How Do I Calculate the Spring Constant from a Linear Equation?

[shootyoup]

Homework Statement

This is a lab and we have data from extending a crossbow and the force produced. We graphed the data (Force v Extension) and find a line of best fit. Just using the y intercept and slope my equation is y=1 + .61x. How do i use that to find the spring constant K?

Homework Equations

k=1/2(kx^2)
f=kx

The Attempt at a Solution

I used my equation and entered in some values for x to get the force. Then used them in the equation f=kx. But the values i obtain are all different based on x and therefore not a spring constant.

 

[rock.freak667]

Homework Equations

k=1/2(kx^2)
f=kx

you have F=kx, so if you plotted F against x you'd get a straight line passing through the origin. The gradient would be F/x which is?

In your case, the gradient of your line would still be F/x.

 

[Sourabh N]

Here's an analogous situation which might help you.
Say I draw a linear fit between position(x) and time(t). What does the slope represent? Also notice, x=vt, where v is the (constant) speed.

Does this help?

 

[shootyoup]

Ahhh ok thanks guys, didn't know it was that simple