Question

A system in which only one particle can move has the potential energy shown in $FIGUREEX10.31$. What is the y-component of the force on the particle at $y=0.5m$and $4m$?

Short answer

y-component of force at $y=0.5m$=$-60N$.

y-component of force at$y=4m$=$15N$.

Step-by-step solution

Force :

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

Explanation : 

The equation gives the y-component of force on the potential energy diagram.

$F_y=-\frac{dU}{dy}$

Particle's potential energy diagram,

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

At $y=0.5cm$, the y-component of force(slope) is,

$$\begin{gathered} F_{y=0.5}=-\frac{\left(0-60\right)J}{\left(0-1\right)m} \\ =-60\left(J/m\right) \\ =-60N \end{gathered}$$

At$y=4m$, the y-component of force(slope) is,

$$\begin{gathered} F_{x=15}=-\frac{\left(60-0\right)J}{\left(1-5\right)m} \\ =15\left(J/m\right) \\ =15N \end{gathered}$$