Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 130,000 kg and a velocity of 0.300 m/s, and the second having a mass of 115,000 kg and a velocity of -0.120 m/s. (The minus indicates direction of motion.) What is their final velocity

Their final velocity is 0.103 m/s

Explanation:

Given;

mass of the first car, m₁ = 130,000 kg

mass of the second car, m₂ = 115,000 kg

initial velocity of the first car, u₁ = 0.300 m/s

initial velocity of the second car, u₂ = -0.120 m/s

Let their final velocity, = v (since they were coupled together, they will have common final velocity)

Apply the principle of conservation of linear momentum;

Total momentum before collision = Total momentum after collision

m₁u₁ + m₂u₂ = v(m₁ + m₂)

(130,000 x 0.3) + (115,000 x -0.12) = v(130,000 + (115,000)

39000 -13800 = 245,000v

25200 = 245,000v

v = 25200 / 245,000

v = 0.103 m/s

Therefore, their final velocity is 0.103 m/s

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