The center of Mass perfectly match the center of Force->

In summary, in a system of several masses, the center of force does not always coincide with the center of mass in geometrical space. This is because the center of force is the point where the sum of all forces acting on the masses is concentrated, while the center of mass is the point where the mass of the system is evenly distributed. In a uniform gravitational field, the center of force and center of mass may coincide, but this may not be true for very large objects. This is demonstrated by the example of a spacecraft falling to Earth, where the force exerted on one side causes it to turn, thus not coinciding with the center of mass. Additionally, the concept of center of force is based on the sum of energies,

The center of force is same as the center of mass

  • Yes

    Votes: 0 0.0%
  • No

    Votes: 0 0.0%
  • Depends (show us on what)

    Votes: 4 100.0%

  • Total voters
    4
  • #1
deda
185
0
In a system of several masses the center of force has same position with the center of mass in the geometrical space;

Yes or No?

Please explain why!
 
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  • #2
I think the answer is no.

In my physics notes, it says, "If a body is placed in a uniform field of gravity then its centre of gracity will concide with the centre of mass. However, this may not be true for a very large object."

Well, I don't know what is one of the examples of "a very large object".
 
  • #3
Originally posted by KLscilevothma
I think the answer is no.

In my physics notes, it says, "If a body is placed in a uniform field of gravity then its centre of gracity will concide with the centre of mass. However, this may not be true for a very large object."

Well, I don't know what is one of the examples of "a very large object".
Does your notes contain equations to support that?
 
  • #4
I think some logic can be useful.
Think an object which you can hold. Keep it steady and release it. You'll see that it does't turn around(neglecting air friction).
But think a very large spacecraft (its length is two times the diameter of the earth) falling(!) to the Earth. A much greater force is exerted to the side which is nearer the earth, so it starts to turn. Obviously CM doesn't match FM.
Am I wrong?

But did you mean where there is no gravitational force between the masses by "center of force"?
 
  • #5
I think you are right, kishtik. The question is just too vague. Are we talking about a situation in which there is a uniform gravitational field and there are no other forces acting on an object?
 
  • #6
Originally posted by deda
In a system of several masses the center of force has same position with the center of mass in the geometrical space;

Yes or No?

Please explain why!

Please defined center of force
 
  • #7
Originally posted by Arcon
Please defined center of force
Actually, that was something that I wanned to request from some of you. Now that I'm being ask for it I'll say:

We have a system of several masses in empty space.
There is force field in every point of space.
The force center will then be exactly that point which contains the sum of all forces each mass is subjected to.
But don't count one force twice as Newton's III sugests while summing the forces.This requires that you relate geometry with force.
My only answer will then be based on summing energies.

[tex]\sum E_i = E_{cf}[/tex]

Since for me [tex]E_i=F_iD_i[/tex] where D is the distance and F is force in D from CF then

[tex]\sum F_iD_i=F_{cf}D_{cf}[/tex]

also

[tex]\sum F_i=F_{cf}[/tex] and [tex]\sum D_i=D_{cf}[/tex]
=> [tex]\sum_{i<>j} F_iD_j=0[/tex]
is the condition for balance in the system.

Now, be soft with your critics. I'm breaking the ice here.
 
  • #8
Originally posted by deda
Now, be soft with your critics. I'm breaking the ice here.

I'm not a native speaker of English. I only tried to say that I did't know deeply what KLscilevothma's notes were about and I would do some guessing and mental experiments etc. I am shocked as I realized what "Some logic can be useful." meant. They do not teach things like this at school or course. I'm sorry.
 
  • #9
Okay, here goes a more "mathematical-style" proof of a physics problem I can't honestly claim I understand.

Suppose center of force = center of mass. Then take a system of such objects where this is true, and for which there is a single (nonzero) center of force.

Add an object which has no force applied to it that is not centered on the center of mass of the system. Then the collective new system has a different center of mass, but the same center of force. So the center of force and the center of mass are not the same.

Quel Est Des-probleme?
 
  • #10
Not enough information given: you can apply a force wherever you want it.

If you're talking about gravity though, the answer is no.
 

What is the center of mass?

The center of mass is a point in a system where the total mass of the system can be considered to be concentrated. It is the point at which an object will balance in all directions.

What is the center of force?

The center of force is a theoretical point where the total force acting on an object can be considered to be applied. It is the point at which the object will experience balanced forces in all directions.

Why is it important for the center of mass and center of force to match?

When the center of mass and center of force perfectly match, an object will be in a state of equilibrium. This means that it will not have any unbalanced forces acting on it, and it will not experience any translational or rotational motion.

How is the center of mass and center of force determined?

The center of mass is determined by considering the distribution of mass within an object or system. The center of force can be determined by analyzing the forces acting on an object and calculating the point at which they balance out.

What are some real-world applications of understanding the center of mass and center of force?

Understanding the center of mass and center of force is important in fields such as physics, engineering, and biomechanics. It is used in designing stable structures, calculating the movement of objects, and predicting the behavior of systems under different forces.

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