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Compression of Spring

  1. May 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A 2kg block is dropped from a height of 40 cm onto a spring of force constant k=1960 N/m. Find the maximum distance the spring is compressed.

    (The answer must be 10 cm)

    3. The attempt at a solution

    Well, I know that if a spring is stretched "y", it will be compressed "y". The problem is that I can't find out how long will the spring stretch once it is dropped from that height. Therefore I tried to use the formula

    [tex]F = ky[/tex]

    Where [tex]F= mg = 2 \times 9.81[/tex] and k =1960 N/m which is 196000 N/cm

    [tex]2 \times 9.81 = (196000) k[/tex]

    [tex]y= \frac{2 \times 9.81}{196000}[/tex]

    But this gives me the wrong answer. Why is that?? :confused:

    By the way, I know that the tension is [tex]T= 2 \pi \sqrt{\frac{m}{k}} = 2 \pi \sqrt{\frac{2}{196000}}= 0.02 N[/tex].
     
  2. jcsd
  3. May 21, 2010 #2

    rock.freak667

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    Homework Helper

    It is best to consider energy for this problem, graviational pe = potential pe of spring


    Also that T is period time and not the tension.
     
  4. May 21, 2010 #3
    I tried that, it doesn't seem to work:

    [tex]mgh= \frac{1}{2} k x^2[/tex]

    2 (9.81) 40 = 1/2 (196000) x2

    x=0.089 cm

    Because the correct answer should be 10 cm! Is there anything wrong with my calculations?

    Yep, my mistake. :blushing:
     
  5. May 21, 2010 #4

    rock.freak667

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    Homework Helper

    Not sure, the only way to get 10cm exact is if the mass was dropped from 50cm.

    Normally, the energy method should work.
     
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