You are a working for a rail company and are studying the effects of rain on open train cars. As a test case, you consider a 6,325 kg open train car rolling on frictionless rails at 27.4 m/s when it starts pouring rain. If 1,250 kg of rain fall into the train car over a few minutes, what will the car's speed become?

22.87 m/s

Explanation:

mass of the train car = 6325 kg

velocity of the train = 27.4 m/s

mass of rain that falls into the train car = 1250 kg

the train car's final speed = ?

Initially, the train has a momentum of

momentum = (mass of train car) x (velocity of the train car)

momentum = 6325 x 27.4 = 173305 kg-m/s

When the mass of water falls into the train, the mass of the system increase to include that of the mass of the rain, but the momentum of the system remains the same according to the laws of conservation of linear momentum.

The new mas = (mass of train car) + (mass of rain)

==> 6325 + 1250 = 7575 kg

The final velocity of the system can be found by using the relationship

initial momentum = final momentum

Final momentum of the system = (final mass of the system) x (final velocity of the system)

==> 7575 x v = 7575v

where v is the final mass of the train car-rain system

Equating the final and initial momenta together, we have

173305 = 7575v

v = 173305/7575 = 22.87 m/s

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