如图所示,倾角为30o的斜面体置于水平地面上,一根不可伸长的轻绳两端分别系着小球A和物块B,跨过固定于斜 10

如图所示,倾角为30o的斜面体置于水平地面上,一根不可伸长的轻绳两端分别系着小球A和物块B,跨过固定于斜面体顶端的光滑支点O。已知A的质量为m,B的质量为4m现用手托住A... 如图所示,倾角为30o的斜面体置于水平地面上,一根不可伸长的轻绳两端分别系着小球A和物块B,跨过固定于斜面体顶端的光滑支点O。已知A的质量为m,B的质量为4m 现用手托住A,使OA段绳恰处于水平伸直状态(绳中无拉力),OB绳平行于斜面,此时物块B静止不动。将 A由静止释放,在其下摆过程中,斜面体始终保持静止,下列判断中正确的是( )
A.物块B受到的摩擦力先减小后增大
B.地面对斜面体的摩擦力方向一直向右
C.小球A与地球组成的系统机械能守恒
D.小球A、物块B与地球组成的系统机械能不守恒

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vanllina
2011-08-27 · TA获得超过1458个赞
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以下文字全是我自己一个字一个字打的,分析了很久,打了很久,如果满意,就采纳吧,太不容易了。

        本人来自四川大学,最近在给一小孩辅导,也碰到了这个题,所以刚好为你解答了。

选 ABC

这个题一定要做好受力分析,而且特别要注意隐含条件和潜在的信息,要有信心做,再加上必要的细心,就一定能做出来。

“现用手托住A,使OA段绳恰处于水平伸直状态(绳中无拉力) ”这个条件中,“绳中无拉”这个条件 非常重要,说明此时B受到的力只有重力和摩擦力。

进行受力分析,可以得到此时受到的摩擦力为2mg(也就是重力在与斜面平行方向的分力4mgsin30'=2mg)也就隐含地得出除摩擦力以后的合力只有大于2mg,才能打破平衡,物体才有可能运动起来,换言之,只要摩擦力若小于2mg,必然为静摩擦力(物体此时静止)

下面对A球分析,刚才已分析了托住A的一瞬间,得到了此时B的摩擦力,放手后,小球做圆周运动(注意是变速圆周运动),用极限法分析,(并假设B未动)当小球A到最低点,即将碰到大物块那一瞬间,可以由向心力公式:F绳-mg=mv^2/r ,再次注意到mv^2与是动能的两倍,因为假设了B未动,所以由机械能守恒,知道Ek=mgr 代入到向心力公式,可知:F绳=3mg

由于A与B是拴在一根绳上,所以B会受到3mg的拉力,此时摩擦力反向,由最初的沿斜面向上变化沿斜面向下了,如果为静止,则为f=mg  (F绳B=mgsin30+f) 由此可知,此时B还是静止的。(此时f=mg是静摩擦力)

以上的分析对解题非常重要,下面就来看选项,我们知道B自始至终都没动,所以没有增加重力势能或者动能,所以C对,D错。 小球A的能量转换为,重力势能只转化成了自身的动能,没有消耗到增加A的动能或者A的重力势能或者A与斜面相对滑动产生的热能上去,因为B始终是静止的。

而D项,由于B一直没有动,其能量变化一直为0,所以考虑B和不考虑B是一样的,任一时刻,总的动能和势能总是一样的,因为只有A在发生势能与动能的转换。

而A项,我们可以分析始末,开始松开球的一瞬间,此时的物体有向下运动的趋势,因为重力分力。但此时B静止,故f=2mg,一旦A动起来,绳子上会产生拉力,初期,拉力与f同向,共同去抵消重力的分力,直到拉力=2mg(重力分力)时,f 反向,又从0开始,直到最终状态,mg.(因为最后一瞬间,绳的拉力为3mg,此时f=mg) 所以摩擦力是由2mg减少至0,再反向,慢慢增大到mg。

B项,这一项是最有难度的,很多人以为f摩力反向后,会导致地面对斜体的摩擦力反向,其实不会,这是因为重力沿斜体垂直的分力会提供斜体向左的分力,这个分力始终会大于向右的分力。

以下是分析:

当f对斜体的力为上时,此时无论是f对斜体的力还是B对斜体的压力,其沿水平方面的分力均向左,要想使斜体静止,必然是地面对斜体的摩擦力向右。

当f对斜体的力向下是,此时的f=mg, 分解到水平方向后是二分之根号三.mg,而重力压斜体的水平分力是根号三,mg,所以水平分力还是向左,要想使斜体静止,必然要使地面对其的f 向右。

所以无论f 是什么方向,地面对斜体的摩擦力都是向右的。

A.物块B受到的摩擦力先减小后增大

B.地面对斜面体的摩擦力方向一直向右

C.小球A与地球组成的系统机械能守恒

D.小球A、物块B与地球组成的系统机械能不守恒

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