Trouble finding F(x) for a particle moving on a horizontal plane

[astenroo]

Homework Statement

A particle of mass m moves along a frictionless, horizontal plane with a speed given by v(x)=k/x, where x is its distance from the origin and k is a positive constant. Find the force F(x) to which the particle is subject.

Homework Equations

F(x)=m\ddot{x}
\ddot{x}=\frac{d\dot{x}}{dt}=\frac{dx}{dt} \frac{d\dot{x}}{dx}=v\frac{dv}{dx}

The Attempt at a Solution

So i figured, if i differentiate v(x)=k/x I end up with v'(x)=-k/x^2, so F(x)= m\ddot{x} and if I substitute my expression for \ddot{x} I end up with F(x)=-mvk/x^2. Why do I get the feeling I'm all wrong about this one?

 

[tiny-tim]

hi astenroo!

… I end up with F(x)=-mvk/x^2. Why do I get the feeling I'm all wrong about this one?

dunno

looks ok … now get rid of the v, to make F a function of x

 

[SammyS]

Remember that v = k/x. Plug that back into your expression for F(x).

 

[astenroo]

Heh, I actually suck at calculus, so when I end up with a fairly straight forward solution, I get the feeling I've done something wrong :) Calculus cannot be simple :D

So, my first attempt was F(x)=-mvk/x^2, and if v(x)=k/x then F(x)=-mk^2/x^3.

Thanks for the hints.

 

[tiny-tim]

btw, note that vdv/dx can also be written d/dx (1/2 v²)

 

[astenroo]

btw, note that vdv/dx can also be written d/dx (1/2 v²)

Heh, so true. Thank you :)