Model a rigid body made of two points linked by a rigid bar

[cicciolo]

Hi all!

I need help..:)

I need to model the dynamic of this system:

I'm in the plane (2-dimensions).
There are two points (with m1 and m2 masses) free to move with different speed vectors (in module and direction).
At some point, when the distance between them is d, the two points became a rigid body (as if between them there is a rigid bar which joins them) through a completely inelastic collision.

What are the forces acting on this system?

I hope you can help me!
Thank you in advance :)

 

[Simon Bridge]

Welcome to PF.

IRL there is no such thing as a point mass.
But you can model a lot by treating an object as though all it's mass were concentrated at it's COM - if the COMs approach close enough, then the actual objects may collide and do all kinds of things. In your case, they stuck together. So you have some sort of adhesion.

Some of the energy in the collision went into joining them together and it is going to take some effort to separate them again. Without more details the exact nature of the sticking forces cannot be ascertained.

Imagine two air-hocky pucks with velcro or double-sided tape around their rims. They'd behave much as described ... free to move in 2D on the air-table but get close enough they behave as a single rigid body.

 

[HallsofIvy]

You know the speed of each of the two particles at the time they "connect" so you know momentum and angular momentum of each and so momentum and angular momentum of the system. Those will be conserved.

 

[cicciolo]

You know the speed of each of the two particles at the time they "connect" so you know momentum and angular momentum of each and so momentum and angular momentum of the system. Those will be conserved.

So what are the forces involved in the system after the collision?
I think every particles have two forces each:
1) F1 = m*a
2) F2 = binding force directed on the "bar" joining the two particles

So, every particles will have F = F1 + F2.

I'm doing it right?

 

[Simon Bridge]

If the system is accelerating then there will be a translating force as you say - and there will be something analogous to tension. If you model the system as two point masses joined by a massless, rigid, 1D, rod - then tension will be pretty much right. The rigid bar has to resist compressing and stretching.

Hit it off-center and you can describe it as having a translating force and a torque.
If the masses are small balls rather than points then it could also have a torque about the long axis.

If you'd just set things in motion, then, after the collision, the composite object will likely be spinning - there will be a centripetal force balanced by tension in the rod.

 

[HallsofIvy]

So what are the forces involved in the system after the collision?
I think every particles have two forces each:
1) F1 = m*a
2) F2 = binding force directed on the "bar" joining the two particles

So, every particles will have F = F1 + F2.

I'm doing it right?

In your original post, you said nothing about forces acting on particles- I assumed that they were moving freely without forces. Of course, the instant the "bar" is put in place, there will be forces acting along the bar but I see no reason to calculate that force. Just use the fact that the two points and bar, as a whole will have momentum, and angular momentum about any point, equal to the system as a whole before the "bar" appears.