Answer:
The magnitude of the force is 1.29*10^-3N in the positive x direction
Explanation:
In order to calculate the magnitude and direction of the force, you take into account that the force is the space derivative of the potential enrgy, as follow:
[tex]F(x)=-\frac{dU(x)}{dx}[/tex] (1)
where:
[tex]U(x)=Ax^4\\\\A=0.0630\frac{J}{m^4}[/tex]
You replace the expression for U into the equation (1) and solve for F:
[tex]F(x)=-\frac{d}{dx}[Ax^4]=-4Ax^3[/tex] (2)
The force on the particle, for x = -0.080m is:
[tex]F=-4(0.630\frac{J}{m^4})(-0.0800m)^3=1.29*10^{-3}N[/tex]
The magnitude of the force is 1.29*10^-3N in the positive x direction
