Question

The potential energy for a conservative force system is given by `U=ax^(2)-bx`. Where a and b are constants find out (a) The expression of force (b) Potential energy at equilibrium.

Answer 1

(a) For conservative force
`F=-(dU)/(dx)=-(2ax-b)=-2ax+b`
(b) At equilibrium F=0
`implies -2ax+b=0 implies x=(b)/(2a)`
`:. U=a((b)/(2a))^(2)-b((b)/(2a))=(b^(2))/(4a)-(b^(2))/(2a)=-(b^(2))/(4a)`