Question

When a particle of mass m is at (x comma 0 )​, it is attracted toward the origin with a force whose magnitude is StartFraction y Over x squared EndFraction . If the particle starts from rest at x equals b and is acted upon by no other​ forces, find the work done on it by the time it reaches x equals a​, 0 less than a less than b.

Answer 1

W = y (b-a) / ab

Step-by-step explanation:

Work is defined by the expression

W = ∫ F. dr

In this case the force is in the same direction of displacement, so the scalar product is reduced to the ordinary product

W = ∫ F dr

The expression of the strength left is

F = -y / x²

let's replace and integrate

W = ∫ (-y / x²) dx

W = -y (-1 / x)

We evaluate between the lower limit x = b + a to the upper limit x = 0 + a

W = -y (-1 / b + 1 / a)

W = y (b-a) / ab

where (b-a) is the distance traveled