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How much work, speed and distance

  1. Oct 13, 2015 #1
    1. The problem statement, all variables and given/known data

    Skjermbilde 2015-10-13 kl. 17.21.15.png


    A child wants to go ride on her sleigh, and she decides to walk up the Big

    Hill, of height 100 m relative to where she starts. There are two ways up;

    the steep way, where the slope is 30.0 degrees, and the not-so steep way, where the

    slope is 15.0 degrees. The coefficient of kinetic friction between snow and sleigh is

    fs k = 0,100. The mass of the sleigh is 8.00 kg, the mass of the child is 30.0kg.

    a) How much work does the child have to do on the sleigh to get it to the

    top of the hill: the steep way? The not-so-steep way? How much potential

    energy does the sleigh now have relative to the starting point?

    b) The child now sits down on the sleigh and slides down the steep side.

    What is her speed as she gets to the bottom of the hill? What if she would

    have gone down the not-so-steep side?

    c) Assuming that after reaching the bottom, she can continue on a horizontal

    surface of snow, how far does she slide before coming to a halt (steep and

    not-so-steep)?



    3. The attempt at a solution

    a) In problem a i got
    The amount of work done on the sleigh the steep way = 2425 J
    The amount of work done on the sleigh the not steep way = 10813 J
    Potential energy=7840 J

    b) Speed down steep side= 40,3 m/s
    Speed down not steep side= 35 m/s

    c) I havent solved c yet.

    All answers are appreciated!
     
  2. jcsd
  3. Oct 13, 2015 #2
    The potential energy the sleigh gained is larger than the work the girl did on it - that can't be possible (in the steep way case).

    I got 39.6 m/s and 34.7 m/s (probably due to different values of g), so I agree.

    You can solve it with energy consistency: you know the kinetic energy and can convert it into work done by the friction of the snow.
     
  4. Oct 13, 2015 #3
    This is the method that i used to calculate the work on steep way:
    Fx= Fsin30-μn=0
    Fy= n-mgcos30=0
    n=mgcos30
    Fsin30-μ(mgcos30)=0
    F=μ(mgcos30)/sin30=14N

    L= distance from standpoint till top
    L= 100m/sin30=200m

    W=F*rcosθ
    W=14N*200m*cos30= 2425J

    the same method used with the not steep way, but with different θ and L

    for the potential energy:

    U=mgy=8kg*9.80m/s^2*100m=7840J
     
  5. Oct 13, 2015 #4
    in b) i did:

    Steep way:
    m=38 , g=9.8, h=100 , fk=6.789, d = 200
    vf= sqrt((2/m)*(mgh-fkd))= 43.46 m/s

    not so steep way:
    m=38 , g=9.8, h=100 , fk=7.57, d = 386.37
    vf= sqrt((2/m)*(mgh-fkd))= -> 42.49 m/s
     
  6. Oct 13, 2015 #5
    If I don't misread your post, you placed the x-axis of the coordinate system parallel to the slope and y-axis perpendicular to it.

    For ΣFx:

    Ff = μ ⋅ N ... friction force
    F ... girl's pulling force → why do you multiply it with the sine of the hill's angle?
    plus: you forgot, that the weight has a component in x-direction to

    ΣFy looks good to me

    The length of the slope L is calculated correctly.

    When calculating the work why do you multiply it with the cosine of θ? The girl is pulling the sleigh parallel to the slope, you already calculated the length L, which you need for the calculation of the work.

    1) Think about the sum of the forces in x-direction again:
    a) direction of the girl's pulling force (or at least the component that is able to do work)
    b) the component of the weight in x-direction

    2) To calculate the work multiply the pulling force with the length the sleigh is actually pulled (the whole slope)

    That is correct and it must be less than the work of the girl, else you create a perpetuum mobile.
     
  7. Oct 13, 2015 #6
    For the friction force I get: Ff = N⋅μ = m⋅g⋅cosθ⋅μ
    θ = 30° → Ff = 32.3 N
    θ = 15° → Ff = 36.0 N
     
  8. Oct 13, 2015 #7
    You are right, i used m=8 on my calculator instead of m=38.
     
  9. Oct 13, 2015 #8
    OK, doing it your way i get:
    In the steep way
    F=46N
    W= 9200 J

    The not steep way:
    F=27.86 N
    W=10755.61 J
     
  10. Oct 13, 2015 #9

    haruspex

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    Looks right.
     
  11. Oct 14, 2015 #10
    That's it, well done!
     
  12. Oct 14, 2015 #11
    In the task it says "How much work does the child have to do on the sleigh". Shouldn't you then use 8kg as the mass?
     
  13. Oct 14, 2015 #12
    It was the calculation of the friction force in the 2nd part: When the girl used the sleigh to slide down. As she is sitting on the sleigh getting downwards the mass is the sum of the masses of the girl and the sleigh, hence 38 kg.
     
  14. Oct 14, 2015 #13

    haruspex

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    ... and anyway, the mass used would be irrelevant in b).
     
  15. Oct 15, 2015 #14
    okey. I thought that you used it in a
     
  16. Oct 15, 2015 #15
    in a): I thought the work done would be the same either jo drag the sleigh the steep- or not-so-steep way, cause the height is the same.
     
  17. Oct 15, 2015 #16
    Missed the friction, sorry
     
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