Locomotive throwing sand in a car

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Homework Help Overview

The problem involves a sand-spraying locomotive that transfers sand into a freight car, which is initially at rest. The scenario is set up such that the distance between the locomotive and the freight car remains constant while the sand is being sprayed at a specific rate and velocity. The objective is to determine the speed of the freight car after a certain time period, given the mass flow rate of the sand and its velocity relative to the locomotive.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the implications of the constant distance between the locomotive and the freight car, questioning how this affects the mass and momentum equations. There are considerations about defining the system, whether to include the incoming sand as part of the system or as an external influence. Various participants express uncertainty about how to set up the equations and the relevance of momentum conservation in this context.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and attempting to clarify their understanding of the momentum changes involved. Some guidance has been offered regarding the conservation of momentum and the treatment of the system, but no consensus has been reached on the best approach to take.

Contextual Notes

Participants note the complexity introduced by the variable mass of the freight car as sand is added, and there are references to previous examples in textbooks that illustrate similar concepts. The discussion reflects a range of assumptions about the system's boundaries and the treatment of the incoming sand.

  • #31
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. :)
 

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