Why doesn't water from a hose affect Earth's rotation?

[StephenP91]

Homework Statement

A wall is firmly in the ground, if you shoot water at it via a hose why does it not have an effect on the world's rotation?

Homework Equations

The Attempt at a Solution

The question is something like that. You get the general idea.

 

[Char. Limit]

well, think about the relative sizes of the force between the water hitting the wall, and the rotation of the earth.

There's a hint.

 

[StephenP91]

well, think about the relative sizes of the force between the water hitting the wall, and the rotation of the earth.

There's a hint.

No, I'm not getting it, ultimately the question is asking for some reference to momentum.

 

[Char. Limit]

No, I'm not getting it, ultimately the question is asking for some reference to momentum.

Well, yes. The Earth's momentum depends on its mass, an extremely large number, and its velocity, another rather large momentum. In contrast, the momentum of the water is negligible by comparison.

 

[StephenP91]

Well, yes. The Earth's momentum depends on its mass, an extremely large number, and its velocity, another rather large momentum. In contrast, the momentum of the water is negligible by comparison.

I read it as no effect. Ahh well, thank you.

 

[HallsofIvy]

This is more a physics problem than a mathematics problem.

It is true that the Earth's mass (and so momentum) is very large compared to that of the water but, in fact, there is exactly 0 net force on the earth- the size of the Earth is irrelevant.

"For every action, there is an equal and opposite reaction".

In order to spray water on the wall, you have to hold the hose that is spraying the water. As the water leaves the hose, it is exerting as much force on you as it will on the wall. And, of course, your feet braced on the Earth prevent you from moving backwards just as the wall's hold on the Earth prevents it from moving. Both you and the wall are exerting the same force on the Earth but in opposite directions. There is no net force on the wall.

This is similar to the suggestion that you can make a sailboat sail without wind by putting a powerful fan, aimed at the sail, in the stern of the boat!