Physics Problem Involving Gravitational Force on an object based on R

In summary, the conversation discusses finding the distance r inside the Earth where the gravitational force due to Earth is equal to the distance r = 4RE outside the Earth. It is assumed that the Earth has a uniform density. Various methods are suggested, including using conservation of energy and Gauss's Law. Ultimately, the link provided proves to be the most useful approach to solving the problem.
  • #1
taylorkrauss
4
0

Homework Statement



At what distance r inside the Earth is the gravitational force due to Earth the same as at
the distance r = 4RE (where the latter distance is clearly outside Earth)? Assume uniform
density of Earth.


Homework Equations



conservation of energy? TME = GPE + KE



The Attempt at a Solution



At first I thought I could do conservation of energy and set both GPE's equal to each other and solve for a new Radius, but this is not working out well. Is there something I need to do involving the density of Earth and the mass? I really have no idea. Thanks for any help!
 
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  • #2
Energy conservation doesn't appear relevant to me... I'd go with Gauss.
 
  • #3
Hmm...I haven't learned Gauss's Law though. This wants Gravitational Force and Gravitational Potential not Electric Force and EPE, so I'm not sure how I'd apply Gauss (after googling, I saw it was a theroem for electric potential). How would you go about using Gauss's Law?
 
  • #5
That was perfect! Thank you!
 

Related to Physics Problem Involving Gravitational Force on an object based on R

What is the formula for calculating the gravitational force on an object?

The formula for calculating the gravitational force on an object is F = Gm1m2/d^2, where F is the force in Newtons, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

How does the distance between two objects affect the gravitational force between them?

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases. For example, doubling the distance between two objects would result in the force being one-fourth of its original value.

What is the difference between mass and weight in relation to gravitational force?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. The gravitational force on an object is directly proportional to its mass, but weight can vary depending on the strength of the gravitational field.

How does the mass of an object affect the gravitational force acting on it?

The gravitational force on an object is directly proportional to its mass. This means that as the mass of an object increases, the force of gravity acting on it also increases. For example, a larger object will experience a stronger gravitational force than a smaller object.

What is the role of the universal gravitational constant in calculating the gravitational force between two objects?

The universal gravitational constant, denoted by G, is a fundamental constant that determines the strength of the gravitational force between two objects. It is a fixed value and is used in the formula for calculating gravitational force to account for the distance and masses of the objects.

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