Hello! I would like to ask for your help with understanding a few things connected to the following problem: 1. The problem statement, all variables and given/known data There is an (infinitly) long thread, on which small beads can move without friction. The beads with mass m are lined up on the thread with a constant distance d between them. Whe start to push one bead with the constant force F and continue to do so all the time. The velocity will eventually reach a final, constant value. What is this value of the collisions between the beads are completely inelastic? 2. Relevant equations F * Δt = Δp v * Δt = Δs 3. The solution When the first bead is accelerated, it will collide into the next one. The beads stuck together and collide in the third one, then the fourth one and so on. If the final velocity is v, the number of new beads attached to the moving "chain" in a time Δt is: n = s/d = v*Δt/d Therefore the change in mass of the moving "chain" is: Δm = m*n = m*v*Δt/d Because the velocity is now constant, the change in momentum is only due to the change in mass: F*Δt = Δp = v*Δm = v2*m*Δt/d Thus: v = (F*d/m)^(1/2) Now, there is nothing wrong with the solution. The thing I don't understant is exactly why a constant final velocity is reached. I know that when the total mass approaches infinity, the acceleration will become zero (a=F/m), but is there anything else which causes the acceleration to stop? I feel like the condiction of infinit number of beads is not directly included in the solution. I do therefore wonder: Is there any outer force which counteracts the pushing force F? I have also thught about an energy aspect. In this case, the work done by F on a distance d should equal the kinetic energy of a new bead, shouldn't it? However, this yields: v = (2F*d/m)^(1/2) , which is one factor √2 to much compared to the answer obtained in the solution above. Why? Thank you very much!