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anonymous
 4 years ago
Derive the force for the following intervals
U(x) = 1, ∞ < x < π
x, π ≤ x ≤ π
sin (x), x > π
anonymous
 4 years ago
Derive the force for the following intervals U(x) = 1, ∞ < x < π x, π ≤ x ≤ π sin (x), x > π

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JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1\[ F = \frac{dU}{dx} \hat{x} \] 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
 4 years ago
Best ResponseYou've already chosen the best response.1Hence, for instance, for x < pi, the force F is the zero vector because the derivative of the potential 1 is zero.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1And I should have included a minus sign. \[ F =  \frac{dU}{dx} \hat{x} \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry, I don't get it :

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1What is the function U(x)? Not its mathematical definition. What is its physical interpretation?
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