Question

the potential energy U(X) of a particles moving along x axis is give by U(X)=ax-bx2 . find the equilliburim position of particles .

Answer 1

Equilibrium position is du/dx = 0 . x = a/2b. Hope it will help you.

Answer 2

Dear student,

It is given that the potential energy of a particle U(x) = ax - bx². We have to find the equilibrium position of the particles implying that we have to position of x where a and b are constants.

By the formula of potential energy, we know that for conservative forces, we have:

                   Fc.f. = - ( du/ dx)

Putting the given values in the formula, we get:

         Fc.f. = - [d(ax - bx²)/dx]

             0 = - [adx/ dx - bdx²/dx]

             0 = - [a - 2bx]

             0 = 2bx - a

             a = 2bx

            x = a/2b

Hence, the equilibrium position of the particles is a/2b.