My Math Forum Force-energy equivalence

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 May 8th, 2011, 05:38 PM #1 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Force-energy equivalence $\text{Prove that }E\,=\,F\frac{dt}{d\vec{v}}c^2\text{.}$
 May 8th, 2011, 07:23 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs Re: Force-energy equivalence Perhaps I'm wrong, as it's been a long time since I fiddled with special relativity, but I don't think we can use Newton's second law of motion in the form F = ma here. I think we need to use it in the form Newton actually gave it: $F=\frac{d\rho}{dt}=\frac{d}{dt}$$m\cdot\text{\vec{ v}}$$$ I believe E = mc² is referred to as mass-energy equivalence.
 May 8th, 2011, 09:01 PM #3 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Correct. Classical mechanics deals with motion of objects large enough, where relativity deals with objects moving very fast. Hence F/a ? E/c².

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### force energy equivalence

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