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In a certain region of space, a force F(r) has an associated potential energy of the form U(r) = a r2 − b r + c , where a , b , and c are positive constants. What are the points, if any, where the force F(r) goes to zero?

Respuesta :

Answer:

r = b/2a

Explanation:

We know that force can be derived from potential energy:

F(r) = -dU(r) / dr

=> F(r) = -d/dr (ar² - br + c)

F(r) = -2ar + b

When this force is equal to zero,

F(r) = 0 = -2ar + b

=> 2ar = b

r = b/2a

This is the point where the force goes to zero.

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