- #31
ovicenzu
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TSny said:
Does the differential, dP, simplify if we look at the the change from P(0) to P(0+dt)?
What Is the Speed of a Freight Car When All the Sand Is Gone?
- Thread starter Saitama
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Homework Help Overview
The problem involves a freight car of mass M that initially contains a mass of sand m. A constant horizontal force F is applied while sand flows out at a constant rate. The objective is to determine the speed of the freight car when all the sand has been expelled, starting from rest.
Discussion Character
- Exploratory, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants discuss the expression for momentum P(t) and its components, questioning whether it accurately accounts for the momentum of the sand that has fallen out. There are attempts to derive expressions for momentum at different times and to analyze changes in momentum over small time intervals.
Discussion Status
There is an ongoing exploration of the momentum equations and the implications of variable mass as sand is expelled. Some participants have suggested methods for expressing momentum changes and have provided hints for further analysis. The discussion reflects a collaborative effort to clarify the mathematical relationships involved without reaching a definitive conclusion.
Contextual Notes
Participants are navigating the complexities of variable mass systems and the associated momentum calculations, with some expressing uncertainty about specific terms and their implications. There is a recognition of the need to handle average velocities in the context of changing mass.
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