# When a particle of mass `m` is at `(x,0)`  , it is attracted toward the origin with a force whose magnitude is `k/x^2`  where  `k` is some constant. If a particle starts from rest at `x=b`  ...

When a particle of mass `m` is at `(x,0)`  , it is attracted toward the origin with a force whose magnitude is `k/x^2`  where  `k` is some constant. If a particle starts from rest at `x=b`   and no other force act on it, calculuate the work done on it by the time it reaches `x=a, 0<a<b`

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the following formula that helps you to evaluate the work done by the force `F = k/x^2` in moving the particle from `a` to `b` , such that:

`W = int_a^b Fdx => W = int_a^b (k/x^2)dx`

Taking the constant `k` out, yields:

`W = k*int_a^b x^(-2)dx => W = k*x^(-1)/(-1)|_a^b`

You need to use the fundamental theorem of calculus, such that:

`W = k*(-1/b + 1/a) => W = k*(b-a)/(ab)`

Hence, evaluating the work done, under the given conditions, yields `W = k*(b-a)/(ab).`

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