Mechanics: Explosion of an Object Vector Diagram

[Lnewqban]

In the following diagram, consider vector R to represent the momentum before any explosion resulting in three fragments.
Consider vectors A, B and C to represent the moment of each fragment after explosion.

Note that the condition of conservation of momentum implies that vector R and the sequence of vectors A, B and C must have a common origin and end.
The momentum of the center of mass is the same before and after the explosion, whether or not the fragments are flying together or dispersing.

 

[AN630078]

In the following diagram, consider vector R to represent the momentum before any explosion resulting in three fragments.
Consider vectors A, B and C to represent the moment of each fragment after explosion.

Note that the condition of conservation of momentum implies that vector R and the sequence of vectors A, B and C must have a common origin and end.
The momentum of the center of mass is the same before and after the explosion, whether or not the fragments are flying together or dispersing.

View attachment 269092

Thank you for your reply. I read the hyper physics page on vectors and found it very informative and helpful thank you So would the error in my latest diagram be that although the vectors share a common origin they do not share a common end, as P3 ends at the origin? How could I amend this because I had previously drawn that P3 ends at the end of P (see post 9) was this correct? I will redraw this diagram more clearly to show what I mean.

 

[Lnewqban]

Thank you for your reply. I read the hyper physics page on vectors and found it very informative and helpful thank you So would the error in my latest diagram be that although the vectors share a common origin they do not share a common end, as P3 ends at the origin? How could I amend this because I had previously drawn that P3 ends at the end of P (see post 9) was this correct? I will redraw this diagram more clearly to show what I mean.

Exactly!
If the after-explosion vectors make a closed loop, that means that the combined or system momentum and velocity is zero, which is not what we have.

 

[AN630078]

Exactly!
If the after-explosion vectors make a closed loop, that means that the combined or system momentum and velocity is zero, which is not what we have.

Ok, yes that does make sense. Thank you very much for your reply and all of your help. I will post my amended diagram shortly