Chapter 4.3, Problem 56E

To determine

To find: The sketch for the graph of the net force function and determine what does the graph says.

Answer to Problem 56E

The required sketch is shown in Figure 1 and the graph indicate that the net force on the middle particle is zero.

Explanation of Solution

Given:

The force that acts on the middle particle is $F\left(x\right)=-\frac{k}{x^2}+\frac{k}{\left(x-2\right)}$ .

The range of the parameter $x$ is $0<x<2$ .

The given diagram for the charge is shown in Figure 1

  

Figure 1

Calculation:

The given figure shows the particle with the charge 1 located at the position 0 and 2 on the coordinate line and the particle with charge $\left(-1\right)$ as the position $x$ between the charge.

The sketch for the graph of the net force function $F\left(x\right)=\frac{-k}{x^2}+\frac{k}{{\left(x-2\right)}^3}$ is shown in Figure 1

  

Figure 1

From the graph it is clear that the net force of function on the middle particle is zero at the midpoint of the particle. This is because the force becomes infinitely strong as the distance between the particle increases.