Sunday, January 3, 2016

Center of Mass Problem and Solution Three Particles at Three Corners of Triangle

Center of mass is a point of a system which represent the motion of a system. We can find the center of mass of any system using mathematical equations we have derived.In the previous posts we had discussed how to find the center of the system using its mathematical derivation.

Let us consider a system which has three identical particles having equal masses placed at the three corners of a equilateral triangle of known side. We would like to measure the center of mass of this system. Let each particle has different masses of 1,2 and 3 kilogram at three corners of the triangle and the side of the triangle is only one meter.

Let one kilogram and 2 kilogram are on the horizontal axis and third body of mass three kilogram is at the third corner of triangle as shown in the video presented.

To find the center of mass of any system, we shall consider a reference point and let one kilogram in this problem is that reference point. We are going to find out center of mass of this system using that reference point. We shall treat that point as horizon and shall measure the position of all particles with reference to that point. 

As shown below, using simple mathematical techniques like Pythagoras rule, we have determined the coordinates of each particle of the system as shown.

As we know the mass of all particles and their coordinates, we can measure the center of mass of this system as shown below. This system has particles in a plane and hence center of mass will have both components of x- axis and y-axis.

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