equation manipulation question (E = 0.5*k*x^2 (this is an elastic spring potential energy); k = F/x (stiffness = force/displacement))

[sarajv]

Hi all,
I found an equation expression, which i'm trying to understand.

E = 0.5*k*x^2 (this is an elastic spring potential energy);
k = F/x (stiffness = force/displacement).
i found E expressed as [math]E = 0.5F^2/k[/math], but i am struggling to see how this was derived.
I can get E = 0.5F*x , but i can't see how to express E as a function of F and k.

Any help would be much appreciated

 

[sarajv]

Hi All,

I came accross an equation expression, which i am trying to derive myself and am struggling.
E = 0.5*k*x^2 (potential energy of a spring)
k = F/x (stiffness of a spring)
Now i came accross this: E = 0.5*F^2/k
I am struggling to see how to get to that. I can see how to get to E = 0.5*F*x, but not the expression above.

Help would be much appreciated
JV

 

[Dr.Peterson]

Hi All,

I came across an equation expression, which i am trying to derive myself and am struggling.
E = 0.5*k*x^2 (potential energy of a spring)
k = F/x (stiffness of a spring)
Now i came across this: E = 0.5*F^2/k
I am struggling to see how to get to that. I can see how to get to E = 0.5*F*x, but not the expression above.

Help would be much appreciated
JV

Solve k = F/x for x, and substitute in E = 0.5kx^2.

The general principle is that you want an equation in only E, F, and k, so you have to eliminate the other variable, x.

 

[stapel]

E = 0.5*k*x^2 (this is an elastic spring potential energy);
k = F/x (stiffness = force/displacement).
i found E expressed as [math]E = 0.5F^2/k[/math], but i am struggling to see how this was derived.
I can get E = 0.5F*x , but i can't see how to express E as a function of F and k.

In [imath]E = \frac{F^2}{2k}[/imath], there is no [imath]x[/imath]. So see if there is a way to use the second equation they gave you to get rid of [imath]x[/imath] in the first equation.

 

[sarajv]

ook, i dont know how, but i sat down on it today and all became perfectly clear and simple to me

Thanks!