Question

As shown in the figure below, cars #1 and #2 are sliding across a horizontal frictionless surface.

The cars are equipped with a coupling arrangement similar to the one on railroad cars. Car #1 overtakes car #2 and they have a totally inelastic collision and become coupled together. You know the mass of each car; m1 = 18.0 kg and m2 = 43.0 kg. In addition, you are provided with the following graph, which shows the momentum of car #1 before, during and after the collision.

The graph provides the following information:

- Momentum on the y-axis (kg·m/s) and t (in seconds) on the x-axis)

- The line starts out at 100 kg·m/s and stays there for awhile, then slopes down at an even rate, and then levels back out at 40 kg·m/s

Answer 1

In an elastic collision, the total momentum of the system is conserved. In a completely inelastic collision, the two cars stick together after the collision.

Step-by-step explanation:

In an elastic collision, the total momentum of the system is conserved. The change in momentum of the two-car system is equal to the initial momentum of car A plus the initial momentum of car B. Since the two cars are initially moving in opposite directions, the change in momentum of the system is equal to the sum of the magnitudes of their initial momenta, that is, 24 kg·m/s + 12 kg·m/s = 36 kg·m/s.

In a completely inelastic collision, the two cars stick together after the collision. The change in momentum of the two-car system is equal to the initial momentum of car A plus the initial momentum of car B, just like in an elastic collision. So the change in momentum of the system in this case is also equal to 36 kg·m/s.