²ÁÁ¦Îª£ºf_m=¦Ì£¨mg+qEsin37¡ã£©=0.25¡Á£¨1¡Á10+6£©=4N
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɿɵãº
qEcos37¡ã-f_m=ma
½âµÃ£ºa=$\frac{8-4}{1}$=4m/s²£»
£¨2£©ÓÉv²-v₀²=2ax¿ÉµÃ£º
v=2$\sqrt{3}$m/s£»
ÓÉÏòÐÄÁ¦¹«Ê½¿ÉµÃ£ºF-mg=m$\frac{{v}^{2}}{r}$
½âµÃ£ºF=22N£»
£¨3£©Ð¡Îï¿é´ÓBµã»¬ÉÏÔ²»¡¹ìµÀºóÔÙ·µ»ØBµã¹ý³Ì£¬Éè·µ»ØËÙ¶ÈΪv£¬Óɶ¯Äܶ¨ÀíÓУº
-W_f=$\frac{1}{2}m{v}^{2}-\frac{1}{2}m{v}_{0}^{2}$
СÎï¿é¼õËÙ£¬¼ÓËٶȴóСΪ£ºa₁=$\frac{{f}_{m}}{m}$=¦Ìg=2.5m/s²£»
ľ°å¼ÓËÙ£¬¼ÓËٶȴóСΪ£ºa₂=$\frac{{f}_{m}}{m}$=¦Ìg=2.5m/s²
´ÓСÎï¿é»¬ÉÏľ°åµ½Ïà¶Ô¾²Ö¹£¬ËùÓÃʱ¼äΪt£¬ÓУº
v-a₁t=a₂t
£¨vt-$\frac{1}{2}$a₁t²£©-$\frac{1}{2}{a}_{2}{t}^{2}$=l
½âµÃ£ºW_f=2.5J
´ð£º£¨1£©Ð¡Îï¿éµÄ¼ÓËÙ¶ÈΪ4m/s²£»
£¨2£©BµãµÄѹÁ¦Îª22N£»
£¨3£©Ð¡Îï¿éÔÚÔ²»¡¹ìµÀÉÏÔ˶¯¹ý³ÌÖп˷þĦ²ÁÁ¦×öµÄ¹¦2.5J£®

µãÆÀ ±¾Ìâ×ۺϿ¼²éÁ˶¯Äܶ¨Àí¡¢Å£¶ÙµÚ¶þ¶¨ÂÉ¡¢Ô˶¯Ñ§¹«Ê½µÈ֪ʶ£¬×ÛºÏÐÔ½ÏÇ¿£¬¹Ø¼üÀíÇåÎï¿éµÄÔ˶¯¹ý³Ì£¬Ñ¡ÔñºÏÊʵĹæÂɽøÐÐÇó½â£®×¢Ò⻹¿ÉÒÔÓÃl=$\frac{v}{2}t$ÇóµÃÏà¶ÔλÒÆ£®