Kinetic energy and momentum p=mv

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Discussion Overview

The discussion revolves around the relationship between kinetic energy (KE) and momentum (p) in physics, specifically exploring the derivation of the equation KE = p²/2m from the standard kinetic energy formula KE = 1/2mv². Participants are examining the mathematical connections and underlying principles involved in this derivation.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses confusion about how the equation KE = p²/2m is derived from KE = 1/2mv², questioning whether calculus is involved.
  • Another participant suggests using the momentum equation p = mv in the kinetic energy equation to find the relationship.
  • A third participant provides a step-by-step derivation of the second equation from the first, showing how to substitute momentum into the kinetic energy formula.
  • Another participant emphasizes the importance of encouraging self-discovery in solving physics problems rather than providing direct answers.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints on how to approach the problem, with some participants providing direct answers while others advocate for a more exploratory learning process. There is no consensus on the preferred method of assistance.

Contextual Notes

The discussion does not clarify whether the derivation is universally accepted or if there are alternative methods or interpretations that could lead to different conclusions.

Who May Find This Useful

Students studying physics, particularly those interested in the concepts of kinetic energy and momentum, as well as those looking for different approaches to problem-solving in physics.

SciSteve
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So I have a physics problem that has the normal equation KE=1/2mv^2 and KE=p^2/2m and i have no idea how they get the second equation is it a derivative or something with calculus? any helps greatly appreciated thanks in advance.
 
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p=mv.

Use that in the first equation.

Zz.
 
Here is how it is derived:

p=mv

KE=(1/2)mv^2

KE=(1/2)mv*v (mv=p)

KE=(1/2)pv (v=p/m)

KE=(1/2)p*(p/m)

KE=(1/2)*(p^2/m)

KE=p^2/2m


Hope that helped.
 
We usually try to get the person to do or discover the answer for him/herself, rather than spoonfeeding the answer completely.

Zz.
 

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