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15 December, 13:26

A potential energy function is given by u (x) = (3.00n) xâ (1.00n/m2) x3. at what position or positions is the force equal to zero?

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  1. 15 December, 15:26
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    I believe the correct form of the energy function is:

    u (x) = (3.00 N) x + (1.00 N / m^2) x^3

    or in simpler terms without the units:

    u (x) = 3 x + x^3

    Since the highest degree is power of 3, therefore there are two roots or solutions of the equation.

    Since we are to find for the positions x in which the force equal to zero, u (x) = 0, therefore:

    3 x + x^3 = u (x)

    3 x + x^3 = 0

    Taking out x:

    x (3 + x^2) = 0

    So one of the factors is x = 0.

    Finding for the other two factors, we divide the two sides by x and giving us:

    x^2 + 3 = 0

    x^2 = - 3

    x = sqrt ( - 3)

    x = - 1.732 i, 1.732 i

    The other two roots are imaginary therefore the force is only equal to zero when the position is also zero.

    Answer:

    x = 0
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