Understanding Potential Energy and Force for a Constant Potential Function

[yamama1]

Homework Statement

Potential energy function is given by U = C/x, where C is a positive constant.
a. Find the force as a function of x.
b. Is this force directed toward the origin or away from it?
c. Does the potential energy increase or decrease as x increases?
d. Answer b, and c if C is a negative constant.

Homework Equations

How do you relate U = C/x to force?

The Attempt at a Solution

I tried the formulas.
F = mg
U = mgy
But I am not sure how you relate both of them together

 

[tiny-tim]

welcome to pf!

hi yamama1! welcome to pf!

potential energy is (minus) the work done by a (conservative) force

in other words, PE = -∫F.dx,

and so F = … ? ​

(see the pf library for some details)

 

[yamama1]

hi yamama1! welcome to pf!

potential energy is (minus) the work done by a (conservative) force

in other words, PE = -∫F.dx,

and so F = … ? ​

(see the pf library for some details)

F = ma.
so PE = - ∫ma.
I don't know what that would equal to.

 

[tiny-tim]

(just got up :zzz: …)

F = ma.
so PE = - ∫ma.
I don't know what that would equal to.

stick to the question … nobody's asked you for a

you're asked for F, you're given PE, and you have an equation relating PE and F …

so what is F (as a function of PE)? ​

(oh, and PE isn't -∫ma. it's -∫ma.dx = -∫mv(dv/dx)dx = -∫mvdv = -1/2 mv²)

 

[Swap]

apply F= -dU/dx