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Summing forces: finding acceleration and F_n

  1. Sep 20, 2015 #1
    K8rI7VE.png
    1. The problem statement, all variables and given/known data

    Use the steps outlined above to find the magnitude of the acceleration a of a chair and the magnitude of the normal force FN acting on the chair: Yusef pushes a chair of mass m = 55.0 kg across a carpeted floor with a force F⃗ p (the subscript 'p' here is lowercase and throughout the question) of magnitude Fp = 160 N directed at θ = 35.0 degrees below the horizontal (Figure 1) . The magnitude of the kinetic frictional force between the carpet and the chair is Fk = 107N .

    What is the magnitude of the acceleration a of the chair? What is the magnitude of the normal force FN acting on the chair?
    Express your answers, separated by a comma, in meters per second squared and newtons to three significant figures.

    2. Relevant equations
    ΣFx = Fpcosθ−Fk = m * a_x
    ΣFy = FN−FG−Fpsinθ =m * a_y

    3. The attempt at a solution

    a_x
    6mSCUfO.jpg

    a
    1N8AEWb.jpg

    F_n
    aI978Q8.jpg

    Answers
    O3x4Vm1.png
     
  2. jcsd
  3. Sep 20, 2015 #2

    Doc Al

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    Staff: Mentor

    Redo your calculation of the normal force. The applied force acts downward and thus must increase the normal force.
     
  4. Sep 20, 2015 #3
    Ah that makes sense. However, in F_N = F_g + F_py, F_py = 160N * sin(325) which gives me a negative number. The problem states that the force is applied at -35 degrees. Intuitively,I now know that greater pushing force increases normal force... but what can I do when I'm given an angle like this? Maybe add 180 degrees?
     
  5. Sep 20, 2015 #4

    Doc Al

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    Staff: Mentor

    Don't just plug in numbers blindly. What does the minus sign mean? Just that it points downward. So be consistent. If F_py is negative, so should F_g be negative. They both point down.
     
  6. Sep 20, 2015 #5
    But leaving it as negative gives me the incorrect answer?

    F_N = F_g + F_py = 539N + 160 * sin(325)
    F_N = 539N - 91.77N = ~447N (incorrect)

    F_N = F_g + F_py = 539N + 160 * sin(325 + 180)
    F_N = 539N + 91.77N = ~631N(correct)
     
  7. Sep 20, 2015 #6

    Doc Al

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    Staff: Mentor

    You must be consistent. If that force is negative, so must be F_g. And the equation you want is ΣF_y = 0.
     
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