Force and torque of a string on a pulley
Force and torque of a string on a pulley
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DOI：
10.1119/1.5016040
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发表时间：
2018-04-01
影响因子：
0.9
通讯作者：
Lemos, Nivaldo A.
中科院分区：
文献类型：
--
作者：
de Oliveira, Thiago R.;Lemos, Nivaldo A.
每一所大学的入门物理课程考虑阿特伍德机器的问题，考虑到滑轮的质量。在通常的处理中，绳子两端的张力被随意地认为作用在滑轮上，并对滑轮的旋转负责。然而，这样一个滑轮上的力的自由体图并不是先验证明，诱导学生构建错误的假设，例如弦将其张力转移到滑轮上，或者某种对称性在起作用。我们重新审视这个问题，通过整合的字符串和滑轮的每个元素之间的接触力，并显示，虽然滑轮的行为，如果张力作用在其两端，这只是作为一个详细的分析的最终结果。我们还讨论了需要多大的摩擦力才能防止绳子滑过滑轮的问题。最后，我们处理的情况下，字符串是在滑动的边缘，并表明，这不能发生，除非满足一定的条件，由静摩擦系数和质量。(C)2018年美国物理教师协会
Every university introductory physics course considers the problem of Atwood's machine taking into account the mass of the pulley. In the usual treatment, the tensions at the two ends of the string are offhandedly taken to act on the pulley and be responsible for its rotation. However, such a free-body diagram of the forces on the pulley is not a priori justified, inducing students to construct wrong hypotheses such as that the string transfers its tension to the pulley or that some symmetry is in operation. We reexamine this problem by integrating the contact forces between each element of the string and the pulley and show that although the pulley does behave as if the tensions were acting on its ends, this comes only as the final result of a detailed analysis. We also address the question of how much friction is needed to prevent the string from slipping over the pulley. Finally, we deal with the case in which the string is on the verge of sliding and show that this cannot happen unless certain conditions are met by the coefficient of static friction and the masses involved. (C) 2018 American Association of Physics Teachers.