Question

8£®Èçͼ1£¬×°ÖÃBOO¡ä¿ÉÈÆÊúÖ±ÖáOO¡äת¶¯£¬¿ÉÊÓΪÖʵãµÄСÇòAÓëÁ½Ï¸ÏßÁ¬½Óºó·Ö±ðϵÓÚB¡¢CÁ½µã£¬×°Öþ²Ö¹Ê±Ï¸ÏßABˮƽ£¬Ï¸ÏßACÓëÊúÖ±·½ÏòµÄ¼Ð½Ç¦È=37¡ã£®ÒÑ֪СÇòµÄÖÊÁ¿m=1kg£¬Ï¸ÏßAC³¤L=1m£¬Bµã¾àתÖáµÄˮƽ¾àÀëºÍ¾àCµãµÄÊúÖ±¾àÀëÏàµÈ£®£¨gÈ¡10m/s²£¬sin37¡ã=0.6£¬cos37¡ã=0.8£©
£¨1£©Èô×°ÖÃÔÈËÙת¶¯µÄ½ÇËÙ¶ÈΪ¦Ø₁ʱ£¬Ï¸ÏßABˮƽÀ­Ö±ÇÒÕÅÁ¦Îª0£¬Çó½ÇËٶȦØ₁µÄ´óС£»
£¨2£©Èô×°ÖÃÔÈËÙת¶¯µÄ½ÇËÙ¶ÈΪ¦Ø₂ʱ£¬Ï¸ÏßAB¸ÕºÃÊúÖ±ÇÒÕÅÁ¦Îª0£¬Çó½ÇËٶȦØ₂µÄ´óС£»
£¨3£©×°ÖÿÉÒÔÒÔ²»Í¬µÄ½ÇËÙ¶ÈÔÈËÙת¶¯£¬ÊÔͨ¹ý¼ÆËãÔÚÈçͼ2µÄ×ø±êϵÖÐ×÷³öϸÏßACÖÐÕÅÁ¦TÓë½ÇËٶȵÄƽ·½¦Ø²Ö®¼äµÄ¹ØϵͼÏó£®

Answer 1

·ÖÎö £¨1£©µ±Ï¸ÏßABÕÅÁ¦ÎªÁãʱ£¬Ð¡ÇòÊÜÖØÁ¦ºÍACÉþµÄÀ­Á¦£¬¿¿Á½¸öÁ¦µÄºÏÁ¦ÌṩÏòÐÄÁ¦£¬¸ù¾ÝСÇòת¶¯µÄ°ë¾¶£¬½áºÏÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö½ÇËٶȦØ₁µÄ´óС£®
£¨2£©Ï¸ÏßABÇ¡ºÃÊúÖ±£¬µ«ÕÅÁ¦ÎªÁãʱ£¬Óɼ¸ºÎ¹ØϵÇó³öACÉþÓëÊúÖ±·½ÏòµÄ¼Ð½Ç£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö½ÇËٶȦØ₂µÄ´óС£®
£¨3£©¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ·Ö±ðÇó³ö$¦Ø¡Ü{¦Ø_{1}}=\frac{5}{2}\sqrt{2}{rad/s}$ʱ¡¢¦Ø₁¡Ü¦Ø¡Ü¦Ø₂ʱ¡¢¦Ø£¾¦Ø₂ʱÀ­Á¦µÄ´óС£¬´Ó¶øÈ·¶¨Ï¸ÏßACÉÏÕÅÁ¦TËæ½ÇËٶȵÄƽ·½¦Ø²±ä»¯µÄ¹Øϵ£¬²¢×÷³öͼÏó£®

½â´ð ½â£º£¨1£©Ï¸ÏßABˮƽÀ­Ö±ÇÒÕÅÁ¦Îª0ʱÓУºmgtan37¡ã=m¦Ø₁²lsin37¡ã
½âµÃ£º${¦Ø}_{1}=\sqrt{\frac{g}{lcos37¡ã}}=\sqrt{\frac{50}{4}}=\frac{5\sqrt{2}}{2}rad/s$£®

£¨2£©Ï¸ÏßABÇ¡ºÃÊúÖ±£¬µ«ÕÅÁ¦ÎªÁãʱ£¬Óɼ¸ºÎ¹ØϵµÃ£º
$cos¦È¡ä=\frac{3}{5}$£¬
ÔòÓУº¦È¡ä=53¡ã
$mgtan¦È¡ä=m{{¦Ø}_{2}}^{2}lsin¦È¡ä$
½âµÃ£º${¦Ø}_{2}=\sqrt{\frac{50}{3}}rad/s$£®
£¨3£©µ±¦Ø¡Ü¦Ø₁ʱ£¬Ï¸ÏßACÕÅÁ¦µÄˮƽ·ÖÁ¿ÌṩÏòÐÄÁ¦£¬ÊúÖ±·ÖÁ¿ÓëСÇòÖØÁ¦Æ½ºâ£¬¼´Tcos¦È=mgµÃT=$\frac{50}{4}$N¦Ø₁¡Ü¦Ø¡Ü¦Ø₀ʱ£¬Ï¸ÏßABËɳڣ¬Ï¸ÏßACÕÅÁ¦µÄˮƽ·ÖÁ¿ÌṩÏòÐÄÁ¦£¬¼´Tsinϕ=m¦Ø²Lsinϕ£¬µÃT=m¦Ø²L¦Ø£¾¦Ø₀ʱ£¬Ï¸ÏßAB¶ÔСÇòÓÐÏòϵÄÁ¦×÷Ó㬵«ÊÇÈÔÈ»ÊÇϸÏßACÕÅÁ¦µÄˮƽ·ÖÁ¿ÌṩÏòÐÄÁ¦£¬¼´Tsin¦Á=m¦Ø²Lsin¦Á£¬
µÃT=m¦Ø²L
×ÛÉÏËùÊö£¬¦Ø¡Ü¦Ø₁ʱ£¬T=$\frac{50}{4}$N=12.5N²»±ä¦Ø£¾¦Ø₁ʱ£¬T=m¦Ø²L=¦Ø²
ËùÒÔ£¬Ï¸ÏßACÉÏÕÅÁ¦TËæ½ÇËٶȵÄƽ·½¦Ø²±ä»¯µÄ¹ØϵͼÏóÈçͼËùʾ£®
´ð£º£¨1£©½ÇËٶȦØ₁µÄ´óСΪ$\frac{5\sqrt{2}}{2}rad/s$£®
£¨2£©Ï¸ÏßAB¸ÕºÃÊúÖ±ÇÒÕÅÁ¦Îª0£¬½ÇËٶȦØ₂µÄ´óСÊÇ$\sqrt{\frac{50}{3}}rad/s$£®
£¨3£©Ï¸ÏßACÉÏÕÅÁ¦TËæ½ÇËٶȵÄƽ·½¦Ø²±ä»¯µÄ¹ØϵͼÏóÈçͼ£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÀíÇåСÇò×öÔ²ÖÜÔ˶¯µÄÏòÐÄÁ¦À´Ô´£¬È·¶¨Ð¡ÇòÔ˶¯¹ý³ÌÖеÄÁÙ½ç״̬£¬ÔËÓÃÅ£¶ÙµÚ¶þ¶¨ÂɽøÐÐÇó½â£®