.(15分)如图所示,质量分别为m和M的两物体P和Q叠放在倾角为θ的斜

.(15分)如图所示,质量分别为mM的两物体PQ叠放在倾角为θ的斜面上,PQ之间的动摩擦因数为μ1Q与斜面间的动摩擦因数为μ2(μ1μ2).当它们从静止开始沿斜面滑下时,两物体始终保持相对静止,则物体P受到的摩擦力大小为多少?

 

 

答案

μ2mgcosθ

 

 解析:

先取PQ为一整体,受力分析如图所示.由牛顿第二定律得:

(Mm)gsinθFfQ=(Mm)a

FfQμ2FN

FN=(mM)gcosθ

以上三式联立可得agsinθμ2gcosθ

再隔离P物体,设P受到的静摩擦力为FfP

方向沿斜面向上,对P再应用牛顿第二定律得:

mgsinθFfPma可得出FfPμ2mgcosθ.

 

 

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