Understanding Newtonian Gravitation

[Quantumsatire]

So for a point mass in an enclosed shell, the net force of gravity is zero (similar to electricity in a Faraday cage I presume). However, what happens when that point mass is placed in side the ring of mass m and uniform density. Say the outer shell has radius r and inner shell has radius x, so the region r-x is a massed shell/ring. How would you find the net force of gravity?

 

[BobG]

If the outer shell alone gives you a net force of zero, then it can be ignored.

You only consider the inner shell and calculate your force in the normal way.

 

[Puneeth423]

So for a point mass in an enclosed shell, the net force of gravity is zero (similar to electricity in a Faraday cage I presume). However, what happens when that point mass is placed in side the ring of mass m and uniform density. Say the outer shell has radius r and inner shell has radius x, so the region r-x is a massed shell/ring. How would you find the net force of gravity?

Net gravitational force on point mass by ring will be always zero. Consider the entire mass of ring as small point equal masses. For every point mass on ring, there will be another point mass symmetrically opposite on the ring. Net force by two opposite masses on the point mass inside cancel out. Thus, net gravitational force is zero

 

[sophiecentaur]

So for a point mass in an enclosed shell, the net force of gravity is zero (similar to electricity in a Faraday cage I presume). However, what happens when that point mass is placed in side the ring of mass m and uniform density. Say the outer shell has radius r and inner shell has radius x, so the region r-x is a massed shell/ring. How would you find the net force of gravity?

Do you mean spherical shell or an annulus? They are not the same and the shell theorem only applies to a spherical shell.

 

[PJC01]

I would like to clarify that there are some inaccuracies in the content provided. Firstly, the concept of Newtonian gravitation applies to all objects with mass, not just point masses. Additionally, the concept of a Faraday cage is related to the behavior of electric fields, not gravitational fields.

To answer the question at hand, the net force of gravity on a point mass placed inside a ring of mass with uniform density can be calculated using the principle of superposition. This means that we can break down the ring into smaller, infinitesimal masses and calculate the individual gravitational forces between the point mass and each infinitesimal mass. These forces can then be vectorially added to find the net force of gravity on the point mass.

The calculation for the net force of gravity would involve integrating the gravitational force equation, which takes into account the masses, distances, and the universal gravitational constant. The result would depend on the specific values of the masses and radii involved in the problem.

It is important to note that the net force of gravity on the point mass would not be zero in this scenario, as there are multiple masses present and their gravitational forces would not cancel out completely. This is in contrast to the situation described in the first part of the content, where the net force of gravity would indeed be zero due to the symmetry of the enclosed shell.

In summary, the net force of gravity on a point mass placed inside a ring of mass with uniform density can be calculated using the principle of superposition and the gravitational force equation. This concept is fundamental to our understanding of Newtonian gravitation and is applicable to a wide range of scenarios in physics.