Derivative of Force in terms of distance?

[Ocata]

Hi,

Suppose I have a function on a graph with a vertical axis is Force and the horizontal axis is distance. Then the area under the curve is given by F*d = Work = Energy, correct? If so, then what would the slope of the curve represent? F/d = ?

Thank you.

 

[AyanGang]

It will give you the force per unit distance if your function is linear in x(like in a spring).
Otherwise it will give you the gradient of the force as a function of x if your function is non-linear(like coulomb's law).
To know more about gradient https://en.wikipedia.org/wiki/Gradient.

 

[Ssnow]

1. The area under the curve in general is given by $\int_{x_{i}}^{x_{f}}F(x)d\,x =W$ , if $F$ is constant then $W=F\Delta x$ (I suppose always $\cos{\theta}=1$)
2. The slope of the curve is $\frac{d}{dx}F(x)$ and represent how the force grow or decrease respect the distance, as example if $F_{Hooke}(x)=-kx$ then $\frac{d}{dx}F_{Hooke}=-k$ is the elastic coefficient ...

 

[CWatters]

Essentially the slope gives you the spring constant at that point.

 

[Ocata]

Thank you all. I will revisit this topic soon. I need to understand a few prerequisite concepts first, for which I need to create a new thread.