Question

A particle is moved along the x-axis by a force that measures 8/(3 + x)2 pounds at a point x feet from the origin. Find the work W done in moving the particle from the origin to a distance of 9 ft.

Answer 1

2 ft·lb

Explanation:

You want the work done on a particle moving it from 0 to 9 ft using a force that is 8/(3+x)² pounds at each point.

Work

The incremental work is the product of the force and the incremental distance:

dW = 8/(3+x)²·dx

The work done over the distance of interest is the integral of this incremental work over that distance.

`\displaystyle W=\int_0^9{(8)/((x+3)^2)}\,dx=(-8(x+3)^(-1))_0^9=-8\left((1)/(12)-(1)/(3)\right)=2`

The work done on the particle is 2 ft·lb.