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Chapter 9: Problem 17

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 at the centroid of the triangle, which is at a distance of \(\frac{L}{2}\) from each corner.

Step by step solution

01

Understanding the Concept

The center of mass of a system of particles is given by dividing the sum of the product of mass and position of each particle by the total mass of the system. In this case, the three masses are equal and positioned at the corners of an equilateral triangle. So, the center of mass will effectively be the centroid of the triangle since the contribution of each mass to the center of mass is equal.
02

Finding the Centroid

The centroid of a triangle is the point where all its medians intersect. Medians are lines from one vertex of the triangle to the mid-point of the opposite sides. In case of an equilateral triangle, any median is also a line of symmetry of the triangle and all medians coincide at one point. Thus, the center of mass will be at a distance of \(\frac{L}{2}\) from any mass (or corner of the triangle), where \(L\) is the side length of the triangle.

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