力学与实践 ›› 2019, Vol. 41 ›› Issue (5): 601-606.DOI: 10.6052/1000-0879-19-037

• 教育研究 • 上一篇    下一篇

质点在斜面上的二维运动

尤明庆1)   

  1. 河南理工大学能源科学与工程学院,河南焦作454010
  • 收稿日期:2019-01-23 修回日期:2019-05-08 发布日期:2019-10-28
  • 通讯作者: 1) E-mail: youmq@hpu.edu.cn

TWO-DIMENSIONAL MOTION OF A PARTICLE ON AN INCLINED PLANE

YOU Mingqing1)   

  1. School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo 454010, Henan, China
  • Received:2019-01-23 Revised:2019-05-08 Published:2019-10-28

摘要: 质点在斜面上受到大小恒定的下滑力和摩擦力而运动,但后者方向随速度而变化。摩擦因子与斜面坡度比值即等效摩擦因子λ> 1 时质点最终在斜面上停止;0:5 <λ≤6 1 时质点不会停止但水平方向运动距离存在限界,而λ≤0:5 时水平方向也可运动至无穷远。相同等效摩擦因子下质点运动轨迹的曲线簇具有包络线。

关键词: 斜面, 摩擦, 包络线, 光滑, 粗糙

Abstract: A particle on an inclined plane is under the action of a constant sliding force due to the gravity and a frictional force, with the direction of the frictional force varying with the velocity. When the ratio of the friction factor to the slope gradient of the inclined plane, i.e. the equivalent frictional factor, λ> 1, the particle will eventually stop on the slope; when 0:5 <λ≤1, the particle will not stop but with a limit in the horizontal direction; and when λ≤0:5, the particle can move to an infinite distance in the horizontal direction. The curves of the particle trajectories have an outer envelope for the same equivalent friction factor.

Key words: inclined plane, friction, envelope, smooth, rough

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