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.

 

[HalfLostAndSearching]

I would approach this problem by first considering the basic principles of gravity and weight. Weight is the force exerted on an object by a gravitational field, and it is directly proportional to the mass of the object. In this case, we can assume that the mass of the person remains constant as they move from the Earth's core to a distance of 3RE above the surface.

To calculate the weight at different distances from the Earth's core, we can use the equation W = mg, where W is weight, m is mass, and g is the acceleration due to gravity. However, in this case, we need to take into account the changing distance from the Earth's center, as well as the changing mass of the Earth.

To do this, we can use the inverse square law, which states that the force of gravity is inversely proportional to the square of the distance between two objects. In this case, the two objects are the person and the Earth's core. So, as the person moves away from the Earth's core, the force of gravity decreases.

We can also use the formula for gravitational force, F = G(m1m2)/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. In this case, m1 is the mass of the Earth and m2 is the mass of the person. As the person moves away from the Earth's core, the distance r increases, causing the gravitational force to decrease.

Combining these two equations, we can find the weight at different distances from the Earth's core by using the formula W = (Gm1m2)/r^2. We can also plot weight vs time by considering the changing distance from the Earth's core and the changing mass of the Earth. As the person moves away from the Earth's core, the weight will decrease due to the decreasing gravitational force.

In conclusion, to find weight moving from the Earth's core up, we can use the equations for gravitational force and the inverse square law to take into account the changing distance and mass. By plotting weight vs time, we can see how weight changes as the person moves away from the Earth's core.