1. Jul 14, 2015

### hbj

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?

2. Jul 14, 2015

### Dr. Courtney

Interesting question. It may depend on what you hold constant: distance from the top edge or volume of liquid in the cup.

3. Jul 14, 2015

### hbj

The volume (we had two cups of 8 oz volume and just different shapes).

4. Jul 14, 2015

### Drakkith

Staff Emeritus
Which one do you think and why?

5. Jul 15, 2015

### CWatters

6. Jul 15, 2015

### hbj

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.

Last edited: Jul 15, 2015
7. Jul 15, 2015

### hbj

Any ideas smart people? :)

8. Jul 15, 2015

### Drakkith

Staff Emeritus
Perhaps I misunderstood your question. Are you asking which one will tip over first (and thus spill), or something else?

9. Jul 16, 2015

### hbj

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. Jul 16, 2015

### hbj

Or to put it another way, which would spill with the least energetic jolt?

11. Jul 18, 2015

### hbj

No ideas, eh?

12. Jul 18, 2015

### dipole

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. Jul 18, 2015

### Drakkith

Staff Emeritus
I'd guess the bowl shape, simply because any liquid trying to flow radially outwards doesn't encounter a wall, but a ramp.

14. Jul 18, 2015

### hbj

Interesting. Thanks!