How Do You Calculate Potential Energy in a One-Dimensional Interaction?

AI Thread Summary
To calculate potential energy in a one-dimensional interaction of two equal mass bodies influenced by a conservative force, one must analyze the given linear momentum equations, p1 = Pexp(-kx) and p0 at infinity. The potential energy is defined as zero at infinity, and the challenge lies in interpreting the exponential function correctly, which represents a decay related to distance x. The problem hints at the need for limits due to the reference point at infinity. Understanding the relationship between momentum and force is crucial, as the force can be derived from the potential energy function. This discussion emphasizes the importance of clarifying mathematical expressions and concepts in physics problems.
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Homework Statement


Consider a one-dimensional interaction of two bodies with equal masses m. The
interaction is governed by a conservative force. The linear momentum of one of the bodies is equal to p1 = Pexp(-kx) and that of other body is equal to p0 at (infinity). Find the potential energy as a function of distance x between these bodies (the potential is equal to zero at infinity). Determine the force acting between the bodies.

The Attempt at a Solution


I don't even know where to begin :( I don't know what exp means. I'm assuming the collision is elastic because it says that the interaction is governed by a conservative force. I guess there's something to do with limits because of the 'infinity' clue? I can't find anything relevant in my textbook (Giancoli Physics for Scientists and Engineers volume 4) Any help is appreciated, thank you!
 
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I don't know how to solve the problem, but Pexp(-kx) would probably mean P^(-kX). (P raised to the negative kx). K should be some kind of constant, while x is most likely the distance between the objects, or some other form of variable distance.

Sorry I can't help more, but that should at least give you a hint as to what you're supposed to be working towards.
 

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