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We have this equation in 1D. If the terms confuse you, just follow the math: m d v/ d t − F = 0 Multiply everything by d x, identify d x / d t = v, and integrate. You need only one constant of integration, E, and put it on the right side. The m and v term is called K (for "kinetic energy" or "energy of motion"). E is the energy ("total energy" or "total mechanical energy"). F isn't constant in general. The F integral is identified with the potential energy: U = − ∫ F d x Write down the resulting equation (the "energy conservation equation").

We have this equation in 1D. If the terms confuse you, just follow the math: m d v/ d t − F = 0 Multiply everything by d x, identify d x / d t = v, and integrate. You need only one constant of integration, E, and put it on the right side. The m and v term is called K (for "kinetic energy" or "energy of motion"). E is the energy ("total energy" or "total mechanical energy"). F isn't constant in general. The F integral is identified with the potential energy: U = − ∫ F d x Write down the resulting equation (the "energy conservation equation").

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
Problem 21PQ
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We have this equation in 1D.  If the terms confuse you, just follow the math:

m d v/ d t − F = 0

Multiply everything by d x, identify d x / d t = v, and integrate.  You need only one constant of integration, E, and put it on the right side.

The m and v term is called K (for "kinetic energy" or "energy of motion").  E is the energy ("total energy" or "total mechanical energy").  F isn't constant in general.  The F integral is identified with the potential energy:

U = − ∫ F d x

Write down the resulting equation (the "energy conservation equation").

 

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