Questions about 3 colliding object. Can i get some help?

[Botond]

The exercise is:

There are three point-like objects in space - far from any other objects - such that their initial velocities are zero, and the distance between any two is the same d. Two of the objects have the same mass of m, and the mass of the third one is 2m. Due to the gravitational force the objects begin to move and they collide with each other.

a) How much distance do they cover until they meet?

b) How much time elapses until the collision of the objects?

I tried to use F=ma, F=G*m₁*m₂*1/r², and a=d²x/dt² to get the time-distance function, but i could't do anything with the sin(alpha). The other problem is i can't find out the lane of the objects.

 

[phinds]

Do you have any sense of the KIND of paths each of the three would take? Can you draw a rough diagram of what the 3 paths would look like from start to collision?

Just as a side note, it is incorrect to say "such that their initial velocities are zero". To be correct, you have to say "such that their initial velocities are zero RELATIVE TO EACH OTHER". If you think this is just semantics, then you misunderstand the nature of motion.

 

[Botond]

Do you have any sense of the KIND of paths each of the three would take? Can you draw a rough diagram of what the 3 paths would look like from start to collision?

Just as a side note, it is incorrect to say "such that their initial velocities are zero". To be correct, you have to say "such that their initial velocities are zero RELATIVE TO EACH OTHER". If you think this is just semantics, then you misunderstand the nature of motion.

I know that the 2m mass will go straight, but i don't knoe the 2 other's path.

 

[phinds]

I know that the 2m mass will go straight, but i don't knoe the 2 other's path.

Yes, and that's a good start. Think about where they start out towards and where they end up at. That will tell you whether or not they go straight. Can you draw the initial force vectors? That will give you a good clue.

 

[Botond]

Yes, and that's a good start. Think about where they start out towards and where they end up at. That will tell you whether or not they go straight. Can you draw the initial force vectors? That will give you a good clue.

But i don't know where they will meet. And the forces aren't constant, so i think them flow can be curve.

 

[phinds]

But i don't know where they will meet. And the forces aren't constant, so i think them flow can be curve.

I agree. I think the heavy one travels in a straight line but the other two curve just a bit. I have not done any math to back this up so it could be wrong. I'm not sure what you point is about "the forces aren't constant". Of course they aren't constant, but that doesn't really seem to be the question, or to solve the issue of their trajectories. The point is that the heavy one is traveling along the line of motion of the center of gravity of the three (and so will continue in a straight line) but the other two are not and so, I think, will not stay on a straight line.

It may be that the center of gravity of the 3 bodies does not change as they move, in which case out belief about the two curved paths will be wrong. As I said, I haven't done any math on this.