ÌâÄ¿ÄÚÈÝ
ÈçͼËùʾ£¬ÖÊÁ¿ÎªMµÄƽ°å³µP¸ßh£¬ÖÊÁ¿ÎªmµÄСÎï¿éQµÄ´óС²»¼Æ£¬Î»ÓÚƽ°å³µµÄ×ó¶Ë£¬ÏµÍ³ÔÀ´¾²Ö¹Ôڹ⻬ˮƽÃæµØÃæÉÏ£®Ò»²»¿ÉÉ쳤µÄÇáÖÊϸÉþ³¤ÎªR£¬Ò»¶ËÐüÓÚQÕýÉÏ·½¸ßΪR´¦£¬ÁíÒ»¶ËϵһÖÊÁ¿Ò²ÎªmµÄСÇò£¨´óС²»¼Æ£©£®½ñ½«Ð¡ÇòÀÖÁÐüÏßÓëÊúֱλÖóÉ60¡ã½Ç£¬Óɾ²Ö¹ÊÍ·Å£¬Ð¡Çòµ½´ï×îµÍµãʱÓëQµÄÅöײʱ¼ä¼«¶Ì£¬ÇÒÎÞÄÜÁ¿Ëðʧ£¬ÒÑÖªQÀ뿪ƽ°å³µÊ±ËٶȴóСÊÇƽ°å³µËٶȵÄÁ½±¶£¬QÓëPÖ®¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì£¬M£ºm=4£º1£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£®Çó£º
£¨1£©Ð¡Îï¿éQÀ뿪ƽ°å³µÊ±ËÙ¶ÈΪ¶à´ó£¿
£¨2£©Æ½°å³µPµÄ³¤¶ÈΪ¶àÉÙ£¿
£¨3£©Ð¡Îï¿éQÂäµØʱ¾àСÇòµÄˮƽ¾àÀëΪ¶àÉÙ£¿
£¨1£©Ð¡Îï¿éQÀ뿪ƽ°å³µÊ±ËÙ¶ÈΪ¶à´ó£¿
£¨2£©Æ½°å³µPµÄ³¤¶ÈΪ¶àÉÙ£¿
£¨3£©Ð¡Îï¿éQÂäµØʱ¾àСÇòµÄˮƽ¾àÀëΪ¶àÉÙ£¿
£¨1£©Ð¡ÇòÓɾ²Ö¹°Úµ½×îµÍµãµÄ¹ý³ÌÖУ¬ÓÐ
mgR£¨1-cos60¡ã£©=
m
½âµÃ£¬Ð¡Îï¿éµ½´ï×îµÍµãÓëQÅöײ֮ǰ˲¼äµÄËÙ¶ÈÊÇ£ºv0=
СÇòÓëÎï¿éQÏàײʱ£¬Ã»ÓÐÄÜÁ¿Ëðʧ£¬¶¯Á¿Êغ㣬»úеÄÜÊغ㣬ÔòÓÐ
mv0=mv1+mvQ
m
=
m
+
m
£¬
½âµÃ£¬v1=0£¬vQ=v0=
¶þÕß½»»»Ëٶȣ¬¼´Ð¡Çò¾²Ö¹ÏÂÀ´£¬QÔÚƽ°å³µÉÏ»¬ÐеĹý³ÌÖУ¬ÏµÍ³µÄ¶¯Á¿Êغ㣬ÔòÓÐ
mvQ=Mv+m?2v
½âµÃ£¬v=
vQ=
СÎï¿éQÀ뿪ƽ°å³µÊ±£¬ËÙ¶ÈΪ2v=
£¨2£©ÓÉÄܵÄת»¯ºÍÊغ㶨ÂÉ£¬Öª
fL=
m
-
Mv2-
m(2v)2
ÓÖf=¦Ìmg
½âµÃ£¬Æ½°å³µPµÄ³¤¶ÈΪL=
£¨3£©Ð¡Îï¿éQÔÚƽ°å³µÉÏ»¬Ðйý³ÌÖУ¬¶ÔµØλÒÆΪs£¬Ôò
-¦Ìmgs=
m(2v)2-
m
½âµÃ£¬s=
СÎï¿éQÀ뿪ƽ°å³µ×öƽÅ×Ô˶¯£¬Æ½Å×ʱ¼äΪ t=
ˮƽ¾àÀëx=2vt=
¹ÊQÂäµØµã¾àСÇòµÄˮƽ¾àÀëΪs+x=
+
£®
´ð£º
£¨1£©Ð¡Îï¿éQÀ뿪ƽ°å³µÊ±ËÙ¶ÈΪ
£»
£¨2£©Æ½°å³µPµÄ³¤¶ÈΪΪ
£»
£¨3£©Ð¡Îï¿éQÂäµØʱ¾àСÇòµÄˮƽ¾àÀëΪ
+
£®
mgR£¨1-cos60¡ã£©=
1 |
2 |
v | 20 |
½âµÃ£¬Ð¡Îï¿éµ½´ï×îµÍµãÓëQÅöײ֮ǰ˲¼äµÄËÙ¶ÈÊÇ£ºv0=
gR |
СÇòÓëÎï¿éQÏàײʱ£¬Ã»ÓÐÄÜÁ¿Ëðʧ£¬¶¯Á¿Êغ㣬»úеÄÜÊغ㣬ÔòÓÐ
mv0=mv1+mvQ
1 |
2 |
v | 20 |
1 |
2 |
v | 21 |
1 |
2 |
v | 2Q |
½âµÃ£¬v1=0£¬vQ=v0=
gR |
¶þÕß½»»»Ëٶȣ¬¼´Ð¡Çò¾²Ö¹ÏÂÀ´£¬QÔÚƽ°å³µÉÏ»¬ÐеĹý³ÌÖУ¬ÏµÍ³µÄ¶¯Á¿Êغ㣬ÔòÓÐ
mvQ=Mv+m?2v
½âµÃ£¬v=
1 |
6 |
| ||
6 |
СÎï¿éQÀ뿪ƽ°å³µÊ±£¬ËÙ¶ÈΪ2v=
| ||
3 |
£¨2£©ÓÉÄܵÄת»¯ºÍÊغ㶨ÂÉ£¬Öª
fL=
1 |
2 |
v | 2Q |
1 |
2 |
1 |
2 |
ÓÖf=¦Ìmg
½âµÃ£¬Æ½°å³µPµÄ³¤¶ÈΪL=
7R |
18¦Ì |
£¨3£©Ð¡Îï¿éQÔÚƽ°å³µÉÏ»¬Ðйý³ÌÖУ¬¶ÔµØλÒÆΪs£¬Ôò
-¦Ìmgs=
1 |
2 |
1 |
2 |
v | 2Q |
½âµÃ£¬s=
4R |
9¦Ì |
СÎï¿éQÀ뿪ƽ°å³µ×öƽÅ×Ô˶¯£¬Æ½Å×ʱ¼äΪ t=
|
ˮƽ¾àÀëx=2vt=
| ||
3 |
¹ÊQÂäµØµã¾àСÇòµÄˮƽ¾àÀëΪs+x=
4R |
9¦Ì |
| ||
3 |
´ð£º
£¨1£©Ð¡Îï¿éQÀ뿪ƽ°å³µÊ±ËÙ¶ÈΪ
| ||
3 |
£¨2£©Æ½°å³µPµÄ³¤¶ÈΪΪ
7R |
18¦Ì |
£¨3£©Ð¡Îï¿éQÂäµØʱ¾àСÇòµÄˮƽ¾àÀëΪ
4R |
9¦Ì |
| ||
3 |
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿