# Gravitational attraction of a cone

• alsinan1989
In summary, the question is about using triple integrals and cylindrical coordinates to solve for equations involving gravitational force and density in an ellipsoid. Part (a) requires setting up the triple integral in terms of ρ, θ, and z, while part (b) involves using a substitution to simplify the integral to a double integral in terms of x and y. The equation for the integral is F = Gρv/r² and the link provided leads to the specific question.
alsinan1989
Hello everyone,

I have been stuck on this geophysics question I have for one of my classes and I really need some help with it. Can anyone solve this question. If you do, please show me how because I am really stuck here. I am stuck on both a and b. Click the link below to see the question.

Thank You

http://i1142.photobucket.com/albums/n619/martin3100/Page1GeophysicsHW.jpg?t=1286671544

equations F= G $$\rho$$ v / r^2

i know that i have to use triple integrals but i don't know how to start

Last edited:
it. For part (a), set up the triple integral using cylindrical coordinates. The integral should be in terms of the variables ρ, θ, and z.The integral will be: ∫∫∫ Gρv/r² dρdθdz where G is the gravitational constant, ρ is the density of the ellipsoid, v is the volume, and r is the distance from the origin. For part (b), use a substitution to simplify the integral. To do this, you can substitute the variables x = ρsinθ and y = ρcosθ, which will reduce the integral to a double integral in terms of x and y. The integral will become: ∫∫ Gρv/r² dx dy where G is the gravitational constant, ρ is the density of the ellipsoid, v is the volume, and r is the distance from the origin.

## 1. What is the formula for calculating the gravitational attraction of a cone?

The formula for calculating the gravitational attraction of a cone is F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.

## 2. How does the height of a cone affect its gravitational attraction?

The height of a cone does not directly affect its gravitational attraction. The gravitational attraction between two objects depends on their masses and the distance between them, not their shape. However, the height of a cone may affect the distribution of mass, which in turn can impact its gravitational attraction.

## 3. Can the gravitational attraction of a cone be negative?

No, the gravitational attraction of a cone cannot be negative. Gravity is always an attractive force, meaning it pulls objects towards each other. If the gravitational attraction between two objects is negative, it means that the force is repulsive, which is not possible according to the laws of gravity.

## 4. How does the density of a cone affect its gravitational attraction?

The density of a cone does not directly affect its gravitational attraction. The gravitational attraction between two objects depends on their masses and the distance between them, not their density. However, a cone with a higher density will have a greater mass, which can impact its gravitational attraction.

## 5. Can the gravitational attraction of a cone be greater than its weight?

Yes, the gravitational attraction of a cone can be greater than its weight. Gravitational attraction refers to the force of attraction between two objects, while weight is a measure of the force of gravity on an object. The weight of a cone depends on its mass and the strength of the gravitational field it is in, while the gravitational attraction between two objects is dependent on their masses and the distance between them.

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