Question

11£®ÈçͼËùʾ£¬Á½¸öÔ²ÐεĹ⻬ϸ¹ÜµÀÔÚÊúֱƽÃæÄÚ½»µþ£¬×é³É¡°8¡±×ÖÐÎͨµÀ£¬´óÔ²µÄ°ë¾¶R=0.9m£¬Ð¡Ô²µÄ°ë¾¶r=0.7m£¬ÔÚ¡°8¡±×ÖÐÎͨµÀµ×²¿ÓÐÈý¸ö´óСÏàͬ£¨Ö±¾¶ÂÔСÓڹܾ¶£©µÄСÇòa¡¢b¡¢c£¨¿ÉÊÓΪÖʵ㣬ÆðʼλÖÿÉÈÏΪÔÚͬһˮƽÃæÉÏ£©£¬ÆäÖÊÁ¿¹ØϵΪ5m_a=5m_c=m_b£¬b¡¢cÁ½Çò¿ªÊ¼Ê±¾²Ö¹£¬aÇòºÍbÇòµÄÅöײûÓÐÄÜÁ¿Ëðʧ£¬aÇòºÍcÇòÅöºóÕ³ÔÚÒ»Æð£¬Ð¡Çòbµ½´ï¡°8¡±×ÖÐÎͨµÀµÄ¶¥µãCºó£¬ÓÖ¾­Ë®Æ½¹â»¬µÄϸֱ¹ÜCD£¬´ÓDµãˮƽÅ׳ö£¬ÆäˮƽÉä³Ìs=4.8m£¬È¡g=10m/s²£®Çó£º
£¨1£©ÅöײǰСÇòaµÄËÙÂÊv₀£®
£¨2£©Èôm_a=m_c=0.7kg£¬ÇóÅöºóСÇòc£¨°üÀ¨a£©µ½´ïCµãʱÊܵ½µÄ¹ìµÀµÄµ¯Á¦´óСºÍ·½Ïò£®

Answer 1

·ÖÎö £¨1£©ÓÉƽÅ×Ô˶¯¹æÂÉÇóµÃСÇòbÔÚ×î¸ßµãµÄËٶȣ¬ÔÙÓÉbÉÏÉý³Ì»úеÄÜÊغã¿ÉÇóµÃÅöºóµÄËٶȣ¬ÔòÓÉabÓɶ¯Á¿Êغ㼰»úеÄÜÊغã¿ÉÇóµÃaÅöÇ°µÄËٶȣ»
£¨2£©ÓɵÚÒ»ÎÊÇó³öÅöºóСÇòaµÄËٶȣ¬ÔÙ¶Ôac¹ý³ÌÓɶ¯Á¿ÊغãÇóµÃºóÀ´µÄËٶȣ»¶øÁ½Ð¡ÇòÕ³ÔÚÒ»ÆðºóÏòÉÏÔ˶¯Ê±£¬»úеÄÜÊغ㣻ÔÙ½áºÏÏòÐÄÁ¦¹«Ê½¼´¿ÉÇóµÃ×î¸ßµãµÄѹÁ¦£®

½â´ð ½â£º¶ÔbÇòÓÉƽÅ×Ô˶¯¹æÂɿɵãº
s=v_bt
h=$\frac{1}{2}$gt²£»
ÁªÁ¢½âµÃ£ºv_b=6m/s£»
ÔÙ¶ÔbÓÉ×îµÍµãµ½×î¸ßµãÓÉ»úеÄÜÊغ㶨Âɿɵãº
mg£¨2R+2r£©=$\frac{1}{2}$mv²_bA-$\frac{1}{2}$mv_b²
½âµÃ£ºbÇòÔÚ×îµÍµãµÄËÙ¶Èv_bA=10m/s£»
ÉèÔÚÅöײ¹ý³ÌÖÐˮƽÏòÓÒΪÕý£»
¶ÔabÅöײ¹ý³ÌÓɶ¯Á¿Êغ㶨Âɿɵãº
m_av_a=m_av_a¡ä+m_bv_bA
ÓÉ»úеÄÜÊغ㶨Âɿɵãº
$\frac{1}{2}$m_av_a²=$\frac{1}{2}$mv_a¡ä²+$\frac{1}{2}$m_bv²_bA
ÁªÁ¢ÒÔÉÏÁ½Ê½½âµÃ£¬v_a=30m/s£»Åöºóv_a¡ä=-20m/s£»
£¨2£©Ð¡ÇòaÓëbÏàÅöºóËÙ¶ÈΪ20m/s£»·½ÏòÏò×ó£¬ÔÙÓëCÏàÅö£»Óɶ¯Á¿Êغ㶨Âɿɵãº
m_av_a¡ä=£¨m_a+m_c£©v
ÔÚacÏòÉÏÔ˶¯¹ý³ÌÖУ¬»úеÄÜÊغ㣬ÔòÓУº
mg£¨2R+2r£©=$\frac{1}{2}$£¨m_a+m_c£©v²-$\frac{1}{2}$£¨m_a+m_c£©v¡ä²
¶øÔÚ×î¸ßµãÓÉÏòÐÄÁ¦¹«Ê½¿ÉµÃ£º
F+mg=m$\frac{v{¡ä}^{2}}{r}$
ÁªÁ¢ÒÔÉϸ÷ʽ½âµÃ£ºF=58N£¬·½ÏòÊúÖ±ÏòÏÂ
´ð£º£¨1£©ÅöײǰСÇòaµÄËÙÂÊv₀Ϊ30m/s£»
£¨2£©Èôm_a=m_c=0.7kg£¬ÇóÅöºóСÇòc£¨°üÀ¨a£©µ½´ïCµãʱÊܵ½µÄ¹ìµÀµÄµ¯Á¦´óСΪ58N£»·½ÏòÏòÏ£®

µãÆÀ ±¾Ì⿼²é¶¯Á¿Êغ㡢»úеÄÜÊغ㡢ƽÅ×Ô˶¯¼°ÏòÐÄÁ¦¹«Ê½£¬ÊÇÒ»µÀ¶à¹ý³ÌµÄ×ÛºÏÌ⣬µ«Ö»ÒªÈÏʶ·ÖÎö£¬Ã÷È·¸÷ÎïÀí¹ý³ÌµÄ¹æÂɼ´¿ÉÕýÈ·Çó½â£®