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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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SUMMARY
The discussion centers on calculating the speed of a freight car when all the sand has been released. The key equation derived is \( v = \frac{Fm}{M\lambda} \), where \( F \) is the applied force, \( m \) is the initial mass of sand, \( M \) is the mass of the freight car, and \( \lambda \) is the rate of sand flow. Participants clarify the momentum conservation approach, emphasizing the need to account for the momentum of sand falling out and the changing mass of the system. The final expression for the change in momentum leads to the differential equation \( (M+m-\lambda t)\frac{dv}{dt} = F \).
PREREQUISITES- Understanding of Newton's laws of motion
- Familiarity with momentum conservation principles
- Basic calculus, particularly differentiation and integration
- Knowledge of variable mass systems in physics
- Study the derivation of the rocket equation and its application to variable mass systems
- Learn about the implications of momentum conservation in non-constant mass scenarios
- Explore differential equations related to motion with changing mass
- Investigate real-world applications of momentum conservation in engineering systems
Physics students, educators teaching dynamics, and engineers dealing with systems involving variable mass, such as rockets or freight transport systems.
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