Potential energy stretched wire

[ahmeeeeeeeeee]

hello ,

when we say that (stress) = dF/dA

If F is variable(And I guess it must be variable) = Kx, what is the value of stress at any time ? I mean what is the "dA" we divide on ? or what is the basic givens I must have in order to calculate the stress ?? , and why it is written sometimes just (stress)= F/A ??

and at this example What is the F(initial / final / avergae) and what is the A(initial / final / average)


2- when we say that the potential energy per unit volume =

W/AXo = .5*(F/A)*(X/Xo) = .5 stress* strain

What is "A" ?? IS it the original A before applying the force ??

Or is is the "A" after moving the (delta X) ??

 

[Thaakisfox]

Stress means the amount of force exerted per unit area.
Now first of all let's say a constant force F is exerted on a given area A, then we say that the stress is F/A.

Now what if that force changes with respect to the surface. Meaning, at one point of the surface we have F1 and at another point we have F2 etc. I.e. the force is not constant on the surface.

Then the stress is the differential of the force with respect to the surface. i.e. dF/dA

The A is just the area on which the force is exerted...