Solved Center of Mass Problems

Here are some pre-worked problems for you to examine before trying some out on your own.

Example 1:

A beam with a mass of 2.5 g which acts at its center and a length of 5.2 m has a block with a mass of 60 g added to one of its ends as shown in the above diagram. What is the system's center of mass?

Solution:

This question is a simple matter of plugging the corresponding values into the formula we discussed on the Center of Mass Page. We need to pick a pivot point and evaluate everything in relation to that point in our formula.

x = (W1x1 + W2x2 + ....) / (W1 + W2 +....)
x = [(0.0245 N)(2.6 m) + (0.588 N)(5.2 m)] / (0.6125 N)
x = (3.1213 N*m) / (0.6125 N)
x = 5.1 m

Now that you have seen a basic example of a typical center of mass problem, you should try some for yourself on my CM Problems Page.

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