Why would the spring constant change?

[backtoearth]

Homework Statement

The experiment the class did was about spring constant and Hooke's Law. The spring was set vertically and we were to hang the pendulums at the end of the spring and measure the extended length to figure out the spring constant.

and I'm trying to find out why the data from spring experiment doesn't follow the Hooke's Law. Plus, why the spring constant is not constant and changes.

The given data is this;

weight of pendulums　　　extended length of spring
---------------------------------------------------------
0.05*9.80 　　　　　　　　　　　　 0.009
0.1*9.80 　　　　　　 　　　　　　0.18
0.15*9.80 　　　　　　　　　　　　0.108
0.2*9.80 　　　　　　 　　　　　　0.108
0.25*9.80 　　　　　　　　　　　 0.108

the initial length of spring is 0.202m.
each pendulum is about 0.05kg.

Homework Equations

kx=mg

The Attempt at a Solution

From the 3rd pendulum, the data suits the relevant equation. However, from the 1st to 2nd try, it doesn't. I mean, it does. But the spring constant would change. Why does this happen? Is it just an error? or are there specific reasons for this?
Plus, our lab group is not the only one with that kind of data. Most of the groups came with drastic change in the first pendulum.

Thanks!

 

[stevenb]

weight of pendulums　　　extended length of spring
---------------------------------------------------------
0.05*9.80 　　　　　　　　　　　　 0.009
0.1*9.80 　　　　　　 　　　　　　0.18
0.15*9.80 　　　　　　　　　　　　0.108
0.2*9.80 　　　　　　 　　　　　　0.108
0.25*9.80 　　　　　　　　　　　 0.108

Is this data correct?

 

[backtoearth]

That data is what I got from the experiment.

 

[gneill]

Would by any chance the "extended length of spring" column be the change in length from the previous entry rather than the overall change in length from the zero load condition? Otherwise it looks as though your spring has "bottomed out" at the 0.15 line.

 

[backtoearth]

That's what I did; I calculated the change in length from the previous entry. Do you mean that in order to find the spring constant, I have to calculate "x" as overall change in length?

 

[gneill]

That's what I did; I calculated the change in length from the previous entry. Do you mean that in order to find the spring constant, I have to calculate "x" as overall change in length?

Well, that's what's implied by F = k*x (ignoring signs which imply directions for the moment). The x is the total spring extension for total load F.

However, if you treat each previous spring length as a new equilibrium position, then you'd have your Δx corresponding to added load Δw = 0.05kg and obtain a value of k for that particular "range" of the spring. I suppose you could then average these k's, or plot them to observe any "nonlinearity" of the spring over different extension ranges.

 

[stevenb]

That's what I did; I calculated the change in length from the previous entry. Do you mean that in order to find the spring constant, I have to calculate "x" as overall change in length?

Yes, exactly. That was a good catch by gneill. The data makes sense now.


This appears to be an extension spring with pre-tension built in. As you stretch the spring more and more coils open up. Once all coils are all open, the spring is more linear. This is just a guess on my part because I haven't seen the spring in operation, but you can confirm or deny this theory.

 

[backtoearth]

Thanks! I got it now. I will try to find an average of k's with Hooke's Law. Anyways, can you please explain more about pre-tension? What happens when the spring becomes more linear?

 

[stevenb]

Thanks! I got it now. I will try to find an average of k's with Hooke's Law. Anyways, can you please explain more about pre-tension? What happens when the spring becomes more linear?

First, let me be clear that I'm not 100% sure that your spring has pretension. This is only my hypothesis based on your data. You will need to confirm that the data and your visual observations are consistent with what I'm saying.

That said, pretension is a force which is built into the spring to keep all the coils fully compressed when unloaded. Extension springs typically have some pretension. You need a nonzero force to get the spring to open up when you have pretension.

Pretension itself is a nonlinearity and makes the spring not obey Hooke's law. However, the plot would still be a straight line with pretension, so you can redefine the zero point and make it look "Hooke-like". However, if all coils do not open at the same time once the spring is loaded at the pretension force, then you will also get a curve that is not a straight line. The value of k will depend on the number of coils that have opened. Then once the spring is loaded beyond the point that all coils have opened up, the force will be very linear (technically, only piecewise linear, or linear in changes). However, if you then overload the spring with too much force, it becomes nonlinear again.