Question :
two railroad boxcars weighing $50,000$ N each are approaching one another at $5$ m/s and $7$ m/s. After they collide and couple together, how fast will the combination be moving and in which direction?
From the problem I have the following setup:
Using $C_i$ as $car_i$ we have weight $C_1 = $ weight $C_2 = 50,000 N$ Then using $g = 10$ we have:
$$ \text{mass } C_1, C_1 = 5000 kg $$
Conservation of linear momentum states
$$ m_1 v_1 + m_2 v_2 = m_1 u_1 + m_2 u_2 $$
As $m_1 = m_2$ this gives
$$ m (v_1 + v_2) = m (u_1 + u_2) $$
Using given values (and taking left to be negative) we have
$$ 5 - 7 = u_1 + u_2 $$
Then we know that, as the cars stick together after the collision they're moving in the left direction, with a velocity of $-2 m/s$
Assuming that the above working is correct - I'm not sure how I would have determined whether or not the cars would have stuck together if the problem hadn't stated that they had? Do I need information about the materials to answer that?
Hopefully the working, and reasoning, is clear and valid.