Reference points in a moving system

[klkc]

Homework Statement

I have been looking at one of my review sheets, and do not know how the professor got the equations.

Here is the relevant paragraph:

Consider two particles of mass m1 and m2 isolated within a box, with respect to which
they have velocities u1 and u2. The box is moving at a steady v0 relative to some external
frame of reference. At some instant, the particles collide and coalesce. The momentum just
before and just after this event must be respectively

Homework Equations

P_before = mass₁(u₁+v₀) + mass₂(u₂+v₀)

P_after = (mass₁+mass₂)(v₁+v₀)

The Attempt at a Solution

The first equation I understand, but doesn't the second equation imply that both masses are traveling the same speed? Why would two different masses collide and then travel the same velocity?

I'm confused because the paragraph says it MUST BE this, implying I'm not getting something, rather than ASSUME, which would be setting conditions.

 

[Filip Larsen]

The problem description describes that the two particles "collide and coalesce". The later means that the two particles stick together after the collision and, hence, they travel with same velocity. Given a priori that the two particle stick together, the momumentum written as P_after is a "must be" thing (assuming here that v₁ is the velocity of the two particles relative to the box after collision).

 

[klkc]

Thanks for the reply!