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当一个力学体系处于稳定平衡时,势能为极小值,这称为最小势能原理.最小势能原理是物理学中一个很重要的原理,在材料力学和弹性力学中有广泛的应用.在中学阶段,通过合理的构建物理模型,寻找系统的能量关系和平衡态的特点,再利用最小势能原理,我们可以解决物理中的一些疑难问题,甚至可以解决一些数学难题.例1.(最佳场址选择问题)设A、B、C三个村子里的学生人数分别为n_1、n_2、n_3,为了使全体学生所走的路程之和最少,应如何选择校址?
When a mechanical system is in a stable equilibrium, the potential energy is a minimum, which is called the principle of minimum potential energy. The principle of minimum potential energy is a very important principle in physics and has a wide range of applications in material mechanics and elasticity. , We can solve some difficult problems in physics and even solve some math problems by reasonably constructing the physical model to find the energy relations and equilibrium states of the system and then using the principle of minimum potential energy. Choice question) Suppose the number of students in A, B, and C villages is n_1, n_2, n_3, respectively. In order to minimize the total distance traveled by all students, how to choose the site?