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Math Help - Spring Constant

  1. #1
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    Spring Constant

    Hi guys, I <3 math but detest physics. Well, my math teacher gave us a project over hooke's law and spring constants. If anyone could just give me a gentle prodding in the right direction or tell me if I'm going about this the correct way, that would be fantastic! Here goes:

    We were given a stretchy band used in physical therapy. It is long and stretchy and we were told to do the following:

    Determine the spring constant k for at least 3 different lengths of your stretchy band.

    - We did this by attaching 1.25 lbs of weight to a string and tying the
    string with weight onto the stretchy band. We premeasured the
    distances where we were tying the string with weight so we could
    find the length before the weight was attached. We then measured
    the length of the stretchy band after the weight was attached. We
    did this three times.

    -To find k, we rearranged Hooke's law to look like this:

    k = F/(delta x)

    -We did our calculations for all three lengths of the band.

    Here's where I get a little confused. We need to find a general equation so that someone could insert a certain length into our equation for our red stretchy band and get the particular k value for that length. I want to graph the three data points we collected in excel and then do a best fit line using a power series. Should my x-axis be change in length, length before stretch, length after stretch, or something else? Should my y-axis be my k value?

    Any help is much appreciated!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    I would suggest

    Quote Originally Posted by elizsimca View Post
    Hi guys, I <3 math but detest physics. Well, my math teacher gave us a project over hooke's law and spring constants. If anyone could just give me a gentle prodding in the right direction or tell me if I'm going about this the correct way, that would be fantastic! Here goes:

    We were given a stretchy band used in physical therapy. It is long and stretchy and we were told to do the following:

    Determine the spring constant k for at least 3 different lengths of your stretchy band.

    - We did this by attaching 1.25 lbs of weight to a string and tying the
    string with weight onto the stretchy band. We premeasured the
    distances where we were tying the string with weight so we could
    find the length before the weight was attached. We then measured
    the length of the stretchy band after the weight was attached. We
    did this three times.

    -To find k, we rearranged Hooke's law to look like this:

    k = F/(delta x)

    -We did our calculations for all three lengths of the band.

    Here's where I get a little confused. We need to find a general equation so that someone could insert a certain length into our equation for our red stretchy band and get the particular k value for that length. I want to graph the three data points we collected in excel and then do a best fit line using a power series. Should my x-axis be change in length, length before stretch, length after stretch, or something else? Should my y-axis be my k value?

    Any help is much appreciated!
    have it be \Delta{x}...are you past\in calculus to apply it here?
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  3. #3
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    Wow that was quick,

    I'm in Calc II.

    I did delta x on my x axis and k for my y axis and got the equation:

    y = 1.2508x^(-.9998) which is extremely close to 1/x, which is what I assumed the relationship would be. However, I do not like the fact that 1.25 shows up within my equation when the general formula needs to hold for all weights. It makes me wonder what the equation would be if I used 2 pounds instead of 1.25...my group members have tried to convince me it doesn't matter, but they don't have any logical arguments....any ideas?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Ok

    Quote Originally Posted by elizsimca View Post
    Wow that was quick,

    I'm in Calc II.

    I did delta x on my x axis and k for my y axis and got the equation:

    y = 1.2508x^(-.9998) which is extremely close to 1/x, which is what I assumed the relationship would be. However, I do not like the fact that 1.25 shows up within my equation when the general formula needs to hold for all weights. It makes me wonder what the equation would be if I used 2 pounds instead of 1.25...my group members have tried to convince me it doesn't matter, but they don't have any logical arguments....any ideas?
    Well then you tell me...thinking about this from a calc perspective does this make sense?
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  5. #5
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    Quote Originally Posted by elizsimca View Post
    .......We need to find a general equation so that someone could insert a certain length into our equation for our red stretchy band and get the particular k value for that length. you do realise that k is the spring constant ? have you read anything about hooke's law ? k does not vary, it is defined as being the force required to stretch a spring by a meter (if your using SI units that is), the only conditions in which k changes is when hooke's law no longer applies, have you been asked to investigate that ? I very much doubt it

    .....I want to graph the three data points we collected in excel and then do a best fit line using a power series. Why would you use a power series when the relationship is linear (well at least while hooke's law applies). use linear regression, or just simply draw a line of best fit on your graph. I think your trying to totally overkill what a very simple problem.
    ..

    Bobak
    Last edited by bobak; April 13th 2008 at 12:51 PM.
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  6. #6
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    mathstud,

    I've been thinking about this for the better part of the week and the thing is, I'm just not sure. I have a really hard time translating my math knowledge and skills (which I promise, I really am quite good at math) into actual real world problems. It's like I completely freeze up and my brain just gets jumbled. I know this is my fault, I just need to work on it. That's why I'm taking engineering physics next semester so I can work on it.

    Bobak,

    I have seen your contributions on this forum and you are obviously extraordinarily intelligent. However, I think you are a tad abrasive in your responses. I know people get frustrated with what they percieve as "stupid questions", we all do. But at the same time we need to remember that at one time we were learning this stuff for the first time as well. For example, instead of saying:

    Why would you use a power series, the relationship is linear (at least while hooke's law applies). you linear regression, or just simply draw a graph and estimate the line of best fit. I think your trying to totally overkill what a very simple problem.

    You could have said:

    Instead of using a power series, you should try to see if it's a linear relationship. You could probably even do this without the computer, just draw a graph on a piece of paper. Maybe you are over thinking this a little bit, you might be making the problem more complex than it needs to be.


    To me, that simple change of wording and punctuation makes a huge difference! And, I think the reason that I am going a little overboard is because it is a project and I am a straight A student. I need to have a professional looking presentation and would like to include a graph from excel of my data. I am over thinking this because I am in uncharted waters and very unsure of myself. I have never taken a physics class, as I said above in my response to mathstud.
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  7. #7
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    Oh, and for the record Bobak, I know that you probably weren't trying to be abrasive. Your words just made me feel extremely dumb, which I can't imagine would be your intended goal. Thank you for taking the time to respond!

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  8. #8
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    Quote Originally Posted by elizsimca View Post
    To me, that simple change of wording and punctuation makes a huge difference! And, I think the reason that I am going a little overboard is because it is a project and I am a straight A student. I need to have a professional looking presentation and would like to include a graph from excel of my data. I am over thinking this because I am in uncharted waters and very unsure of myself. I have never taken a physics class, as I said above in my response to mathstud.

    I don't want this to digress into a conversation, the PM system exists for that. Yes the English in my reply was a bit poor, sorry about that. Believe it or not I am trying to be helpful. My comment may have seemed harsh but I am pointing you in the right direction, Hopefully now you have read a bit about the required physics and understand the problem better so you can now produce piece of quality work.

    There are teachers who will always give "nice" soft response to student regardless to how wrong they are, then they put you down as a "C" grade student watch you fail and be happy and you hitting you target. You need to learn to appreciate it when a teacher give you a what appears to be a "Harsh" response and not take it personally, be grateful that they are actually helping you rather than putting you down as a idiot.

    Best wishes with your future studies.

    Bobak
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