Force between a unform sphere and a particle* outside of the sphere

In summary, the conversation is about finding the potential energy of gravitational interaction and the gravitational force between a particle of mass m located outside a uniform sphere of mass M at a distance R from its center. The variables used in the equations are G, which represents the gravitational vector field, г which is Newton's gravitational constant, m for the mass of the object creating the gravitational field, r for the distance between the masses, R for the displacement between the masses, and ф which represents the negative gravitational potential. The speaker is unsure of why the problem is considered unsolvable, as it can be solved using the given equations and variables.
  • #1
obing007
4
0
Q. a particle of mass m is located outside a uniform sphere of mass M at a distance R from its centre find:-

a) potential energy of gravitational interaction of the particle and the sphere

b)the gravitational force which sphere exerts on the particle



using G=-г m/r^3 R and ф=-г m/r this is unsolveable


it would be kind enough of anybody who can help
 
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  • #2
obing007 said:
Q. a particle of mass m is located outside a uniform sphere of mass M at a distance R from its centre find:-

a) potential energy of gravitational interaction of the particle and the sphere

b)the gravitational force which sphere exerts on the particle
using G=-г m/r^3 R and ф=-г m/r this is unsolveable
Could you define your variables? The representations you are using are a little different from the way I'm familiar with. To me, the best I can tell from your equations,
  • G: The gravitational vector field. (Force per unit mass, at a particular location R.)
  • г: Newton's gravitational constant.
  • m: mass of the object* creating the gravitational field. (*either a point particle or spherically symmetrical object.)
  • r: The magnitude of the distance between the mass creating the field and the test mass.
  • R: The vector displacement between the mass creating the field and the test mass. The direction is from the mass creating the field to the test mass.
  • ф: [strike]Negative[/strike] gravitational potential. (i.e. [strike]the negative of the[/strike] potential energy per unit mass, relative to r = ∞)
However, I'm not sure that's exactly what you mean. (I typically use different variables to represent some of those things. But we can use your notation if you'd like.)

If my above assumptions are corect, why do you think the problem is unsolvable? (It seems perfectly solvable to me in terms of masses 'm', 'M', distances 'r', 'R', and constant 'г'.)

[Edit: Nevermind what I originally wrote about the "negative of" gravitational potential energy. The value of ф is naturally a negative number with respect to ∞, as your equation shows. I've corrected my mistaken phrasing.]
 
Last edited:

1. What is the formula for calculating the force between a uniform sphere and a particle outside of the sphere?

The formula for calculating the force between a uniform sphere and a particle outside of the sphere is given by the equation F = G * (m1 * m2) / r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the sphere and the particle respectively, and r is the distance between the center of the sphere and the particle.

2. How does the distance between the sphere and the particle affect the force between them?

The force between a uniform sphere and a particle outside of the sphere is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases and vice versa.

3. What is the direction of the force between a uniform sphere and a particle outside of the sphere?

The force between a uniform sphere and a particle outside of the sphere is always attractive, meaning that it pulls the two objects towards each other. The direction of the force is along the line connecting the center of the sphere and the particle.

4. How does the mass of the sphere and the particle affect the force between them?

The force between a uniform sphere and a particle outside of the sphere is directly proportional to the product of their masses. This means that as the mass of either object increases, the force between them also increases.

5. Can the force between a uniform sphere and a particle outside of the sphere be repulsive?

No, the force between a uniform sphere and a particle outside of the sphere is always attractive. This is because the equation for gravitational force only accounts for the magnitude of the masses and the distance between them, and not their signs. Therefore, the force will always be attractive regardless of the masses involved.

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