The force on a particle is directed along an x axis and given by F = F0(x/x0 - 1) where x is in meters and F is in Newtons. If F0 = 1.5 N and x0 = 4.5 m, find the work done by the force in moving the particle from x = 0 to x = 2x0 m.

The work done is 28.9 j

Explanation:

The work is defined as a force doing a movement, and it can be calculated as W = F*d

The force is:

F = 1.5N*(x/(4.5m - 1m)) = (1.5)N*x/3.5m

the distance that d = 2x0 = 2*4.5m = 9m

But the force changes in function of x, so we must do a integration:

Where i used d as the integral of dx betwen 0m and 9m, so the only thing inside the integral is the equation for the force.

this integral is equal to:

W = (2.5N*x^2)/(2*3.5m) valued between x = 0m and x = 9m

W = (2.5*9^2)/7 J = 2.5*81/7 J = 28.9J

it is a negative acceleration