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I came across a situation similar to the one in the picture shown below, where you have a water bottle that is being knocked over by accident. Naturally, I wondered how much I would have to fill a bottle with water to make sure it is the most resilient to being knocked over.

enter image description here

When I googled around I found this answer, but when I asked some engineers, they told me I would also have to take into account the inertia of the water.

Basically, I found two philosophies surrounding this problem:

  1. The fuller the bottle, the more mass it has and therefore the more inertia it has
  2. The lower the center of mass, the more likely the bottle is to tip back after being knocked over

I started thinking about the physics behind both philosophies, but I find it hard to figure out a way to compare both approaches. Does anyone have any tips to get me on the right track?

Please do let me know if you need more information.

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closed as off-topic by Aaron Stevens, Jon Custer, ZeroTheHero, GiorgioP, tpg2114 Jul 5 at 23:48

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  • $\begingroup$ Try totally empty. $\endgroup$ – Chet Miller Jul 3 at 17:23
  • $\begingroup$ If you can arrange that the water stays at the bottom and does not move that would help... $\endgroup$ – user207455 Jul 3 at 18:23
  • $\begingroup$ @ChetMiller thank you for the input, however, a bottle that does contain water is a bit heavier than an empty bottle so I have to conclude that does not work. SolarMike thank you too for the input, I thought so too but that could make a significant difference between the theoretical solution and what happens in reality $\endgroup$ – JansthcirlU Jul 3 at 18:42
  • $\begingroup$ it would help also if you describe where do you push the bottle $\endgroup$ – Sartem Cacartem Jul 3 at 22:57
  • $\begingroup$ @SartemCacartem Also, can we assume that the impact transfer a fixed amount of momentum from the hand (or let's say it's a projectile for simplicity) to the bottle? $\endgroup$ – Keith McClary Jul 4 at 4:56