Collision of Unequal Mass Particles in a Gravitational Field

In summary, if there is a uniform gravitational field, the CMs of two particles will collide at the center of mass.
  • #1
gianeshwar
226
14
Dear friends!
If there are two particles of unequal masses in a system on which there are no external forces.When let free they collide under the influence of gravitation.
Should they always collide at CM.
If the system were under an external force of uniform gravitational field will the collision occur at CM only.
Thanks!
 
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  • #2
Draw a picture of the two particles and mark by dots the locations of their centres of mass. Draw a line between the two dots. Then draw two vector arrows, showing the direction of the gravitational force on each of the two particles.

Then you need to clearly specify what you mean by 'collide at CM'. For almost all particles, the CM is inside the particle, so it is impossible for the CMs of the two particles to touch one another. Which definition you choose will affect the answer to the second part of the question.
 
  • #3
Thanks andrewkirk! Yes I understand their centre of mass cannot touch due to their sizes as they are assumed rigid bodies.
If I assue them to be point particles then what happens?
 
  • #4
If there are no other things around, the center of mass of an n-body system does not change, whatever the individual objects do.
 
  • #5
With two point particles and no other bodies, the forces on the two bodies are along the line that connects the two particles, so they move towards one another. Is there any reason for either of them to deviate from that line? If not, they will eventually collide.

If there's a uniform gravitational field, imagine it in an x-y plane, first where the two points have the same y coordinates and the grav field points in the positive y direction. Then you can consider the vertical and horizontal components of velocity separately, because the axes are orthogonal and do not change direction. The horizontal components are the same as in the first case. So if in the first case the two particles collide at time T, what happens in the second, assuming the only difference between the two cases is the gravitational field?

More generally, the grav field may not be orthogonal to the line between the two particles. In that case, it imparts an additional horizontal acceleration to both particles, as well as the vertical accelerations. But since that horizontal acceleration is the same for both, it doesn't affect when they collide.
 
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  • #6
gianeshwar said:
Should they always collide at CM.
The geometry of the situation means that has to be correct if the bodies are points. When they are together, they are at the CM. Where else could the CM be? It has to be between them and can't be outside the system. If one body is much bigger than the other then they won't get close enough and the CM can be below the surface of one of them.
 
  • #7
Thanks mathman,andrewskirk and sophicentaur!
 

1. What is a collision between unequal mass particles in a gravitational field?

A collision between unequal mass particles in a gravitational field occurs when two objects with different masses collide in an environment where gravity is present. This can happen in various scenarios, such as a planet's atmosphere or in outer space.

2. How does gravity affect the collision of unequal mass particles?

Gravity plays a significant role in the collision of unequal mass particles. It causes the objects to accelerate towards each other and determines the force with which they collide. The more massive object will exert a greater gravitational force on the smaller object, causing it to accelerate faster towards the larger object.

3. What happens to the energy during a collision of unequal mass particles in a gravitational field?

In a collision of unequal mass particles, energy is conserved. Some of the kinetic energy of the objects will be converted into potential energy as they move closer together due to gravity. After the collision, this potential energy is converted back into kinetic energy as the objects move away from each other.

4. How does the speed of the particles affect the collision in a gravitational field?

The speed of the particles will affect the collision in a gravitational field. If the particles are moving at high speeds, the collision will be more energetic and result in a greater exchange of energy between the objects. On the other hand, if the particles are moving at slower speeds, the collision will be less energetic, and the exchange of energy will be lower.

5. How does the angle of collision affect the outcome in a gravitational field?

The angle of collision can significantly affect the outcome in a gravitational field. If the particles collide head-on, the exchange of energy will be more direct, resulting in a more significant change in the objects' velocity. However, if the particles collide at an angle, some of the energy will be deflected, resulting in a less energetic collision and a smaller change in the objects' velocity.

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