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A railroad car of length L and mass m0 when empty is moving freely on a smooth horizontal track while being loaded with sand from a stationary chute at a rate dmdt=q Knowing that the car was approaching the chute at a speed v0. (Initially at t = 0sec)Total length of the sand equal to the Railroad car length L. DetermineThe speed of the car vf at the instant when the car has cleared the chute is V0e−2qLnm0v0. The value of n is

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answer is 2.

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Detailed Solution

Let v be the velocity of the car when it has cleared x–distance as shown in figure andlet m be the mass of it (including the load) at this instant. Then thrust force on it (dueto change in mass) will be qv in backward direction. HenceFt = qv or ma = –qvor mvdvdx=−qvFrom conservation of linear momentummv = m0v0Hence  m0v0dvdx=−qvSolving this we get  Vf=V0e−qLm0v0
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A railroad car of length L and mass m0 when empty is moving freely on a smooth horizontal track while being loaded with sand from a stationary chute at a rate dmdt=q Knowing that the car was approaching the chute at a speed v0. (Initially at t = 0sec)Total length of the sand equal to the Railroad car length L. DetermineThe speed of the car vf at the instant when the car has cleared the chute is V0e−2qLnm0v0. The value of n is