Force of Gravitation, Determining dM

[TimeInquirer]

Homework Statement

After doing some general solution problems for the force of gravitation on various objects (rods, thin rings, semi-circles, etc), I have noticed that dM varies drastically. For instance on a rod, dM=(M/L)dr while for a semi-circle its (M/2*pi*r)*Rd(theta). I was not able to identify a pattern for determining dM. Can someone help?

Homework Equations

F=Gm1m2/r^2 and F=Gmdm/r^2[/B]
dM=...

The Attempt at a Solution

Was not able to identify a pattern[/B]

 

[SteamKing]

Homework Statement

After doing some general solution problems for the force of gravitation on various objects (rods, thin rings, semi-circles, etc), I have noticed that dM varies drastically. For instance on a rod, dM=(M/L)dr while for a semi-circle its (M/2*pi*r)*Rd(theta). I was not able to identify a pattern for determining dM. Can someone help?

Homework Equations

F=Gm1m2/r^2 and F=Gmdm/r^2[/B]
dM=...

The Attempt at a Solution

Was not able to identify a pattern[/B]

Why do you think there is some pattern to identifying dM?

The objects which you mentioned in the OP all have different geometries, and there is no one method which will easily treat them all. For instance, thin rods are best analyzed using cartesian coordinates; circular disks are probably handled easier by using polar coordinates.

You work problems like these to help you develop some experience in selecting the proper method of analysis.

 

[TimeInquirer]

Considering what you said, do you mind determining if my analysis of this problem is correct? A thin rod of length 2a has uniform density. The rod is centered at the origin along the x axis. Write an integral expression for the x and y components of the gravitational field at the point (x, y, 0). I can't seem to able to related cos(theta)dx/r^2 where I boxed it in on my paper. Look at top left for a picture.

 

[SteamKing]

Considering what you said, do you mind determining if my analysis of this problem is correct? A thin rod of length 2a has uniform density. The rod is centered at the origin along the x axis. Write an integral expression for the x and y components of the gravitational field at the point (x, y, 0). I can't seem to able to related cos(theta)dx/r^2 where I boxed it in on my paper. Look at top left for a picture.

In the problem from the attached post, you are trying to determine the effect of gravity on the rod, I think, w.r.t. the point (a,b), but it's not entirely clear from your description.

 

[TimeInquirer]

It is with respect to the rod

 

[SteamKing]

w.r.t. = with respect to

 

[TimeInquirer]

Sorry, just got it. What do you suggest then?