细直杆无滑动脱离水平面的必要条件

NECESSARY CONDITIONS FOR SEPARATION OF STRAIGHT BAR FROM HORIZONTAL PLANE WITHOUT SLIDING

  • 摘要: 该文研究的是起初竖直静置于水平面上的非均质细直杆的倾倒过程,利用质心运动定理、机械能守恒定律和定轴转动定理导出了直杆在下端不滑动情况下所受支持力的表达式,据此指出了直杆能够脱离水平面的必要条件同时包括两部分:对直杆质量分布的要求;对直杆与水平面之间的静摩擦因数的要求。

     

    Abstract: In this paper, the toppling process of a non-uniform slender rod in the initial vertical stationary position on a horizontal support surface is studied. Based on the motion theorem of the center of mass, the law of conservation of mechanical energy and the theorem of fixed axis rotation, the expression of the bearing force of a straight rod without slip is derived. It is pointed out that the necessary conditions for a straight bar to be separated from the horizontal plane include two requirements: the mass distribution of the straight bar and the minimum static friction coefficient between the straight bar and the supporting surface.

     

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