Answer to Question #203632 in Classical Mechanics for Aratunde Tobiloba

Question

Obtain the corresponding potential energy function of the intermolecular force. 1. F(r) = -ar^-7 + br^-9. 2. at what value of 'r' will the potential energy function be minimum

Answer 1

$F(r)=-ar^{-7}+br^{-9},$

$F'(r)=\frac{7a}{r^8}-\frac{9b}{r^{10}}=\frac{7ar^2-9b}{r^{10}},$

$F'(r)=0,$

$r_{min}=\sqrt{\frac{9b}{7a}}.$