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Hooks Law F = kx Book answer wrong I think

  1. Sep 30, 2015 #1
    1. The problem statement, all variables and given/known data

    Hello, two basic questions on the same topic and I think the book answer is wrong so I've posted both here if that's okay.

    Q1. What force is required to stretch a spring with spring constant 0.2 N/cm a distance of 5 cm?

    Q2. A vertical spring stretches 5 cm under a load of 100 g. Determine the spring constant.


    2. Relevant equations

    F = kx k = spring contant x = extension in spring


    3. The attempt at a solution

    Q1. F = kx
    F = 0.2 x 5
    F = 1 N

    1 Newton is my answer but the book says 0.01 N.

    Q2. 100g = 0.1kg therefore weight (force) = 0.1 x 10 = 1 N

    F = kx
    1 = 5k
    k = 0.2 N/cm

    0.2 N/cm is my answer but the book says 0.05 N/cm.


    I can't see where I've gone wrong. Please advise.
     
  2. jcsd
  3. Sep 30, 2015 #2
    Are you sure the dimension of the spring constant is N/cm and not N/m?

    The solution in the book seems to be the inversed value of the spring constant, again using the common dimension N/m for it.
     
  4. Sep 30, 2015 #3
    Yes absolutely sure
     
  5. Sep 30, 2015 #4
    Your calculations seem to be correct to me.

    Q1:

    If you take k = 0.2 N/m, then

    F = 0.2 N/m ⋅ 0.05 m = 0.01 N

    Q2:

    If you take k in N/m, then

    k = 1 N / 0.05 m = 20 N/m → 1/k = 0.05 m/N

    Maybe this is where the answers are coming from, but they have to have messed up several times.
     
  6. Sep 30, 2015 #5
    1 Newton is equal to 1 kg m/s2. The cm and m cannot cancel each other out. Change the cm to m first, then solve.
     
  7. Oct 1, 2015 #6

    rude man

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    1N is correct unless somebody meant k = 0.2N/m.
    The book here is wrong no matter what. Your answer is correct.
     
  8. Oct 1, 2015 #7
    Thanks all. The book authors were trying to explain (somewhere earlier in the text) that the "spring constant can be in N/cm or N/mm as long as the extension is measured in the same units". So I think the authors go mixed up with all the units somewhere because they've been working in metres up to that point in the book
     
  9. Oct 1, 2015 #8
    I just read this and seems to make sense.
    So for Q1 What force is required to stretch a spring with spring constant 0.2 N/cm a distance of 5 cm?

    0.2N/cm = 20N/m
    5 cm = 0.05 m

    F = kx
    F = 20 x 0.05
    F = 1 N

    So the same answer as mine. This book is just wrong.
     
  10. Oct 1, 2015 #9

    rude man

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    Ya. get a new book!
     
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