Calculating the Spring Constant from Force-Extension Graph

[Jadaa]

Homework Statement

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Force Extension in (m)
1.0 0.014.
1.5 0.032.
2.0 0.053.
2.5 0.071.
3.0 0.090.
3.5 0.110.
4.0 0.130.
4.5 0.148.
5.0 0.166.

Homework Equations

RESULTS FROM GRAPH.
F= kx.
k=F/x,m= vertical side/ horizontal rise.

The Attempt at a Solution

I plotted a graph of force against extension and found the gradient to be 26.3N/m using the points (0.014,0.1) and (0.166,0.5).
It's my understanding that the gradient should be equal to the answer obtained from k= F/x but when I work it out the answers are not similar and I'm not sure where I went wrong.

 

[TomHart]

but when I work it out the answers are not similar

Can you explain what that means. Does that mean that your answer is significantly different than the book?

 

[Jadaa]

Can you explain what that means. Does that mean that your answer is significantly different than the book?

When I work it out it's not equal to the gradient which my teacher says it should be. I think it's because I'm not sure how to probably use the formula when there are so many quantities.

 

[TomHart]

I plotted the data. It appears that it doesn't intersect at x=0, F=0 very well. That has to be what is causing the discrepancy.

 

[Jadaa]

I plotted the data. It appears that it doesn't intersect at x=0, F=0 very well. That has to be what is causing the discrepancy.

Ooo I see my teacher has advised us that we could have started from 0.5 F instead of 0 instead as we were getting errors. Thank you I'll try to recover my previous set of data.

 

[TomHart]

That should help because if I find an equation for the line based on the 26.3 slope, it shows an offset of 0.63 N.

 

[Jadaa]

Thanks again