Question

ÈçͼËùʾ£¬Ë®Æ½¹â»¬µØÃæÉÏÍ£·Å×ÅÒ»Á¾Ð¡³µ£¬×ó²à¿¿ÔÚÊúֱǽ±ÚÉÏ£¬¹â»¬Ô²»¡¹ìµÀABµÄ×îµÍµãBÓë×ã¹»³¤µÄˮƽ¹ìµÀÏàÇУ¬Õû¸ö¹ìµÀ´¦ÓÚͬһÊúֱƽÃæÄÚ£®¿ÉÊÓΪÖʵãµÄÎï¿é´ÓAµãÕýÉÏ·½H´¦ÎÞ³õËÙ¶ÈÏÂÂ䣬ǡºÃÂäÈëС³µÔ²»¡¹ìµÀ£¬²¢Ñذ뾶ΪRµÄËÄ·ÖÖ®Ò»Ô²»¡¹ìµÀ»¬Ï£¬×îÖÕС³µÓëÎï¿éÒ»ÆðÔ˶¯£®ÒÑ֪С³µµÄÖÊÁ¿ÎªM£¬Îï¿éµÄÖÊÁ¿Îªm£¬²»¿¼ÂÇ¿ÕÆø×èÁ¦ºÍÎï¿éÂäÈëÔ²»¡¹ìµÀʱµÄÄÜÁ¿Ëðʧ£¬£¨ÖØÁ¦¼ÓËÙ¶ÈÓÃg±íʾ£©£®Çó£º
£¨1£©Îï¿éµ½´ïBµãʱµÄËٶȴóС£¿
£¨2£©Îï¿éµ½´ïÔ²»¡¹ìµÀ×îµÍµãBʱ£¬¹ìµÀ¶ÔËüµÄÖ§³ÖÁ¦µÄ´óС£¿
£¨3£©Îï¿éºÍС³µµÄ×îÖÕËٶȴóС£¿

Answer 1

·ÖÎö£ºÓÉ»úеÄÜÊغ㶨ÂÉÇó³öµ½´ïBµãʱµÄËٶȴóС£®Îï¿é¾­¹ýBµãʱ£¬ÓÉÖØÁ¦ºÍ¹ìµÀÖ§³ÖÁ¦µÄºÏÁ¦ÌṩÏòÐÄÁ¦£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö¹ìµÀ¶ÔËüµÄÖ§³ÖÁ¦µÄ´óС£®
¸ù¾Ý¶¯Á¿Êغ㶨ÂÉÇó³ö¹²Í¬µÄËٶȣ®

½â´ð£º½â£º£¨1£©ÉèÎï¿éµ½´ïBµãµÄËÙ¶ÈΪv_B£¬ÓÉ»úеÄÜÊغãµÃ£º
mg£¨H+R£©+0=0+

1

2

m

v

2 B

½âµÃ£ºv_B=

2g(H+R)

£¨2£©ÉèÖ§³ÖÁ¦ÎªF_N£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵÃ
F_N-mg=

mv 2 B

R

½âµÃF_N=mg+

2mg(H+R)

R

£¨3£©ÉèÎï¿éºÍС³µµÄ×îÖÕËÙ¶ÈΪv£¬ÓÉϵͳ¶¯Á¿ÊغãµÃ£º
mv_B=£¨M+m£©v£¬
½âµÃ£ºv=

m

m+M

2g(H+R)

´ð£º£¨1£©Îï¿éµ½´ïBµãʱµÄËٶȴóСÊÇ

2g(H+R)

£¨2£©Îï¿éµ½´ïÔ²»¡¹ìµÀ×îµÍµãBʱ£¬¹ìµÀ¶ÔËüµÄÖ§³ÖÁ¦µÄ´óСÊÇmg+

2mg(H+R)

R

£¨3£©Îï¿éºÍС³µµÄ×îÖÕËٶȴóСÊÇ

m

m+M

2g(H+R)

µãÆÀ£º±¾ÌâÊ×ÏÈÒª·ÖÎöÎïÀí¹ý³Ì£¬È·¶¨Ñо¿¶ÔÏó£¬Æä´ÎÒª°ÑÎÕ½âÌâµÄ¹æÂÉ£¬²ÉÓûúеÄÜÊغ㡢¶¯Á¿Êغã½áºÏÑо¿£¬ÄѶÈÊÊÖУ®