Calculate velocity in a "simple electric train"

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To calculate the terminal velocity of a simple electric train moving in a coiled copper wire with magnets, one must consider the forces acting on the train, including magnetic forces and resistance. The terminal velocity occurs when the net force on the train is zero, meaning the magnetic force equals the drag force. The discussion emphasizes the importance of understanding the interaction between the magnetic field and the electric current in the wire. Additionally, participants are encouraged to share their own calculations and methodologies to enhance the understanding of the topic. Engaging in collaborative problem-solving can lead to more accurate results and insights.
raymondd
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Homework Statement
How do you calculate the velocity of the battery with 2 magnets attached on polar ends moving in a coiled copper wire
Relevant Equations
unknown
How do you calculate the terminal velocity of the train moving in a coiled copper wire with two magnets attached to the polar ends?
I have attached someone else's work I've found on the internet here and need help 1662076917721.png1662076905411.png1662076725371.png
 
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What are your own thought and attempts?
 
Thread 'Chain falling out of a horizontal tube onto a table'
My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...

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