How to find weight moving from the Earth's core up?

[Garretg06]

Homework Statement

Imagine standing on a scale and riding in an elevator at constant speed in a radial direction from the center of the Earth to a distance 3RE above the surface- I'm supposed to plot weight vs time so what I'm looking for an equation(s) I can use to find weight.

*Assuming uniform desnity

Homework Equations

Forcegrav=G*m1*m2/d^2
Earth Radius= 6378100 meters
Weight=mass*forcegravity
*the Inverse square law 1/r^2 I think this may come into play

The Attempt at a Solution

I can find the force form gravity but I'm having a hard time deciding if I need to incorporate /how find out the decreasing mass of the Earth as I (the individual) move to the center of the Earth.
I know that at the center of the Earth the weight is 0 because the mass of the Earth is surrounding "me" and is evenly distributed...but other than that I am stuck. Help?

 

[haruspex]

I know that at the center of the Earth the weight is 0 because the mass of the Earth is surrounding "me" and is evenly distributed...but other than that I am stuck. Help?

Do you know what the net field is inside a uniform spherical shell (whether it be a gravitational field or electrostatic field)?

 

[Garretg06]

I think it is supposed to be the gravitational field but I'm not sure how to calculate it.

 

[haruspex]

I think it is supposed to be the gravitational field but I'm not sure how to calculate it.

Standard result you should know:
If a force field follows an inverse square law and the source of the field is uniformly distributed over a spherical shell then;
- the field outside the shell is independent of the radius of the shell, i.e. it is the same as if all the source (charge, mass, whatever) were concentrated at the sphere's centre;
- the field inside the shell is zero.
I don't know whether you are expected to prove this or know it. It is not trivial to prove, but not toweringly difficult either. You should be able to find a proof on the net.