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Finding tension between two objects with different fs

  1. Nov 25, 2014 #1
    1. The problem statement, all variables and given/known data
    What is the tension in the strap which the boy uses to hold onto the pack?
    Mass of Boy=45kg
    Mass of Pack=25kg
    θ=42°
    Coefficient of kinetic friction between boy and incline=0.35
    Coefficient of kinetic friction between pack and incline=0.48
    Acceleration of boy=4m/s^2
    Capture.JPG
    2. Relevant equations
    Fnet=F1+F2+F3...+Fn
    F=ma

    3. The attempt at a solution
    Mass of boy=M
    Mass of pack=m
    Fpb=parallel force of boy
    etc...

    Fpb=Mgsinθ
    Fpp=mgsinθ
    fsb=0.35Mcosθ
    fsp=0.48mcosθ

    a(M+m)=Fpb+Fpp-fsb-fsp-T

    I'm really confused as to how to solve this since both acceleration and tension are unknowns. I've tried doing a lot of things to try and get a value for acceleration but none of them have given me the correct answer which is T=15N.
     
  2. jcsd
  3. Nov 25, 2014 #2

    Simon Bridge

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    Draw free body diagrams for the boy and the pack separately.
    Apply ##\sum \vec F = m\vec a##, and you'll end up with four equations with four unknowns which have to be true simultaneously.
     
    Last edited: Nov 26, 2014
  4. Nov 26, 2014 #3
    Thanks so much! Can't believe I messed that up haha. If anyone wants the solution

    1. Fpb-T-Fsb=Ma
    2. Fpp+T-Fsp=ma

    Add them together

    FpB+Fpp-Fsb-Fsp=Ma+ma
    a=(FpB+Fpp-Fsb-Fsp)/(M+m)
    After putting values in
    a=3.67m/s^2

    Rearranging first equation

    T=Fpb-fsb-Ma
    T=15N
     
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