Help Gravitational Force Question.

[eco742]

A mass M is ring shaped with radius r. A small mass m is placed at a distance x along the ring's axis. Show that the gravitational force on the mass m due to the ring is directed inward along the axis and has magnitude

F= GMmx/(x^2+r^2)^3/2

Hints:
-Think of the ring as made up of many small point masses dM
-Sum over the forces due to each dM
-Use symmetry

I am just confused on where to begin! Any help would be greatly apperciated!

 

[housemartin]

draw a ring (or a circle) on paper, take one little part of it, the force of that part, which mass is dM is F = GmdM/(L^2), and L is distance from dM to m. You can find this distance using Pythagoras theorem (L^2 = x^2 + r^2). Also notice, that the little element dM has his opposite element on the other side of the circle, which exerts same force (in magnitude) as dM. Draw those two forces in other paper ;] then you maybe notice that component of those forces along rings radius cancels, and stays only the component along rings axis if you sum them.
hope this help a little, I am not very good at writing thoughts ;]

 

[jack action]

To make the problem easier, imagine that instead of a ring you have 4 different masses of mass M/4, at a distance r from the axis. Find the resultant gravity force for each mass M with the mass m at a distance x (don't forget a force is a vector). Then separate all those forces into 2 components: one along the axis, the other perpendicular to it. You will find that all components perpendicular to the axis will cancel each other and the net resultant force will be the sum of all the ones parallel to the axis.

 

[eco742]

Great, thanks that was helpful!