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 = 44.0 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

here,

m1 = 19.5 kg

m2 = 44 kg

initial speed of car 1, u1 = 100 /m1

u1 = 100/19.5 = 5.13 m/s

final speed of cars , v = 40/m1

v = 40/19.5 = 2.05 m/s

let the initial speed of car 2 be u2

using conservation of momentum

m1*u1 + m2*u2 = ( m1 + m2) * v

19.5 * 5.13 + 44 * u2 = ( 19.5 + 44) * 2.05

u2 = 0.685 m/s

the speed of m2 before collison is 0.685 m/s

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