anonymous
  • anonymous
Derive the force for the following intervals U(x) = 1, -∞ < x < -π |x|, -π ≤ x ≤ π sin (x), x > π
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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JamesJ
  • JamesJ
\[ F = \frac{dU}{dx} \hat{x} \] So just calculate and notice there will be points where the force is not defined because the derivative is not defined. (Or if you know Dirac delta functions, should be written in terms of them.)
JamesJ
  • JamesJ
Hence, for instance, for x < pi, the force F is the zero vector because the derivative of the potential 1 is zero.
JamesJ
  • JamesJ
And I should have included a minus sign. \[ F = - \frac{dU}{dx} \hat{x} \]

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JamesJ
  • JamesJ
Making sense?
anonymous
  • anonymous
Sorry, I don't get it :|
JamesJ
  • JamesJ
What is the function U(x)? Not its mathematical definition. What is its physical interpretation?

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