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

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To calculate the spring constant (K) from a linear equation derived from a Force vs. Extension graph, the slope of the line represents the spring constant. The equation provided, y = 1 + 0.61x, indicates that the slope (0.61) corresponds to K in the relationship F = kx. By using the slope directly, one can determine the spring constant without needing to manipulate additional values for x. The discussion clarifies that the gradient of the line is equivalent to the force divided by extension, reinforcing the straightforward nature of the calculation. Understanding this concept simplifies the process of finding the spring constant from experimental data.
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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.

 
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shootyoup said:

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