- #1
giraffe
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Homework Statement
The work-energy theorem relates the change in kinetic energy of a particle to the work done on it by an external force: [itex] \triangle K = W = \int F\, dx [/itex]. Writing Newton's second law as [itex] F = \frac{dp}{dt} [/itex], show that [itex] W = \int v\, dp [/itex] and integrate by parts using the relativistic momentum to obtan equation 2.34.
(this is a 2 part problem. one part is showing that [itex] W = \int v\, dp [/itex] and the second is integrating that equation. i am using modern physics 3rd edition kenneth kramer. i have no idea what equation 2.34 as i can not find it in the chapter.)
Homework Equations
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the equations listed in the problem
relativistic momentum (in [itex] \frac {\text{kg} \cdot \text{m}}{\text{s}}[/itex] ) [itex]\vec{p} = \frac{m\vec{v}}{\sqrt{1-\frac{v^2}{c^2}}} [/itex]
relativistic momentum (in MeV) [itex] pc = \frac{mvc}{\sqrt{1-\frac{v^2}{c^2}}} = \frac{mc^2(\frac{v}{c})}{\sqrt{1-\frac{v^2}{c^2}}} [/itex]
The Attempt at a Solution
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first part, not quite sure. i know i have to make the substitution for F so [itex] \int{\frac{dpdx}{dt}}\ [/itex] after that i don't know.
second part probably going to need help with that integral once i figure this first part out. i need to use the second equation to isolate v and than integrate what's left somehow.
thanks for the guidance.