Question

$FIGUREEX10.34$shows the potential energy of a system in which a particle moves along the x-axis. Draw a graph of the force $F_x$as a function of position x.

Short answer

As a function of position x, the graph of the force $\left(F_x\right)$is,

The component of the force is constant, and it remains negative in direction in half of the journey, while it is positive in the other half.

Step-by-step solution

Force : 

The force exerted on a mass item that causes it to alter velocity.

Explanation : 

On the potential energy diagram, the equation gives the y-component of force,

$F_x=-\frac{dU}{dx}$

Particle's potential energy diagram,

The slope of the potential energy diagram is the x-component of force.

At $x=0.5m$, the x-component of force is,

$$\begin{gathered} F_{x=0.5}=-\frac{\left(0-2\right)J}{\left(0-0.5\right)m} \\ =-4\left(J/m\right) \\ =-4N \end{gathered}$$

At $x=1m$, the x-component of force is,

$$\begin{gathered} F_{x=1}=-\frac{\left(2-0\right)J}{\left(0.5-1\right)m} \\ =4\left(J/m\right) \\ =4N \end{gathered}$$

As a function of position x, the graph of the force is,

The component of the force is constant, and it remains negative in direction in half of the journey, while it is positive in the other half.