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# 9.6: Center of Mass

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Suppose a beam is 10 meters long, and that there are three weights on the beam: a 10 kilogram weight 3 meters from the left end, a 5 kilogram weight 6 meters from the left end, and a 4 kilogram weight 8 meters from the left end. Where should a fulcrum be placed so that the beam balances? Let's assign a scale to the beam, from 0 at the left end to 10 at the right, so that we can denote locations on the beam simply as $$x$$ coordinates; the weights are at $$x=3$$, $$x=6$$, and $$x=8$$, as in Figure 9.6.1.

### Contributors

• Integrated by Justin Marshall.