What Is the Speed of a Freight Car When All the Sand Is Gone?

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The discussion focuses on calculating the speed of a freight car after all the sand has flowed out, given a constant force applied and a constant rate of sand loss. The initial momentum of the system is zero, and as the sand exits, the momentum of both the freight car and the sand must be considered. Participants explore the correct expressions for momentum over time, addressing the complexities of variable mass systems and the average velocity of the sand that falls out. The conversation also touches on the merits of using momentum equations versus direct acceleration integration for solving such problems. Ultimately, the participants arrive at a differential equation that relates force, mass, and acceleration for the freight car as the sand is lost.
  • #31
TSny said:
I'm not sure what you're getting at here. Can you expound on this?

Does the differential, dP, simplify if we look at the the change from P(0) to P(0+dt)?
 
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  • #32
ovicenzu said:
Does the differential, dP, simplify we look at the the change from P(0) to P(0+dt)?
Yes. What do you get for dP from P(0) to P(0+dt)? How would you use this to solve the problem?
 
  • #33
TSny said:
Yes. What do you get for dP from P(0) to P(0+dt)? How would you use this to solve the problem?

The same result just quicker thereby expediting the solution process. Thank you very much for your help.
 

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