Question

As a particle moves along an x axis, a force in the positive direction of the axis acts on it. The plot shows the magnitude F of the force versus position x of the particle. The curve is given by F = a/x2, with a = 9.0 N·m2. Find the work done on the particle by the force as the particle moves from x = 1.0 m to x = 3.0 m by integrating the force function.

Answer 1

The work done on the particle is 6 J

Step-by-step explanation:

The work done on the particle is equal to:

`W=\int\limits^3_1 {Fx} \, dx =\int\limits^3_1 {(a)/(x^(2) ) } \, dx =a\int\limits^3_1 {(dx)/(x^(2) ) } \, \\W=9((-1)/(x) )_(1)^(3) =-9((1)/(3) -1)=6J`