## Illustration 13.2: Center of Mass and Gravity

The first animation shows two blocks of equal mass (position is given in meters). The center of mass of the system is shown by a red dot and its position is calculated for you. Drag the right-hand green block to the right or to the left. What do you notice about the location of the center of mass as you change the block's position? Restart.

Now suppose the two blocks have unequal masses as shown in Animation 2. Is the center of mass at the center of the system? By viewing the location of the center of mass, you know which block is more massive. So which one is more massive?

How can we calculate the ratio of the mass of the blue block to the mass of the red block? If you only have two blocks, then the ratio of the distances of each block from the center of mass is related to the ratio of their masses. Therefore, by measuring the distance from each block to the center of mass, you can calculate the ratio of their masses.

In terms of the location of the two objects, the center of mass is located at:

Xcm = (x1m1 + x2m2)/(m1 + m2) ,

for a one-dimensional, two-object system.

A concept similar to that of the center of mass is that of the center of gravity. In fact the two are often used interchangeably. The center of mass is defined above; the center of gravity is defined as the point on a system where gravity can be considered to act. The center of gravity takes into account the fact that the force of gravity—and therefore the acceleration due to gravity—is different for different heights above the surface of Earth. For this Illustration the center of mass is equivalent to the center of gravity. Only if the system is really large might the acceleration due to gravity be different at different parts of the system, thereby causing the center of gravity to differ from the center of mass.

Illustration authored by Aaron Titus and Mario Belloni.
Script authored by Aaron Titus.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

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