Determining the spring constant from Force vs dL data

[tdoyzz]

1. To the intelligent mind, need some help with the following:

Here is a table of the force applied to a spring and the resulting extension, Δl.

Force (N) Δl (m)
281 0.10
353 0.15
665 0.30
977 0.45
1049 0.50Plot a graph of Force vs. Δl.
What is the spring constant?2. F = -kx; U = .5kx^2 3. I figured this was pretty simple at first. But then, after plotting the data, I found that the slope is not consistent. Also, after rearranging for k and plugging in the values, I got a different k value every time.
Please help. Thanks

 

[berkeman]

1. To the intelligent mind, need some help with the following:

Here is a table of the force applied to a spring and the resulting extension, Δl.

Force (N) Δl (m)
281 0.10
353 0.15
665 0.30
977 0.45
1049 0.50


Plot a graph of Force vs. Δl.
What is the spring constant?


2. F = -kx; U = .5kx^2


3. I figured this was pretty simple at first. But then, after plotting the data, I found that the slope is not consistent. Also, after rearranging for k and plugging in the values, I got a different k value every time.
Please help. Thanks

Can you fill out the table with the k values that you calculate? (Hint -- use the "code" tags to enclose the table to keep the columns lined up)

If there are variations in k, are they monotonic or more random? What explanations can you think of for the variations?

 

[hotvette]

--deleted-- ...I like Berkeman's approach better.

 

[tdoyzz]

Ok..

From the Table and using k=F/x:

Force (N) Δl (m) k (N/m)
281 0.10 2810
353 0.15 2353.3
665 0.30 2216.7
977 0.45 2171.1
1049 0.50 2098

Could the variations have something to do with the springs pot. energy?

This is a question on my pre-lab and I believe we are experimenting with a bosun's chair attached to a spring attached to the ceiling... if that helps.

 

[tdoyzz]

Sorry for the columns not being lined up again... I'm new to this site.