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Magnitude of force acting on an object

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data

    A 1.84kg mass is observed to accelerate at 10.66m/s^2 in a direction 28.8 degrees north of east. There is a force directed north acting on the object and a force directed east acting on the object. What is the magnitude of the force acting east on the object?


    2. Relevant equations

    F=ma, Fx=ma, Fy=ma

    3. The attempt at a solution

    *FA=force directed north, FB=force directed east, FN=normal force

    Fx=ma
    -mgsinθ+FAcosα+FBsinβ=ma
    -(1.84)(9.8)(sin28.8)+FA(cos61.2)+FB(sin61.2)=(1.84)(10.66)
    -8.68698+0.48175FA+0.8763FB=19.6144
    0.48175FA+0.8763FB=28.30138
    FA=(28.30138-0.8763FB)/0.48175

    Fy=ma
    FN+FAsinα-FBcosβ-mgcosθ=ma
    FN+FAsin61.2-FBcos61.2-(1.84)(9.8)(cos28.8)=(1.84)(10.66)
    FN+0.8763FA-0.48175FB-15.8=19.6144
    FN+0.8763FA-0.48175FB=35.416
    FA=(35.416-FN+0.48175FB)/0.8763

    If I put the two equations together to cancel out FA, I still have two unknowns. I don't know what I'm doing wrong. Maybe my FBD was wrong?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 24, 2009 #2

    Pengwuino

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    Gold Member

    Re: Forces/Acceleration

    Does this problem explicitly say gravity is even involved? This sounds like a simple vector problem.
     
  4. Oct 25, 2009 #3
    Re: Forces/Acceleration

    You're right. I didn't need to use forces to solve this:

    F = m*a
    = 1.84*10.66
    = 19.6 N

    If I draw a line from the origin 28.8deg north of east and derive the components, then Fx=the force eastward:

    Fx = 19.6 *cos(28.8) = 17.2 N
     
  5. Oct 25, 2009 #4

    Redbelly98

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    Staff Emeritus
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    Homework Helper

    Re: Forces/Acceleration

    Looks good :smile:

    p.s. Welcome to Physics Forums.
     
  6. Oct 26, 2009 #5
    Re: Forces/Acceleration

    Thank you. I know that I'll be using this forum a lot more :approve:
     
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