The problem referred to in this question is missing and it is;
Two hockey pucks of identical mass are on a flat, horizontal ice hockey rink. The red puck is motionless; the blue puck is moving at 2.5 m/s to the left. It collides with the motionless red puck. The pucks have a mass of 15 g. After the collision, the red puck is moving at 2.5 m/s, to the left. What is the final velocity of the blue puck?
Answer:
The condition is that p_f - p_i which is the change in momentum will not be equal to zero but equal to the impulse (Ft).
Explanation:
In the problem described, by inspection, we can say that since there is no friction, we have a closed system and thus momentum is conserved.
Since momentum is conserved, we can say that;
Initial momentum(p_i) = final momentum(p_f)
Now, in this question we are told that some friction wants to be introduced on the ice and it's possible to still use conservation of momentum.
From impulse - momentum theory, we know that;
Impulse = change in momentum
Impulse is zero when no force is acting on the ice and we have; 0 = p_f - p_i
This will yield initial momentum = final momentum.
Now, since a force is applied, we know that impulse is; J = F × t
Thus;
Ft = p_f - p_i
Where F is the force due to friction.
Thus, the condition is that p_f - p_i will not be equal to zero
