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With this unequal loading, the beam will tip down on the left hand side, as indicated by the red arrow. This seems like a very simple thing, but it is a very important fact. Let me point out what happens here. As soon as the weight on one side of the pivot is bigger than the weight on the other side (both weights being an equal distance from the pivot point), then the heavy plank starts to move. Why does it move? Because gravity is pushing the weights downwards.

One other point is that the distance from the pivot point is also important. If the added weights "m" are equal but placed at different distances from the pivot point, then the plank will also tip over:

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