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Consider this example:

images

  • Treat G as 10.
  • The blue blocks provide lift of 10N, or -1KG.
  • The red block has a weight of 20N, or 2KG.
  • The black bar has no weight.
  • All have their center of gravity in their center.
  • All three have infinite strength.
  • We ignore air resistance.
  • We assume all the pieces are joined.

In the first example, all three are centered, and in line with each other.

In the second, the red block is centered between the blue blocks.

My question is which would be the most stable, i.e. less likely to roll into its more natural state with the lift above the weight, where the center of gravity in the red block to shift to one side. Which would allow the most shift before flipping?

The second one? By how much?

My initial thoughts were about center of gravity, but i'm not sure this even applies anymore, is it more about torque from the systems weight and lift once it has passed the last stable point?

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3 Answers

up vote 2 down vote accepted

You could think of it in terms of torque. It's going to require a greater shear force in the second example, to overcome the torque provided by the lifts being farther apart. Since torque is the cross-product of F, the force and r, displacement vector. r is greater in the second example for the lifts, so more external torque will be required to cause the system to rotate (and become unstable)

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An easy way to think about it is to take your diagram, and then move the gravity vector left or right by some angle.

Which configuration can tolerate a larger change in the direction of gravity without one of the blocks or the composite tipping over?

enter image description here

Actually, I'm assuming there is no glue here, so the actual CG of the group on the left should be somewhat to the left of center, because when it tips far enough to the left, the rightmost blue block ceases to have any weight on it, so it is no longer part of the composite. That makes the necessary angle even smaller.

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Both cases are unstable. Any small shift in the position of red will cause the black bar to flip. The second case will flip a little slower because the system has a larger moment of inertia.

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