Question

ÈçͼËùʾ£¬Æ½°å³µPµÄÖÊÁ¿ÎªM£¬Ð¡Îï¿éQµÄÖÊÁ¿Îªm£¬´óС²»¼Æ£¬Î»ÓÚƽ°å³µµÄ×ó¶Ë£¬ÏµÍ³Ô­À´¾²Ö¹Ôڹ⻬ˮƽµØÃæÉÏ£®Ò»²»¿ÉÉ쳤µÄÇáÖÊϸÉþ³¤ÎªR£¬Ò»¶ËÐüÓÚQµÄÕýÉÏ·½¸ßΪR´¦£¬ÁíÒ»¶ËϵһÖÊÁ¿Ò²ÎªmµÄСÇò£¨´óС²»¼Æ£©£®½ñ½«Ð¡ÇòÀ­ÖÁÐüÏßÓëÊúֱλÖóÉ60¡ã½Ç£¬Óɾ²Ö¹ÊÍ·Å£¬Ð¡Çòµ½´ï×îµÍµãʱÓëQÅöײµÄʱ¼ä¼«¶Ì£¬ÇÒÎÞÄÜÁ¿Ëðʧ£¬ÒÑÖªQÀ뿪ƽ°å³µÊ±ËٶȴóСÊÇƽ°å³µËٶȵÄÁ½±¶£¬QÓëPÖ®¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì£¬M£ºm=4£º1£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£®Çó£º
£¨1£©Ð¡Çòµ½´ï×îµÍµãÓëQÅöײ֮ǰ˲¼äµÄËÙ¶ÈÊǶà´ó£»
£¨2£©Ð¡Îï¿éQÀ뿪ƽ°å³µÊ±Æ½°å³µµÄËÙ¶ÈΪ¶à´ó£»
£¨3£©Æ½°å³µPµÄ³¤¶ÈΪ¶àÉÙ£¿

Answer 1

·ÖÎö£ºÐ¡Çòµ½´ï×îµÍµãʱÓëQµÄÅöײʱ¼ä¼«¶Ì£¬ÇÒÎÞÄÜÁ¿Ëðʧ£¬Âú×㶯Á¿ÊغãµÄÌõ¼þÇÒÄÜÁ¿Êغ㣮СÎï¿éQÔÚƽ°å³µPÉÏ»¬¶¯µÄ¹ý³ÌÖУ¬¶þÕßÏ໥×÷Ó㬶¯Á¿Êغ㣬²¿·Ö¶¯ÄÜת»¯ÎªÄÚÄÜ£®

½â´ð£º½â£º£¨1£©¡¢Ð¡ÇòÓɾ²Ö¹°Úµ½×îµÍµãµÄ¹ý³ÌÖУ¬»úеÄÜÊغ㣬ÔòÓУº
mgR£¨1-cos60¡ã£©=

1

2

m

v

2 0

¡à½âµÃСÎï¿éµ½´ï×îµÍµãÓëQÅöײ֮ǰ˲¼äµÄËÙ¶ÈÊÇ£º
v₀=

gR

£¨2£©¡¢Ð¡ÇòÓëÎï¿éQÏàײʱ£¬Ã»ÓÐÄÜÁ¿Ëðʧ£¬Âú×㶯Á¿Êغ㣬»úеÄÜÊغ㣬ÔòÖª£º
mv₀=mv₁+mv_Q

1

2

m

v

2 0

=

1

2

m

v

2 0

v

2 1

+

1

2

m

v

2 Q

ÓÉÒÔÉÏÁ½Ê½¿ÉÖª¶þÕß½»»»Ëٶȣºv₁=0£¬v_Q=v₀=

gR

£¬
СÎï¿éQÔÚƽ°å³µÉÏ»¬ÐеĹý³ÌÖУ¬Âú×㶯Á¿Êغ㣬ÔòÓУº
mv_Q=Mv+m?2v
ÓÖÖªM£ºm=4£º1
ÔòСÎï¿éQÀ뿪ƽ°å³µÊ±Æ½°å³µµÄËÙ¶ÈΪ£ºv=

1

6

vQ=

gR

6

£¨3£©¡¢Ð¡Îï¿éQÔÚƽ°å³µPÉÏ»¬¶¯µÄ¹ý³ÌÖУ¬²¿·Ö¶¯ÄÜת»¯ÎªÄÚÄÜ£¬ÓÉÄܵÄת»¯ºÍÊغ㶨ÂÉ£¬Öª£ºmg¦ÌL=

1

2

m

v

2 Q

-

1

2

Mv²-

1

2

m¡Á£¨2v£©²
½âµÃƽ°å³µPµÄ³¤¶ÈΪ£ºL=

7R

18¦Ì

´ð£º£¨1£©¡¢Ð¡Îï¿éµ½´ï×îµÍµãÓëQÅöײ֮ǰ˲¼äµÄËÙ¶ÈÊÇ

gR

    £¨2£©¡¢Ð¡Îï¿éQÀ뿪ƽ°å³µÊ±Æ½°å³µµÄËÙ¶ÈΪ

gR

6

£¬
    £¨3£©¡¢Æ½°å³µPµÄ³¤¶ÈΪ

7R

18¦Ì

£®

µãÆÀ£ºÖðÒ»·ÖÎöÎïÌå¼äµÄÏ໥×÷Óùý³Ì£¬·ÖÎöµÃµ½ÎïÌå¼äÏ໥×÷ÓÃʱÂú×ãµÄ¹æÂÉ£º¶¯Á¿Êغ㡢ÄÜÁ¿ÊغãµÈ£¬½ø¶øÇó³öÒªÇóµÄÎïÀíÁ¿£®