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Can someone help me with this proof?

  • Thread starter belleamie
  • Start date
  • #1
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A) Given ((mdx^2)/(dt^2))=F(x)
prove conservation of energy
 

Answers and Replies

  • #2
quasar987
Science Advisor
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Bonjour mon amie. Vous êtes belle aujourd'hui.

Here's how roughly: Define K(x) as [itex]K(x) = \frac{1}{2}mv(x)^2[/itex]. Define [itex]W_{a \rightarrow b}[/itex] as [itex]\int_a^b F(x')dx'[/itex]. Show that [itex]W_{a \rightarrow b} = K(b) - K(a)[/itex]. Then define U(x) as [itex] -\int_s^x F(x')dx'[/itex] where s is a fixed arbitrary point, and show that [itex]U(b) - U(a) = -W_{a \rightarrow b} [/itex]. Then define the energy E of the system as E(x) = K(x) + U(x). Show how the previously found result imply that E is a constant.
 

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