Plastic Water Bottle Rolling Down Ramp

[mathkechu]

Results show me that if I increase the volume of water inside a bottle the time taken for it to roll down a ramp and then a particular distance along a horizontal plane increases. How would we explain this relationship.

 

[bp_psy]

One reason is that more water in the bottle means that you have more momentum at the bottom of the ram. The friction forces involved will not increase enough to reduce the momentum of the bottle in the same time.
There may be some other more complex factors involving the shape of the bottle and the behavior of the fluid but I think this is the major cause for what you observed.

 

[mathkechu]

is it something to do with the viscosity of water

 

[bp_psy]

is it something to do with the viscosity of water

I don't think it would make much of a difference if it isn't very viscous . With most fluids there would be more friction inside the bottle but since you have a plastic bottle its angular momentum is small and the distance that the whole system travels is determined my the linear momentum of the fluid.
If the fluid fills the bottle and is viscous enough to start rotating with respect to the central axis of the bottle the traveled distance would be considerably bigger though.

EDIT.
Sorry I misread the initial question. As Phrak points out the time interval should be smaller not bigger with more water volume.

 

[Phrak]

Results show me that if I increase the volume of water inside a bottle the time taken for it to roll down a ramp and then a particular distance along a horizontal plane increases. How would we explain this relationship.

Isn't it the other way around? Where did you get these results?

 

[mathkechu]

Yes it is sorry, as the volume of water in a plastic bottle increases the time taken for it to roll down a ramp and a particular distance along a horizontal plane decreases in that it is faster.

 

[bp_psy]

Yes it is sorry, as the volume of water in a plastic bottle increases the time taken for it to roll down a ramp and a particular distance along a horizontal plane decreases in that it is faster.

If the fluid doesn't fill the bottle and is not viscous enough to roll with the bottle, than the bottle with more water volume will have a greater inertia and be slowed down less by the friction forces(primarily air friction) than the bottle with less water.

 

[mathkechu]

how does the moment of inertia of the bottle and water change compared to the bottle by itself.

 

[tiny-tim]

welcome to pf!

hi mathkechu! welcome to pf!

this motion is governed by an energy equation

there are two ways that energy can be "wasted" in a https://www.physicsforums.com/library.php?do=view_item&itemid=632" bottle …

i] it can literally be wasted, by loss of energy to heat caused by the viscosity

ii] it can go into rotational motion as well as linear motion …

PE + linear KE + rotational KE = constant​

… so the result is different from what it would be if none of the mass was rotating (or sloshing)

I'm pretty sure it comes down to the definition of mass. Mass is related to volume in that sense that increasing volume of water increases mass. More mass means more gravitational force towards Earth and which means it will rotate about inertia slowly. that's how I see it. If you draw a diagram of certain forces affecting the water bottle, you'll notice that gravity slows the net force down in comparison to less mass. That is if the angle from the horizontal is the same for both analysis. the normal force would be the mass times gravity times cos theta. but yea if you did all this youd notice that gravity affects the force on the way down and how much time it takes to reach the bottom.

Rayquesto, this is almost meaningless. Please don't confuse people with posts like this.

 

[mathkechu]

how does the moment of inertia of the bottle and water change compared to the bottle by itself.

 

[tiny-tim]

how does the moment of inertia of the bottle and water change compared to the bottle by itself.

work it out!

what do you get? ​

 

[mathkechu]

Wait I think I have the answer to that question. But the mgh= 0.5mv2 +0.5Iomegasquared. Since the moment of inertia is greater with greater volume can we say that the gravitational potential energy is converted to more rotational energy and therefore the bottle is faster.

 

[tiny-tim]

hi mathkechu!

(have an omega: ω and try using the X² tag just above the Reply box )

Wait I think I have the answer to that question. But the mgh= 0.5mv2 +0.5Iomegasquared. Since the moment of inertia is greater with greater volume can we say that the gravitational potential energy is converted to more rotational energy and therefore the bottle is faster.

isn't it the other way round …

if some of the PE (per mass) has to be converted to rotational KE, then there's less linear KE (per mass), ie less speed?

 

[mathkechu]

ignoring effects of slipping if the bottle rotates faster it is going to go down the slope faster.

 

[mathkechu]

Results show me that if I increase the volume of water inside a bottle the time taken for it to roll down a ramp and then a particular distance along a horizontal plane decreases. How would we explain this relationship.