# Are internal forces necessary for particles to form a system?

• ognik
In summary, if particles are a system, then the internal forces cancel and we can consider all external forces to be acting through the center of mass, and nett force = total of external forces. The equation of motion for the relative coordinate would be μ(2nd derivative of r) = F1 on 2, where r = r2 - r1, and F1 on 2 is the force exerted by 1 on 2.
ognik
Just something, probably obvious, that I want to be sure about, please confirm or correct the following:

If we have 2 (or n) particles, they are a system only if there are internal forces between them? So, no internal forces implies forces on one won't affect the other...

If particles are a system, then the internal forces cancel and we can consider all external forces to be acting through the center of mass, and nett force = total of external forces. The eqtn of motion would be something like ## M \frac{d^2 r}{dt^2} ##?

The 'relative coordinate vector' would be the position vector of the center of mass? What would be the difference between the eqtn of motion in this sense, as opposed to the one above? Enlightenment much appreciated.

You can always call it "system". The system is just boring if there is no interaction between its components.
ognik said:
If particles are a system, then the internal forces cancel and we can consider all external forces to be acting through the center of mass, and nett force = total of external forces.
Sometimes you can split the analysis up like that, sometimes (e. g. if the external force depends on the position) you cannot.

ognik said:
Just something, probably obvious, that I want to be sure about, please confirm or correct the following:

If we have 2 (or n) particles, they are a system only if there are internal forces between them? So, no internal forces implies forces on one won't affect the other...

If particles are a system, then the internal forces cancel and we can consider all external forces to be acting through the center of mass, and nett force = total of external forces. The eqtn of motion would be something like ## M \frac{d^2 r}{dt^2} ##?

The 'relative coordinate vector' would be the position vector of the center of mass? What would be the difference between the eqtn of motion in this sense, as opposed to the one above? Enlightenment much appreciated.
In a 2-particle system, the relative coordinate vector is the position vector of one particle relative to the other.

In a 2-particle system, the relative coordinate vector is the position vector of one particle relative to the other.

Does that mean making one particle at the origin, then the relative position vector if the position vector of the other? Which would be the same as one position vector minus the other position vector?

What would be the eqtn of motion, I think ## F_1 + F_2 = (m_1 + m_2) \frac{d^2r}{dt^2} ## ?

The relative coordinate is indeed the position vector of one particle relative to the other. Your equation of motion for the relative coordinate is not correct. The correct equation, in the absence of external forces is,

μ(2nd derivative of r) = F1 on 2

where r = r2 - r1, and F1 on 2 is the force exerted by 1 on 2. μ is the reduced mass m1 m2 / (m1+m2)

Reduced mass (at centre of mass?) now understood, thanks

Chandra Prayaga said:
in the absence of external forces

But in this case there are external forces, ##F_1## on ##m_1##, and ##F_2## on ##M_2##?
And don't the internal forces cancel?

ognik said:
Reduced mass (at centre of mass?)
The reduced mass doesn't have a position.
ognik said:
And don't the internal forces cancel?
Not for the relative position.

ognik said:
Reduced mass (at centre of mass?) now understood, thanks
But in this case there are external forces, ##F_1## on ##m_1##, and ##F_2## on ##M_2##?
And don't the internal forces cancel?
Here is the complete derivation. Check the uploaded Word document:

#### Attachments

• 2-particle system.docx
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ognik
Chandra Prayaga said:
Here is the complete derivation. Check the uploaded Word document:
Incidentally, following your last question, the internal forces cancel only in the CM equation of motion, not for the relative coordinate.

ognik
Thanks - good summary doc.

## 1. What are the types of forces that act on a particle system?

There are four types of forces that act on a particle system: gravity, electromagnetic, strong nuclear, and weak nuclear. Gravity is the force of attraction between two objects with mass. Electromagnetic force is the force of attraction or repulsion between electrically charged particles. Strong nuclear force holds the nucleus of an atom together, while weak nuclear force is responsible for radioactive decay.

## 2. How do forces affect the motion of a particle system?

Forces can cause a particle system to accelerate, decelerate, or change direction. The magnitude and direction of the force determine the resulting motion of the particles. If the forces acting on a particle system are balanced, the particles will remain at rest or continue moving at a constant speed in a straight line. If the forces are unbalanced, the particles will accelerate in the direction of the net force.

## 3. How do you calculate the net force on a particle system?

The net force on a particle system is the vector sum of all the individual forces acting on the particles. To calculate the net force, you must first determine the magnitude and direction of each force. Then, add all the forces together using vector addition. The resulting vector is the net force on the particle system.

## 4. How does mass affect the forces on a particle system?

According to Newton's Second Law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a particle system with a greater mass will experience a smaller acceleration for the same net force compared to a system with a smaller mass. Therefore, mass plays a crucial role in determining the effects of forces on a particle system.

## 5. Can forces on a particle system be balanced?

Yes, forces on a particle system can be balanced. When the net force on a particle system is zero, the forces are considered to be balanced. This means that the particles will remain at rest or continue moving at a constant speed in a straight line. In real-world scenarios, it is rare to have perfectly balanced forces, as there is always some friction or air resistance present. However, understanding how to balance forces is crucial in engineering and design applications.

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