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 = 41.0 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.

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) =2.051m/s
Momentum of car No. 2 after collision = 41* V? = 41*(40/19.5)
Total Momentum after collision = 40 + 41*(40/19.5) = 124.091
Total momentum before collision = 100 + 41*V?
Applying the principle of conservation of Momentum befor and after:
100 + 41*V? = 124.091 ? V? = 0.5875m /sec.
Velocity of car #2 before the collision. = 0.5875 m/sec.

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