I Mapertius's Principle and 2nd Newton's law

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The discussion focuses on deriving the second Newton's law using the Mapertius principle in the context of perfectly elastic collisions and free fall acceleration. The original poster is encountering a persistent issue with obtaining a coefficient of 2 in their final calculations. Participants are asked to provide insights or explanations for this discrepancy. The conversation aims to clarify the application of principles and calculations involved in the derivation process. Assistance is sought to resolve the confusion surrounding the coefficient.
MP97
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Hi, I have been working on deriving the second Newton's law from the Mapertius principle applied to a perfectly elastic collision from a free fall acceleration problem. These are my calculations, but I keep getting a coefficient of 2 in my final answer for some reason. Could someone explain to me what I am doing wrong?

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I appreciate any help you can provide!
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

This argument is another version of my previous post. Imagine that we have two long vertical wires connected either side of a charged sphere. We connect the two wires to the charged sphere simultaneously so that it is discharged by equal and opposite currents. Using the Lorenz gauge ##\nabla\cdot\mathbf{A}+(1/c^2)\partial \phi/\partial t=0##, Maxwell's equations have the following retarded wave solutions in the scalar and vector potentials. Starting from Gauss's law $$\nabla \cdot...
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