Answer:
The potential energy is [tex]-4x^3[/tex]
Explanation:
Given that,
Force [tex]F=-\alpha x^2 i[/tex]
We need to calculate the potential energy
Using formula of work done
[tex]\Delta U=F(x) dx[/tex]
Put the value of F
[tex]\Delta U=-\alpha x^2\ dx[/tex]
On integration
[tex]U=-\alpha \dfrac{x^3}{3}+C[/tex]
[tex]U=-\dfrac{\alpha x^3}{3}+C[/tex]...(I)
U = 0, x = 0 so C = 0
Put the value of c and α in equation (I)
[tex]U=-\dfrac{12x^3}{3}+0[/tex]
[tex]U=-4x^3[/tex]
Hence, The potential energy is [tex]-4x^3[/tex]
