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Total energy, speed, resistive force

  1. Oct 28, 2011 #1
    1. The problem statement, all variables and given/known data

    A skier of mass 70 kg sets off, with initial speed of 5 m(s^-1), down the line of greatest slope of an artificial ski-slope. The ski-slope is 80 metres long and is inclined at a constant angle of 20° to the horizontal. During the motion the skier is to be modelled as a particle.
    - Ignoring air resistance and friction, calculate the speed of the skier at the bottom of the slope.
    - The skier actually reaches the bottom of the slope with speed 6 m(s^-1). Calculate the magnitude of the constant resistive force along the slope which could account for this final speed.


    2. Relevant equations



    3. The attempt at a solution

    For the first question my work looks like this:
    (Total energy at the top of the slope) = (total energy at the bottom of the slope)
    => (PE at the top of the slope + KE at the top of the slope) = (PE at the bottom of the slope + KE at the bottom of the slope)
    => ((70g x 80sin20) + (0.5 x 70 x 5^2)) = (0 + (0.5 x 70 x v^2))
    Taking g=10
    => v = sqrt(((56000sin20) + (35 x 25))/35) = 23.9 m(s^-1) (to 3 s.f.)

    However, the correct answer is 23.4 m(s^-1)

    For the second question my work looks like this:
    (PE + KE) at the top of the slope - (80F) = (PE + KE) at the bottom of the slope
    Where F is the constant resistive force
    This gives (56000sin20) + (35 x 25) – 80F = 35 x 36
    => 80F = (56000sin20) + (35 x 25) – (35 x 36)
    => F = ((56000sin20) + (35 x 25) – (35 x 36))/80
    => F = 234.6 N (to 1 d.p.)

    However, the correct answer is 224 N newtons (to 3 s.f. probably).

    What am I missing here?
     
  2. jcsd
  3. Oct 28, 2011 #2

    ehild

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    Homework Helper
    Gold Member

    Use g=9.8 m/s^2 instead of 10.


    ehild
     
  4. Oct 31, 2011 #3
    i know i'm supposed to use g=10 but i used g=9.8 anyway and that gives 23.7 ms^-1 and 230 N, which are both incorrect.
    anything else?
     
  5. Oct 31, 2011 #4

    ehild

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    Homework Helper
    Gold Member

    I think your results are the correct ones. I have got the same.

    ehild
     
  6. Nov 1, 2011 #5
    then i wasted literally hours making the same calculations over and over. yay for textbook typos.
    thanks for your help
     
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