How Does Adding More Springs Affect Extension in Hooke's Law Experiments?

[thang08]

Homework Statement

This isn't acctually a problem but I really don't know what to do. I was doing a simple activity about Hooke's Law during class today where I have to set up a apparatus and measure the extension of spring when when we put different masses on it. I didn't do it properly so I have difficulty answering it

This is my graph if it helps any

http://img156.imageshack.us/img156/8913/clipuw9.jpg
you see, I only did the experiment with 1 spring. I didn't do the following required experiments, so I have no idea how to answer.

Homework Equations

Q6. Write how much extension do you think there would be (compared to the extension for one spring) if you now had two springs, identical to the one used, joined one after the other

Q7. Observe what happens (describe). Explain

Q8. Do the same, but this time for two springs side by side

Q9 What about three side by side, or four, or three in a row, or four?

The Attempt at a Solution

Q6. I think it remains the same because F and k remains the same => x remains
Q7. Observation would suit what I just said
Q8. 2 springs side by side so forced is distributed even onto both springs thus making the extension halved
Q9. I don't even understand the question

Thanks in advance:!)

 

[denverdoc]

I like q8 response a lot!

So let's call a new spring constant K'eq that which satisfies the eqn,

f=-kx. the force is the same, and as you propose extention is halved,
f=-keq*.5x divide be
f=-kx and you will find k'eq=2k. For q9 extend your logic for 3 or more springs.

now q6 is a bit more subtle, but if you think more about it, you may start to doubt your answer.

 

[thang08]

I don't get why Q6 response is wrong, well as far as I understand force constant of a spring shows us how stiff it is. If two identical springs connected in 'series', the stiffness of the 'combined' spring doesn't change. If we don't increase the mass, i.e. no change in weight force, the extension (x) of the spring shouldn't change.

 

[thang08]

err, no suggestion? T_T I keep on think my way of thinking is right and some online experiment tells me that it's wrong. Explanation please

 

[denverdoc]

Been gone, think about this thought experiment forget on-line proof etc. You have a bungee like cord and want to stretch it by 2 inches. Cut the bungee cord in half and see how much more effort it requires to stretch the same 2 inches. Or if you want to save yourself a buck and have some rubberbands handy, for grins tie 4 in series and compare that with one in terms of stretch force and displacement.
The math is relatively trivial thing to prove, but I'm thinking it might be more helpful to get it out of the purely math realm. Hope this helps a bit.