Which Cup Shape is More Prone to Spilling?

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In summary, the question was whether a cylindrical or bowl-shaped coffee cup is more likely to spill, given equal volume and composition. The answer may depend on what is held constant, such as distance from the top edge or volume of liquid. The cylindrical cup may have less inertial buildup in the direction of the spill due to diffused forces, but conservation of energy suggests the spill will eventually occur. The bowl shape may be worse due to the liquid encountering a ramp rather than a wall when trying to flow outwards.
  • #1
hbj
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If you have 2 coffee cups of equal volume and composition, if one is a shaped like a sector of a cylinder and the other is shaped with a more tapered bowl shape, which is more likely to spill?
 
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  • #2
Interesting question. It may depend on what you hold constant: distance from the top edge or volume of liquid in the cup.
 
  • #3
Dr. Courtney said:
Interesting question. It may depend on what you hold constant: distance from the top edge or volume of liquid in the cup.

The volume (we had two cups of 8 oz volume and just different shapes).
 
  • #4
hbj said:
If you have 2 coffee cups of equal volume and composition, if one is a shaped like a sector of a cylinder and the other is shaped with a more tapered bowl shape, which is more likely to spill?

Which one do you think and why?
 
  • #6
My gut tells me that with the cylindrical one there'd be less inertial buildup in the direction of the spill because the forces would be more greatly diffused, but conservation of energy would say that in a round cup eventually those forces have to come around and support the spill. It would just happen later. That would give the spill vector energy time to dissipate.

It sort of "feels" like what's happening when you watch the cups though.

But that's completely a gut feeling of course.
 
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  • #7
Any ideas smart people? :)
 
  • #8
hbj said:
My gut tells me that with the cylindrical one there'd be less inertial buildup in the direction of the spill because the forces would be more greatly diffused, but conservation of energy would say that in a round cup eventually those forces have to come around and support the spill. It would just happen later. That would give the spill vector energy time to dissipate.

Perhaps I misunderstood your question. Are you asking which one will tip over first (and thus spill), or something else?
 
  • #9
Oh sorry. No I meant given some arbitrary jolt to the cup (with the cup held perfectly parallel to the direction of gravity), which would spill first.
 
  • #10
Or to put it another way, which would spill with the least energetic jolt?
 
  • #11
No ideas, eh?
 
  • #12
You can probably crudely model this using inelastic collisions with some particle of arbitrary or random incidence, and computer on average which shape has a larger upward components of reflection. My guess is the curved cup is worse.
 
  • #13
hbj said:
No ideas, eh?

I'd guess the bowl shape, simply because any liquid trying to flow radially outwards doesn't encounter a wall, but a ramp.
 
  • #14
Interesting. Thanks!
 

1. Which cup shape is more prone to spilling?

The answer to this question is that taller, narrower cups are more prone to spilling than wider, shorter cups. This is because the center of gravity of the liquid inside a taller cup is higher, making it easier to tip over.

2. Why are taller, narrower cups more prone to spilling?

Taller, narrower cups have a higher center of gravity, making them easier to tip over. Additionally, the liquid inside a taller cup has more distance to travel when the cup is tipped, increasing the chances of a spill.

3. Are there any cup shapes that are less prone to spilling?

Yes, wider, shorter cups are less prone to spilling because they have a lower center of gravity and the liquid has less distance to travel when the cup is tipped.

4. What other factors can contribute to cup spilling?

Aside from cup shape, other factors that can contribute to spilling include the material of the cup (plastic cups are more slippery than paper cups), the stability of the surface the cup is on, and the amount and consistency of the liquid inside the cup.

5. Is there a way to prevent spills from happening?

While there is no foolproof way to prevent spills, some tips to reduce the chances include using wider, shorter cups, filling cups only partially, avoiding sudden movements while holding a cup, and using cups with lids or spill-proof mechanisms. Additionally, practicing good hand-eye coordination and being mindful while handling cups can also help prevent spills.

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