Finding K in Hooke's spring

[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

 

[rwisz]

I would first clarify the units of the data and the equation used. In this case, it seems like the units of force are being measured in Newtons (N) and the units of extension are being measured in meters (m). The equation for Hooke's Law is typically written as F = -kx, where F is the force, k is the spring constant, and x is the displacement. The negative sign indicates that the force and displacement are in opposite directions.

To find the spring constant, we can use the slope of the line of best fit in the graph of force vs. extension. In this case, the slope is 0.61. However, since the equation used in the lab is y=1 + 0.61x, we need to first rearrange it to be in the form of F = -kx. This can be done by subtracting 1 from both sides and then multiplying both sides by -1, giving us F = -0.61x - 1.

Comparing this to the equation F = -kx, we can see that the spring constant (k) is equal to 0.61 N/m. This means that for every meter of displacement, the spring produces a force of 0.61 N in the opposite direction.

In summary, to find the spring constant from a graph of force vs. extension, we can use the slope of the line of best fit. However, we need to make sure that the equation used is in the correct form (F = -kx) to get an accurate value for k.