Can error bars contain values that don't make physical sense?

[Chrrristian]

I'm doing some physics homework involving uncertainties and errors. However, even though I feel I've calculated the uncertainties correctly, I'm getting error bars containing values that result in undefined answers or answers that make no physical sense.

For example. I have the equation for spring constant k to equal k=DeltaM*g/(.4 cm +/- .4 cm). The denominator denotes the change in length of the spring once additional weight is attached to it. Obviously, at the bottom of that uncertainty range I have 0 in the denominator, resulting in an undefined k.

Equally as strange is that for some values later in the problem, the uncertainty gives me negative values for change in spring length. This means that as I am adding more mass the spring is actually going up and acting against gravity.

Have I messed up severely somewhere? Or is this just something that happens with uncertainty? I don't really understand where I could have messed up.

 

[topsquark]

You seem to be saying that the length of your spring extension is 0.4 cm and your error is 0.4 cm?? That means that your spring might have never been extended. This is why things are getting screwy.

Can you tell us how you got your data? What is the actual experiment?

-Dan

 

[Chrrristian]

You seem to be saying that the length of your spring extension is 0.4 cm and your error is 0.4 cm?? That means that your spring might have never been extended. This is why things are getting screwy.

Can you tell us how you got your data? What is the actual experiment?

-Dan

So the problem is regarding a spring that is hanging from the ceiling that extends when a mass is attached to it. The only numbers provided are 8 masses and the associated final lengths of the spring (relative to the ceiling) once attached. We are also provided with the information that there is an uncertainty of .2 centimeters for each measurements of the length. We are tasked with finding the spring constant and the length of the spring with no weight attached to it, along with the associated uncertainties. We are also supposed to find a least square regression line, but I will cross that bridge when I get there.

My thought process is to find the difference between one mass and another mass, along with the change in length L and its uncertainty.

So, for example, a mass 1 (m1) of 200 grams will result in a 5.1 cm final spring length (L1), whereas a mass 2 (m2) of 300 grams will result in a 5.5 final spring length (L2). Thus, 100 G will of weight is associated with a .4 cm +/1 .4 cm change in spring length. (This is where I suspect things first went awry).

I used two equations provided for us to work out the equation outlined in my OP: F=mg and F=kd. I simply solved for k, resulting in k=mg/d. I recognized that these are linear, and as such I can say make m equal to the change in mass and d equal to the change in final length of the spring. So, I can make my equation k=(m2-m1)g/((L2-L1)+/- .4 cm.

I recognize that this is an incomplete process and that I still need to find the uncertainty of k, but I would like to figure out if I'm even doing the more basic first step correctly first before I delve further into the problem and make it even more confusing for myself.