Force of Gravitation, Determining dM

In summary, there is no one method that can easily treat all objects with different geometries when determining the dM for the force of gravitation. It is important to analyze each object individually and develop experience in selecting the proper method of analysis. In a specific example, for a thin rod of length 2a with uniform density centered at the origin along the x axis, an integral expression for the x and y components of the gravitational field at the point (x,y,0) can be determined by relating cos(theta)dx/r^2.
  • #1
TimeInquirer
32
0

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]
 
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  • #2
TimeInquirer said:

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.
 
  • #3
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.
 

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  • #4
TimeInquirer said:
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.
 
  • #5
It is with respect to the rod
 
  • #6
w.r.t. = with respect to
 
  • #7
Sorry, just got it. What do you suggest then?
 

FAQ: Force of Gravitation, Determining dM

What is the force of gravitation?

The force of gravitation is a natural phenomenon that describes the attraction between two objects due to their mass. It is a fundamental force in the universe and is responsible for keeping planets in orbit around the sun, as well as objects on Earth from floating away into space.

How is the force of gravitation calculated?

The force of gravitation is calculated using Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

What is the unit of measurement for the force of gravitation?

The unit of measurement for the force of gravitation is Newtons (N). This unit is named after Sir Isaac Newton, who first described the concept of gravity.

How do you determine the mass (dM) of an object using the force of gravitation?

To determine the mass (dM) of an object, you can use the equation F=ma, where F is the force of gravitation, m is the mass of the object, and a is the acceleration due to gravity. By rearranging the equation to solve for m, you can calculate the mass of the object.

Can the force of gravitation be measured on different planets?

Yes, the force of gravitation can be measured on different planets. However, the value of the force will vary depending on the mass and distance of the planet. For example, the force of gravity on Earth is much stronger than on the moon, due to Earth's larger mass and closer distance to the objects on its surface.

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