Question

A 125,000 kg locomotive is traveling south at 1.0 m/s through a switching yard. A connected set of parked gondola cars weighing 1,750,000 kg are directly ahead. Determine the speed and direction of the completed train after the locomotive has been coupled to the cars.

Answer 1

The speed of the completed train is 0.0
`\bar 6` m/s

The direction of the completed train is South

Step-by-step explanation:

The given parameters are;

The mass of the locomotive, m₁ = 125,000 kg

The initial speed of the locomotive, v₁ = 1.0 m/s

The mass of the gondola cars, m₂ = 1,750,000 kg

The initial sped of the gondola cars, v₂ = 0

Let v₃ represents the speed of the completed train. From the principle of conservation of linear momentum, we have;

m₁·v₁ + m₂·v₂ = (m₁ + m₂)×v₃

Substituting the known values, gives;

125,000 × 1.0 + 1,750,000 × 0 = (125,000 + 1,750,000) × v₃

∴ v₃ = (125,000 × 1.0 + 1,750,000 × 0)/(125,000 + 1,750,000) = 1/15 = 0.0
`\bar 6`

v₃ = 0.0
`\bar 6` m/s

The speed of the completed train = 0.0
`\bar 6` m/s

The direction of the completed train = The direction of the locomotive = South.