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Work Problem/Graph Given/Find final velocity.

  1. Apr 6, 2009 #1
    1. The problem statement, all variables and given/known data

    The graph shows the net external force component F cos θ along the displacement as a function of the magnitude of the displacement s. The graph applies to a 65 kg ice skater.

    http://img9.imageshack.us/img9/3441/0671.gif [Broken]


    (a) How much work does the net force component do on the skater from 0 to 3.0 m?
    93 Joules (Correct)

    (b) How much work does the net force component do on the skater from 3.0 m to 6.0 m?
    0 Joules (Correct)


    (c) If the initial speed of the skater is 2.4 m/s when s = 0, what is the speed when s = 6.0 m?


    2. Relevant equations

    W=F(Δx)
    KE=.5mv2


    3. The attempt at a solution

    For part C.

    Here is my attempt.

    Firstly, I do not understand the reason that FCosΘ was used as a Force instead of simply F, due to the way the graph is drawn, I chose to simply represent it as F, which may have been my mistake, but I doubt that.

    I know the WorkTotal done on the skater was 93 Joules. So I thought that perhaps the change in Kinetic Energy would be equivalent to 93 Joules, allowing me to solve for Vf.

    So I tried that below.

    FCosΘ=31N

    W=FCosΘ(Δx)

    FCosΘ(Δx)=.5mvf2-.5mvi2

    .5mvf2=FCosΘ(Δx)+5mvi2

    vf2=(2(FCosΘ(Δx))/m) + vi2

    which means to solve for vf I would use.

    vf=((2(FCosΘ(Δx))/m)0.5)+vi

    Yet that answer is wrong. I think my concept of this problem is wrong..

    For Δx I used 3 instead of 6, since the force drops off to zero and the environment is frictionless, so it shouldn't make a difference.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 6, 2009 #2

    rl.bhat

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    Homework Helper

    Your last step is wrong.
    Check it.
     
  4. Apr 6, 2009 #3

    LowlyPion

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    Homework Helper

    Seems a little complicated.

    W = ΔKE

    What is the initial KE?

    Just add the Joules from a) and then solve for velocity?
     
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