定滑轮中的力学原理

MECHANICAL PRINCIPLES OF FIXED PULLEY

定滑轮是最简单的机械,但其运行原理却涉及诸多方面;它内涵丰富,几乎可涵盖非物理专业力学部分的全部教学范围.本文全面分析定滑轮运行涉及的力学原理,包括选取的体系不同动力学方程有不同的表现形式,或同一种表现形式适用不同体系时有不同的解释;着重讨论摩擦力矩是定滑轮的转动动力.为此选择与轮缘接触的任一无穷小绳元,其两端张力合力的法向分量产生绳元和轮缘间的摩擦力.所有绳元对轮缘的摩擦力矩的总和使轮子的角动量变化,而轮缘对绳元的摩擦力则与张力合力的切向分量平衡.静摩擦力起中介作用将定滑轮两边悬挂的重物和地球体系势能变化的一部分转化为轮子的转动动能.文章最后指出随着选取的体系不同重力既可理解为外力也可理解为内力,从而功能原理的具体表现也有所区别.

Perhaps the fixed pulley,also known as Atwood＇s machine,consisting of a disk that can rotate about a fixed axis with a string passing over it and two blocks connected to the two ends of the string,is the simplest machine.However its operation involves plenty of mechanical principles,including dynamics of mass point,rotation of rigid body about a fixed axis,dynamical significance of static friction,and the law of energy conservation.This paper comprehensively analyzes the mechanics principle relevant to the fixed pulley,including the different forms of dynamic equation in different selected system,and the different explanations of the same equation form used in different systems.Especially,we focus on the friction torque,which is the turning power of the fixed pulley.Analysis shows it is the friction between the string and the disk rim that causes the disk to rotate,transferring part of the potential energy change of the two blocks into the rotational kinetic energy of the disk.Meanwhile it is shown that the forces of gravity acting on the blocks can be considered either internal forces or external forces,depending on which objects are included in the system considered.