Question

A particle of mass m has a speed v=α/x, where x is it’s

displacement. Find the force F(x) responsible.

F(x)=-mα2

/x3

Answer 1

$v=\frac{a}{x} \\ \frac{dv}{dx}=-\frac{a}{x^2} \\ \frac{dv}{dt} = \frac{dv}{dx} \times \frac{dx}{dt} \\ = v\frac{dv}{dx} \\ a = v\frac{dv}{dx} \\ = -\frac{va}{x^2} \\ = -\frac{a}{x} \times \frac{a}{x^2} \\ = -\frac{a^2}{x^3} \\ F = ma \\ = m(-\frac{a^2}{x^3}) \\ F(x) = -\frac{ma^2}{x^3}$