Physic(s) Work Force of Particle

Question

A particle moves in a straight line, parallel to the x axis, from xi to xf. It is acted upon by a force that is also parallel to the x axis and is given by f(x)= b/x

A.

Write an expression for the work done by the force.

W = ___

B.

If b==3.81 N⋅m, and the particle moves from xi=3.47 m to xf=7.03 m, then what is the work, in joules, done by the force?

Answer 1

By the definition of work

W = ∫(b/x)dx

where the definite integral is taken from xi to xf

The indefinite integral

∫(b/x)dx = b ln(x)

Therefore W = b(ln(xf) - ln(xi))

Substituting the numbers given in B

W = 3.81×(ln(7.03) - ln(3.47)) = 2.69 J