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

• Garretg06
In summary, you are trying to plot weight vs time while standing on a scale in an elevator moving at a constant speed in a radial direction from the center of the Earth to a distance 3RE above the surface. You need to use the equation for force of gravity, considering the Earth's radius and the inverse square law. The weight will be zero at the center of the Earth due to the evenly distributed mass, and the net gravitational field inside a uniform spherical shell is zero. You can find a proof of this concept online.
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
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?

Garretg06 said:
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)?

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

Garretg06 said:
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.

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.

1. How does the Earth's gravitational pull affect the weight of objects?

The Earth's gravitational pull is what gives objects weight. The closer an object is to the Earth's core, the stronger the gravitational pull and the heavier the object will feel. As an object moves away from the core, the gravitational pull decreases and the weight of the object decreases as well.

2. Can the weight of an object change as it moves from the Earth's core up?

Yes, as an object moves from the Earth's core up, its weight will change due to the changing gravitational pull. The weight will decrease as it moves further away from the core.

3. How can we calculate the weight of an object at different locations in the Earth?

To calculate the weight of an object at different locations in the Earth, we can use the formula W = mg, where W is the weight in Newtons, m is the mass of the object in kilograms, and g is the gravitational acceleration at that location. The value of g will vary depending on the distance from the Earth's core.

4. Is weight the same as mass?

No, weight and mass are not the same. Mass is the amount of matter in an object, while weight is the measure of the force of gravity on an object. While mass will remain constant, weight can change depending on the location of the object and the strength of the gravitational pull.

5. How does the weight of objects differ at the Earth's surface and at the core?

The weight of objects at the Earth's surface is greater than at the core due to the stronger gravitational pull at the surface. As objects move closer to the core, the weight will decrease as the gravitational pull decreases.

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