# A particle located in one dimensional potential field has potential energy function U(x) = #a/x^2 - b/x^3# where a and b are positive constants. The position of equilibrium corresponds to x =?

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(1) #(3a)/b#

(2) #(2b)/(3a)#

(3) #(2a)/(3b)#

(4) #(3b)/(2a)#

(1)

(2)

(3)

(4)

##### 1 Answer

Sep 7, 2017

(4)

#### Explanation:

You are looking for a point where the force on the system goes to zero.

By inspection notice that the numerator will be zero when both of those terms are equal. One of the terms includes an

The functional form of

graph{(-3 + 2 x)/x^4 [-1, 5, -0.1, 0.2]}

However the particular magnitudes will change depending on the constants

The graph of

graph{1/x^2 - 1/x^3 [-1, 5, -0.1, 0.2]}