A particle moves in a potential given by U(x) = -7 x5 + 52 x + 85 (J). Calculate the x coordinate of the stable equilibrium of this potential, in m. Note that your answer could be positive or negative.

A particle moves in a potential given by U(x) = -7 x5 + 52 x + 85 (J). Calculate the x coordinate of the stable equilibrium of this potential, in m. Note that your answer could be positive or negative.

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Question

A particle moves in a potential given by U(x) = -7 x⁵ + 52 x + 85 (J). Calculate the x coordinate of the stable equilibrium of this potential, in m. Note that your answer could be positive or negative.

(Please answer to the fourth decimal place - i.e 14.3225)

Expert Solution

Step 1

The given potential is

$U (x) = - 7 x^{5} + 52 x + 85 [1]$

At equilibrium, the derivative of potential with respect to distance is zero.

$\begin{array}{l} \frac{d U}{d x} = 0 \\ - 35 x^{4} + 52 = 0 \\ x^{4} = \frac{52}{35} \\ x = \pm 1.1040 m [2] \end{array}$

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