Wet wheel and conservation of momentum

[jbriggs444]

Isn't this scenario exactly the same as picking up a bucket of water, moving it 2m to the right and putting it back down?

I have not seen it nailed down carefully. My take was a wet wheel (or saturated paint roller) losing water (or paint) as it rolls on a dry surface at what is expected to be an unvarying speed while subject to no net thrust.

The puddle that the wheel starts in seems to be window dressing only -- intended to motivate an initial condition of a moving wheel saturated with water.

 

[russ_watters]

The puddle that the wheel starts in seems to be window dressing only -- intended to motivate an initial condition of a moving wheel saturated with water.

Ahh. That's...odd.

 

[Dale]

I claim this bike-paint roller device

I thought that your interest was in the paint/water and explicitly not in the combined system. I have to say that this is pretty annoying. I made a valid point for which you complained that it was not relevant, only to have you now make it explicitly relevant.

Please review and respond to my previous comment which you had previously dismissed as it is now directly relevant.

 

[jbriggs444]

Well I guess I need to make some design changes:

A cyclist has a paint roller attached to the end of the handlebar, he drives past a wall onto which the roller paints a line.

Now I claim this bike-paint roller device is a kind of a rocket, the propellant is the paint, the momentum of the propellant goes to the rest of the rocket and nowhere else.

Since you seem to be attempting to eliminate friction with the wall, why not eliminate the wall?

You are a passenger in a weightless environment of some sort. You have a long roll of transparent wrap which you have removed from the box. You look at the roll end on and see that the wrap winds in a long clockwise spiral path from the center toward the outside. You give the roll a hard spin in the clockwise direction. The right hand edge is moving "down" and the left hand edge is moving "up".

You trigger a release of some sort exactly when the leading edge of the plastic is at the right hand side of the roll. The freed wrap proceeds in a straight line downward.

You watch as the cardboard tube inside the plastic roll rises slowly in the air despite the absence of any external force on the tube+wrap system.

Is that a scenario you are after? Did you want to claim any violations of conservation of momentum, angular momentum or energy based on its predicted behavior?

 

[jartsa]

In the ideal case, during the time that the water interacts with the Earth its momentum does not change. It is only during the time that the water interacts with the wheel that its momentum changes. The thing that gets the water’s momentum should be clear.

So I guess you are hinting that the Earth does not get the momentum, but instead the bike gets the momentum.

Well that sounds sounds plausible.

(What else should I say? I can't say if it's right or wrong, I don't have such authority here)I have been wondering the following:

Energy has momentum v*E/c². So the battery of a speeding electric car is losing momentum. That momentum has to go to the Earth or to the car. Well maybe it goes to the car. So the device that takes the momentum of the energy and puts it to the car is the wheel, because that's where the energy is going, right?

 

[Nugatory]

So the battery of a speeding electric car is losing momentum. That momentum has to go to the Earth or to the car. Well maybe it goes to the car.

It depends on whether the car is changing speed or not. And there are two ways you can define the speed of the car: Relative to the earth, which is assumed to be immobile; and relative to an arbitrary fixed point in space. The first way is a really excellent approximation and it's easy to calculate with, so it's how we usually work problems involving things moving around on the surface of the Earth - but it is an approximation, and momentum is not exactly conserved by that approximation because it neglects the (very very small) changes in the Earth's momentum.

Either way, in any reasonable electrical vehicle the battery and the rest of the car are solidly connected to one another so move together. Thus, thinking about them as separate systems only complicates things: you have to consider the second-law force pair between the car and the battery, but these forces are internal to the car+battery system so do not change its momentum.

 

[Dale]

Energy has momentum v*E/c2. So the battery of a speeding electric car is losing momentum. That momentum has to go to the Earth or to the car. Well maybe it goes to the car. So the device that takes the momentum of the energy and puts it to the car is the wheel, because that's where the energy is going, right?

Assuming no dissipation and assuming the car’s mass is negligible compared to the earth, then the energy from the battery goes into the KE of the car. The total energy does not go down, and the momentum increases as v increases.

 

[jartsa]

It depends on whether the car is changing speed or not. And there are two ways you can define the speed of the car: Relative to the earth, which is assumed to be immobile; and relative to an arbitrary fixed point in space. The first way is a really excellent approximation and it's easy to calculate with, so it's how we usually work problems involving things moving around on the surface of the Earth - but it is an approximation, and momentum is not exactly conserved by that approximation because it neglects the (very very small) changes in the Earth's momentum.

Either way, in any reasonable electrical vehicle the battery and the rest of the car are solidly connected to one another so move together. Thus, thinking about them as separate systems only complicates things: you have to consider the second-law force pair between the car and the battery, but these forces are internal to the car+battery system so do not change its momentum.

Why is change in Earth's momentum very very small? Is your car moving at speed very close to c on the surface of the earth?

At speeds where Newtonian physics is a good approximation the magnitudes of momentum changes of the car and the Earth are almost the same.

 

[Dale]

Why is change in Earth's momentum very very small?

He meant that the change in the earth’s speed is small.

 

[jartsa]

Assuming no dissipation and assuming the car’s mass is negligible compared to the earth, then the energy from the battery goes into the KE of the car. The total energy does not go down, and the momentum increases as v increases.

So the energy gives the Earth impulse x, and to the car the energy gives an impulse -x + the momentum of the energy itself. This conserves momentum.

 

[jartsa]

Is that a scenario you are after? Did you want to claim any violations of conservation of momentum, angular momentum or energy based on its predicted behavior?

Yes to the first question. No the the rest.

 

[Nugatory]

Why is change in Earth's momentum very very small? Is your car moving at speed very close to c on the surface of the earth?

At speeds where Newtonian physics is a good approximation the magnitudes of momentum changes of the car and the Earth are almost the same.

This has absolutely nothing to do with any relativistic effects, so we can take Newtonian physics to be exact.

The change in the earth’s momentum is exactly equal to and opposite to the change in the car’s momentum. And that change in the earth’s momentum is very small, by many decimal orders of magnitude, compared with what it would it take for us to notice. Thus we normally ignore it and recognize that because we’re not counting it we will seem to lose it somewhere.Only when someone starts a “where did the momentum go?” thread do we point out that this tiny change in the earth’s speed is being ignored.