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Further Exploration Answers
A fingertip is a smaller base than the palm of your hand, and balancing requires at least one of the same conditions as STANDing - that the center of gravity be directly above the base. It is harder to make sure the middle of an object is directly above the small tip of a finger than it is to make sure it is above the much larger, flatter area of the hand.
The supports extend the base of the crane, allowing the arm of the crane, which might be carrying a load almost as heavy as the crane itself, to extend further out without the center of mass going past the base!
The extra machinery serves a second use as a counterbalance. By extending the weight of the machinery to the left, more weight can be carried on the right without moving the center of gravity past the base.
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