2. The following principle is used frequently in physics: if system S of point m

Question

2. The following principle is used frequently in physics: if system S of point masses is given, then we can regard the system as a single point mass located at the center of mass of S and having mass equal to the total mass of S. For example, a large asymmetric object might, for simplicity, be regarded as only occupying a single point in space and that the mass of this large object might be regarded as concentrated at this single point. The natural candidate for such a point is the center of mass of the object. In this exercise, you will provide a mathematical justication for why this is "natural"



Let S be the system of point masses p1, ...., pk, and let T be the system of point masses pk+1, ...., pn.Suppose that each point mass, pi, has mass mi at that each that each point pilies on the real line and has x-coordinate equal to xi. Prove that the center of mass of thesystem S U T of consisting of all of the point masses,p1, ...., pk,, is equal to the center of mass of the system consisting of two specialpoint masses: one point mass pS which has a mass equal to the totalmass of the system S and which has x-coordinate equal to the centerof mass of the system S and a second point mass pT denedanalogously with respect to the system T.

Explanation / Answer

E=MC2" redirects here. For other uses, see E=MC2 (disambiguation). 4-meter-tall sculpture of Einstein's 1905 E = mc2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant.

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