Question

Èçͼ16-11Ëùʾ£¬abcÊǹ⻬µÄ¹ìµÀ£¬ÆäÖÐabÊÇˮƽµÄ£¬bcΪÓëabÏàÇеÄλÓÚÊúֱƽÃæÄڵİëÔ²£¬°ë¾¶R=0.30 m.ÖÊÁ¿m=0.20 kgµÄСÇòA¾²Ö¹ÔÚ¹ìµÀÉÏ£¬ÁíÒ»ÖÊÁ¿M=0.60 kg¡¢ËÙ¶Èv₀=5.5 m/sµÄСÇòBÓëСÇòAÕýÅö.ÒÑÖªÏàÅöºóСÇòA¾­¹ý°ëÔ²µÄ×î¸ßµãcÂäµ½¹ìµÀÉϾàbµãΪl=R´¦£¬ÖØÁ¦¼ÓËÙ¶ÈÈ¡g=10 m/s².Çó£º

ͼ16-11

(1)Åöײ½áÊøʱ£¬Ð¡ÇòAºÍBµÄËٶȵĴóС.

(2)ÊÔÂÛ֤СÇòBÊÇ·ñÄÜÑØ×Å°ëÔ²¹ìµÀµ½´ïcµã.

Answer 1

(1)6 m/s  3.5 m/s  (2)²»ÄÜ

½âÎö:

(1)ÒÔv₁±íʾСÇòAÅöºóµÄËٶȣ¬v₂±íʾСÇòBÅöºóµÄËٶȣ¬v₁¡ä±íʾСÇòAÔÚ°ëÔ²×î¸ßµãµÄËٶȣ¬t±íʾСÇòA´ÓÀ뿪°ëÔ²×î¸ßµãµ½ÂäÔÚ¹ìµÀÉϾ­¹ýµÄʱ¼ä£¬ÔòÓÐv₁¡ät= ¢Ù

gt²=2R                                                                      ¢Ú

mg(2R)+ mv₁¡ä²=mv₁²                                                       ¢Û

Mv₀=mv₁+Mv₂                                                                 ¢Ü

ÓÉ¢Ù¢Ú¢Û¢ÜÇóµÃ

v₁=,v₂=v₀-

´úÈëÊýÖµµÃv₁=6 m/s,v₂=3.5 m/s.

(2)¼Ù¶¨BÇò¸ÕÄÜÑØ×Å°ëÔ²µÄ¹ìµÀÉÏÉýµ½cµã£¬ÔòÔÚcµãʱ£¬¹ìµÀ¶ÔËüµÄ×÷ÓÃÁ¦µÈÓÚÁã.ÒÔv_c±íʾËüÔÚcµãµÄËٶȣ¬v_b±íʾËüÔÚbµãÏàÓ¦µÄËٶȣ¬ÓÉÅ£¶Ù¶¨ÂɺͻúеÄÜÊغ㶨ÂÉ£¬ÓУ¬Mv_c²+Mg(2R)=Mv_b²

½âµÃv_b=

´úÈëÊýÖµµÃv_b=3.9 m/s.

ÓÉv₂=3.5 m/s£¬¿ÉÖªv₂<v_b£¬ËùÒÔСÇòB²»ÄÜ´ïµ½°ëÔ²¹ìµÀµÄ×î¸ßµã.