Calculating Gravitational Force on a Point Mass in the Presence of a Cavity

In summary, the question is how to find the force acting on a point mass without knowing the radius of the cavity and the position of the point mass. The attempted solution involves finding the radius of the cavity using the mass of the cavity and the position of the center of mass, but the radius cannot be found. The conversation suggests modeling the problem with two contributions, one from the big sphere and a "negative" contribution from the small sphere.
  • #1
maurice2705
6
0

Homework Statement


The question is presented as picture.


Homework Equations


We do not have the radius of the cavity and the position of the m. How can we find the force acted on it?


The Attempt at a Solution


r=1/(M-m)*Ʃmr=1/(M-m)*4/3ρR'^3*r where m is the mass of cavity ,R' is the radius of the cavity and r is the position of center of mass. But I can't find R'.
 

Attachments

  • Gravitation force.jpg
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  • #2
Can you solve this problem if there was no cavity? If so, perhaps you can think of a way to model the problem so that the force on the point mass is the sum of two contributions, one from the big sphere and a "negative" from the small sphere?
 

Related to Calculating Gravitational Force on a Point Mass in the Presence of a Cavity

1. What is gravitation force at a point?

Gravitation force at a point is a force between two objects that is caused by their masses and distance from each other. It is also known as the force of gravity.

2. How is the magnitude of gravitation force at a point calculated?

The magnitude of gravitation force at a point is calculated using the formula 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.

3. What is the direction of the gravitation force at a point?

The direction of the gravitation force at a point is always towards the center of mass of the two objects. This means that the force is attractive and pulls the two objects towards each other.

4. How does the distance between two objects affect the gravitation force at a point?

The gravitation force at a point is inversely proportional to the square of the distance between the two objects. This means that as the distance increases, the force decreases and vice versa.

5. What is the difference between mass and weight in terms of gravitation force at a point?

Mass is the measure of the amount of matter in an object, while weight is the measure of the force of gravity on an object. Gravitation force at a point is affected by the masses of two objects, not their weights.

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