Explanation:
The potential energy function for a system of particles is given by :
[tex]U(x)=2x^3-2x^2-3x[/tex]
(a) The relation between the force and the potential energy is given by :
[tex]F=\dfrac{dU}{dx}[/tex]
[tex]F=\dfrac{d(2x^3-2x^2-3x)}{dx}[/tex]
[tex]F=6x^2-4x-3[/tex]
(b) Putting the equation of force equals to 0 such that,
[tex]6x^2+4x+3=0[/tex]
On solving the above equation we get the values of x as :
x = -0.448 m
x = 1.115 m
So, at x = -0.448 m and x = 1.115 m the value of force equal to zero.
Hence, this is the required solution.
