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Chapter 9: Problem 13

Three equal masses lie at the corners of an equilateral triangle of side \(L\). Find the center of mass.

Short Answer

Expert verified
The center of mass of the system is located at the centroid of the equilateral triangle, which is a distance of \(\frac{L}{3}\) from each vertex of the triangle.

Step by step solution

01

Understand the concept of center of mass

The center of mass is the point in an object or a system of particles where all the mass can be considered to be concentrated. This point moves as if the total force and torque on the system of particles were acting on a single particle with all the mass of the system located at this point.
02

Apply the concept on an equilateral triangle

In an equilateral triangle, all sides and angles are equal. Therefore, the masses at each vertex can be assumed to be distributed uniformly. The centroid, or the geometric center of any polygon, for an equilateral triangle is the point where the perpendicular bisectors of the triangle intersect. This carries equal distances from the vertices of the triangle. So, here the center of mass will coincide with the centroid of the triangle.
03

Specify the center of mass location

The center of mass or centroid of an equilateral triangle is equidistant from each vertex, so it is located at a distance of L/3 from each vertex, where L is the length of a side of the triangle. Thus, the location of the center of mass is at a height of L/3 from the base of the triangle.

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