The Law of Gravitation

In summary: The force of b on A is equal to GMm/r^2, where r is the distance between A and B. The force of c on A is also equal to GMm/r^2, where r is the distance between A and C. To find the net force, we can set these two equations equal to each other and solve for x, the distance between A and C. In summary, to find the net gravitational force on particle A from particles B and C, we need to set the force from B equal to the force from C and solve for the distance x between A and C.
  • #1
TS656577
62
0

Homework Statement


One dimension. In Fig. 13-33, two point particles are fixed on an x-axis separated by distance d. Particle A has mass mA and particle B has mass 7.00 mA. A third particle C, of mass 75.0 mA, is to be placed on the x-axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero?

Homework Equations


F=sqrt((GMm)/r^2) Where G=6.67E-11


The Attempt at a Solution


I know that M=75 and m=7. Multiplying that by 6.67E-11 I got 3.5E-8/r^2. If i set that equal to 0, then I the r to disappear
 

Attachments

  • fig13-5.gif
    fig13-5.gif
    1.8 KB · Views: 637
Physics news on Phys.org
  • #2
Here you are going to have two forces on A, the force from B and the force from C.

HINT:

You want the net force on A to be zero:

[tex]\Sigma F = 0[/tex]

Can you write the net force in terms of the force from B and C?
 
Last edited:
  • #3
So would it be the gravitational potential energy between A and C plus the GPE of A and B and add them? and set that = to F(theta)? because in the picture, there is no C
 
  • #4
Personally, I think it would be more straight forward to work with Forces here and not potential energies. Also, I do not know why you are using a theta variable, which I assume is an angle. All three masses will be on the same line. There is no C in the picture because you need to figure out where to place it so the net force on A is 0 N. That is the problem.

Try answering these questions to start:

Can you give me a formula for the force from B, in terms of the distance d?

If so, then can you give me a formula for the force from C in terms of x, the position you want to find?

If you can do that as well can you write the net force in terms of the above quantities you just found?
 
  • #5
The forces need to cancel out. This means that the force of c on a and b on a must be equal and opposite, right? No need to work with angles as G01 said, since you're restricted to one dimension.
 

What is the Law of Gravitation?

The Law of Gravitation, also known as Newton's Law of Universal Gravitation, is a fundamental physical law that explains the force of attraction between two objects with mass.

Who discovered the Law of Gravitation?

The Law of Gravitation was first described by Sir Isaac Newton in 1687 in his book "Philosophiæ Naturalis Principia Mathematica". However, the concept of gravity has been studied and observed by many scientists throughout history.

How does the Law of Gravitation work?

The Law of Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them. This means that the greater the mass of an object, the stronger its gravitational pull, and the farther apart two objects are, the weaker the gravitational force between them.

What are some real-life examples of the Law of Gravitation?

The Law of Gravitation can be observed in many everyday situations, such as the movement of planets around the sun, the falling of objects towards the Earth, and the tides caused by the gravitational pull of the moon on the Earth's oceans.

Is the Law of Gravitation always accurate?

While the Law of Gravitation is a well-established and widely accepted scientific principle, it is not always accurate in extreme cases, such as at the quantum level or in the presence of extremely strong gravitational fields, where the laws of general relativity come into play.

Similar threads

  • Introductory Physics Homework Help
Replies
16
Views
496
  • Introductory Physics Homework Help
Replies
3
Views
276
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
5
Views
524
  • Introductory Physics Homework Help
2
Replies
42
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
819
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
784
  • Introductory Physics Homework Help
2
Replies
41
Views
2K
Back
Top