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

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 = 19.5 kg and m2 = 42.0 kg. In addition, you are provided with the following graph, which shows the momentum of car #1 before, during and after the collision. Determine the velocity of car #2 before the collision.

_______________m/s

Explanation / Answer

Let V velocity of car No. 1, V velocity of car No. 2,
and V common velocity of car 1 and car 2. after collision.
The graph shows the momentum of Car-1 after collision = 40 V = (40/19.5)
Momentum of car No. 2 after collision = 42* V = 42*(40/19.5)
Total Momentum after collision = 40 + 42*(40/19.5) = 126.153
Total momentum before collision = 100 + 42*V
Applying the principle of conservation of Momentum befor and after:
100 + 42*V = 126.153 V = (126.153 - 100) / 42 = 33.714 / 41 = 0.622 m /sec.
Velocity of car #2 before the collision. = 0.6226 m/sec.

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