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Let's say I have a 10cm x 10cm x 50 cm wooden stick that weights 5kg total. The 10cm x 10cm base is touching the floor and it protrudes from the floor 50cm which is the height of the stick. Based on this configuration, I would expect the wooden stick to never fall over.

Let's say I attach a 10cm x 10cm x 10cm metal box on the side of the wooden stick 40cm from the base. The metal box weighs 5kg as well. Now the center of gravity should be on the very edge of the wooden stick.

Wooden stick and metal box diagram

I assumed that if the center of gravity was under the wooden stick (where it makes contact with the ground), then the stick won't fall over. If it's outside the wooden stick, then the stick will fall over.

However, I tried simulating this phenomenon on Bullet and Newton physics engine. On Newton, if the metal box weighs more than 4.72 kg, it would eventually fall over. On Bullet, if the metal box weighs more than 4.9 kg, it would eventually fall over. If I move the metal box down the shaft of the wooden stick, the stick would take a longer time to fall over.

Can anybody explain this phenomenon. Even better yet, can someone give me a formula that might be useful in predicting if an object will fall over or not?

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    $\begingroup$ Are you sure this isn't just a problem with the simulations, not actual physics? $\endgroup$ – knzhou Feb 18 '19 at 12:40
  • $\begingroup$ hmm, could be a problem with simulations but I'm pretty sure the simulations are capturing some major physics rule that I'm not thinking about. I'm not even sure if my statement: "I assumed that if the center of gravity was under the wooden stick (where it makes contact with the ground), then the stick won't fall over. If it's outside the wooden stick, then the stick will fall over" is true. Thus, I asked this question to get an explanation on how balance works $\endgroup$ – aztrorisk Feb 18 '19 at 13:01
  • $\begingroup$ In addition, why would moving the metal box to the center of the wooden stick make it more stable? The only change in the center of gravity would be in the height-related coordinate which shouldn't affect where it makes contact with the ground. $\endgroup$ – aztrorisk Feb 18 '19 at 13:03
  • $\begingroup$ The answer also depends a bit on the shape of the base. For example, if the base is slightly curved, then only one point is ever actually touching the ground, meaning it won't be stable unless the CM is right above that point. $\endgroup$ – knzhou Feb 18 '19 at 13:07
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    $\begingroup$ You might have specified it as flat, but who knows how it's actually treated in the simulation? Videogame designers specify you can't go through walls, but it happens all the time. Point is, it's probably some fiddly detail deep inside the code that has little to do with reality... $\endgroup$ – knzhou Feb 18 '19 at 13:34
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If the center of gravity is right on the edge, the system is not stable. The slightest perturbation to the right in your illustration will tip it over. The numerical simulation introduces those perturbations (whether or not by design). Note that the higher the center of gravity is, the more torque the structure experiences for a given tilt angle-- that's why it falls faster when the block is higher.

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  • $\begingroup$ But why does it fall for when the mass is not negligibly less than $5\ \rm{kg}$? $\endgroup$ – BioPhysicist Feb 19 '19 at 3:36
  • $\begingroup$ Without knowing the numerical method used in the simulation, we can't know. It would be interesting to approach the "edge" configuration from both sides (a little bit in toward a little bit out and vice versa) and see how the simulation behaves, because even if the center of gravity is slightly inside the edge, a big enough perturbation toward the right can tip it over. $\endgroup$ – S. McGrew Feb 19 '19 at 11:11

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