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A force in the +x-direction has magnitude F = b/xn, where b and n are constants. For n > 1, calculate the work done on a particle by this force when the particle moves along the x-axis from x = x0 to infinity.

Answer :

Answer:

[tex]W=-\dfrac{b}{n-1}x_o^{1-n}[/tex]

Explanation:

The magnitude of force in the +x direction is given by :

[tex]F=\dfrac{b}{x^n}[/tex]

We need to find the work done. The integral form of work done is given by :

[tex]W=\int\limits {F.dx}[/tex]

[tex]W=\int\limits^{\infty}_{x_{o}}{\dfrac{b}{x^n}.dx}[/tex]

[tex]W=b \int\limits^{\infty}_{x_{o}}{\dfrac{1}{x^n}.dx}[/tex]

[tex]W=b \int\limits^{\infty}_{x_{o}}{x^{-n}.dx}[/tex]

[tex]W=\dfrac{bx^{1-n}}{1-n}|_{x_{o}}^\infty[/tex]

[tex]W=-\dfrac{b}{n-1}x_o^{1-n}[/tex]

Hence, this is the required solution.

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