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Find the magnitudes of all of the forces acting on the sled

  1. Apr 7, 2015 #1
    1. The problem statement, all variables and given/known data
    A person pulls on a rope attached to a 5 kg sled. The rope makes an angle of 30 degrees with the horizontal. Sled accelerates horizontally at 1.7 m/s^2. There is no friction.

    2. Relevant equations
    ma = Fnet
    mg = Fgravity

    3. The attempt at a solution
    Fnorm = earth force up on sled
    Fr = the force of the rope of the sled being pulled

    The x and y components for Fr would be y = Frsinθ and x=Frcosθ.
    Vector of Fnorm = <0, Fnorm>
    Vector of Fg = <0, -50>
    Vector of Fr = <Frcos30, Frsin30>

    Fnetx => 8.5 = Frcos30
    Fnety => 0 = Fc - 50 + Frsin30

    So I got this far and starting doing algebraic stuff to solve for Fr and then plugging that into the second equation. From there, I solved for Fc, and the value was 45.095 N. And from the Fnetx equation, Fr = 9.8 N.
    However, when I added all the magnitudes of forces, my answer does not equal to the Fnet, which is ma = 8.5 N.
    Can someone help me with this? Have I forgotten something? Am I even doing this right?
     
  2. jcsd
  3. Apr 7, 2015 #2
    Show us how you added up the forces to get the net force. Your answers so far look OK.

    Chet
     
  4. Apr 7, 2015 #3
    For the net force, I did the force magnitude of Fnorm plus force magnitude of Fr minus the force magnitude of Fg, which is 8.5 N + 45.095 N - 50 N. That answer got me 3.595 N.
     
  5. Apr 7, 2015 #4
    The forces have to be added as vectors, not as scalars.

    Chet
     
  6. Apr 7, 2015 #5
    How do I do that?
     
  7. Apr 7, 2015 #6
    You do it by adding their components. But, you've already done that.

    Chet
     
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