Locomotive throwing sand in a car

Thread starter Saitama
Start date Aug 22, 2013
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Car Locomotive

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A locomotive sprays sand into a freight car, which starts from rest with a mass of 2000 kg. The sand is added at a rate of 10 kg/s with a velocity of 5 m/s relative to the locomotive, and the distance between the locomotive and the car remains constant. The discussion focuses on applying conservation of momentum to determine the car's speed after 100 seconds, considering the car as a variable-mass system. Participants explore the equations of motion, the impact of the sand on the car's momentum, and the appropriate reference frames for analyzing the problem. Ultimately, the solution involves deriving a differential equation to express the car's velocity in relation to the mass of the sand added over time.

Aug 23, 2013

Saitama

ehild said:

If you use the car as system of reference, you can not speak about the change of its velocity. In its own frame of reference,the velocity is identically zero.
It has no sense choosing a system as frame of reference, the motion of which you do not know. You want to find the velocity of the car with respect to the ground as function of time.

As voko said, choosing the car as frame of reference means a non-inertial frame. In that frame, the virtual force -ma acts on every mass m, and the equation you got from conservation of momentum is not valid.

Thanks ehild and voko! This was an interesting thread. :)