Circular motion and Newton's law question

[bokonon]

1. A 78.0 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much?



2. I think that this has to do with with the radius being different at the north pole and equator, which would cause different centripetal accelerations. So I assume I'm supposed to find the net force on the man in both places.


3. I'm lost on how to visualize this. A man on the north pole, on the very top of the axis, isn't in circular motion at all, except around the sun, ,right?

Any help, much appreciated.

 

[D H]

Forget about the Sun. It is irrelevant to this problem.

I'm assuming you are talking about a spring scale here, which measures force, as opposed to a fancy doctor's scale, which measures mass.

Most introductory physics texts define weight as mass times acceleration due to gravity. Others define it as what a spring scale weighs. These are two different things. A spring scale measures the sum of all forces acting on a body except for gravity. What you have to do then is find all of the forces except for gravity that act on the person, sum them up, and voila! you have the scale measurement.

So, what forces act on the person? Are they the same everywhere on the surface of the Earth, or different?

 

[bokonon]

Thanks. So the forces acting on the man other than gravity are the centripetal force and the normal force. The normal force would be -mg, and the centripetal force would be mass*omega^2*radius?

 

[D H]

So the forces acting on the man other than gravity are the centripetal force and the normal force.

Correct.

The normal force would be -mg

Correct, but the way you wrote that suggests you think g is the same everywhere. What makes you think that?

and the centripetal force would be mass*omega^2*radius?

Correct, but what is the radius?

 

[bokonon]

Is gravity different based on how far from the center of the Earth one is? Am I supposed to look up the radius at the Earth vs. the equator? How do I calculate different g's? I'm conceptually lost on this one . . .

 

[D H]

Is gravity different based on how far from the center of the Earth one is?

What is Newton's law of gravitation?

Am I supposed to look up the radius at the Earth vs. the equator?

That is a very good idea.