I with a Hooke's law experiment I did

[addy360]

I did an experiment where I measured the stretch on a spring from its initial position when masses were added on the end of it, in increments of 50g. I plotted a graph of Force against length stretched and the graph does not go through the origin, or at least it is not linear for forces below around 1N.

My problem is I want to prove F=kx, so I need to calculate the gradient of a linear line which goes through the origin to get the spring constant k, though if you just look at the linear part of my graph it has a F intercept of 1, so I get F=kx+1.. just a little confused on how to get the spring constant, anybody out there know how to help out?

Here is a table with my data and my graph:

http://imgur.com/a/vJUi0

thanks!

 

[Simon Bridge]

You need to find some way to estimate the slope from the data of course.
Normally you'd look for a "best fit" line.

If the data is obviously non-linear for small forces, perhaps it is not obeying Hook's law in that part and you can safely ignore those points? It will depend on your course.

If you ignore them - will the best-fit line go through the origin?

Usually is the theory says a line will go through the origin and the data does not, though, it means there is some systematic error in the measuring process. This can come from badly calibrated equipment or incomplete control over variables.

 

[Simon Bridge]

[looking at your data]
Your work is very good - you have mislabelled the vertical axis though ... what you have plotted is the mass vs extension ... so the theoretical equation for your line should be m=(k/g)x (why?) [hmmm... unless you are using g=10N/kg?]

It looks like the first couple of masses were needed to knock out the kinks in the spring and your offset just reflects that this is not an ideal spring. You'll need to make a note about why you are neglecting the earlier points.

You did avoid a number of mistakes that people usually make - like you did not force the line through the origin (very good), you did not use any of your data points to compute the slope (excellent) and you did put your working on the graph itself (good).
You need to correct that axis label (if needed) and add a title. Make sure you correctly interpret the slope.

 

[addy360]

thank you for your feedback! but I plotted force on the vertical axis, which I got from multiplying the masses by the acceleration of gravity (F=ma). What leads you to think I plotted mass?

 

[Simon Bridge]

For F=1N for m=0.1kg, you must have used g=10N/kg ... that's OK.
I'm used to 9.8N/kg... your value of k will be out but the important lesson is about the linearity.

No worries.
BTW: you could have plotted m vs x and still found the slope as k/g then multiplied by g to get k.