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Homework Help: Work-Energy Theorem Question

  1. Mar 16, 2010 #1
    1. The problem statement, all variables and given/known data

    A skier comes crashing into the netting at the bottom of a ski hill. The skier has a mass of 85 kg and is moving at a speed of 65 km/h (234 m/s).

    (a) How much work is done by the netting while bringing the skier to rest?
    (b) If the "spring" constant for the netting is 13500 N/m, how far is the netting stretched when the skier comes to rest?

    m = 85 kg
    v1 = 234 m/s
    v2 = 0 m/s
    k = 13500 N/m
    w = ?
    [PLAIN]http://upload.wikimedia.org/math/f/5/d/f5d889f32d6794e1bc2ed394e9688c76.pngx[/URL] [Broken] = ?

    2. Relevant equations

    (F)(d) = [1/2(m)(v2^2)] - [1/2(m)(v1^2)]
    KE = [1/2(m)(v^2)]
    PEe = [1/2(k)(x^2)]

    3. The attempt at a solution

    (a)

    W = [PLAIN]http://upload.wikimedia.org/math/f/5/d/f5d889f32d6794e1bc2ed394e9688c76.pngKE[/URL] [Broken]

    = [1/2(m)(v^2)]
    = [1/2(85 kg)(234 m/s)^2]
    = 2327130
    = 2.3 x 10^6 J

    This answer seems reasonable.

    (b)

    Now here is where I need help.

    2.3 x 10^6 J = [1/2(k)(x^2)]
    2.3 x 10^6 J = [1/2(13500 N/m)(x^2)]
    x = sqrt{[-2.3 x 10^6 J]/[1/2(13500 N/m)]}
    x = 18 m

    Does this look right?
    Thanks in advance!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 16, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    65 km/h ≠ 234 m/s

    1h = 3600 s.

    Convert it over.
     
  4. Mar 16, 2010 #3
    Ahh! I multiplied by 3.6 instead of dividing! Thanks!
     
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