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Finding the direction of acceleration in degrees

  1. May 25, 2009 #1
    1. The problem statement, all variables and given/known data
    "Forces of 10.6 N north, 19.1 N east, and 16.0 N south are simultaneously applied to a 3.62 kg mass as it rests on an air table. What's the direction of acceleration in degrees (Take east to be 0 degrees and counterclockwise to be positive.) "

    Using components, I already figured out the magnitude of acceleration.
    a=5.48m/s/s
    Fnet=19.8N --> broken into components: F(x)=19.1N, F(y)=-5.4N


    2. Relevant equations
    Fnet=ma
    Trig ratios for sin and cos


    3. The attempt at a solution
    Using components, I figured out the total force in the x and y directions, and then used the pythagorean theorem to calculate the Fnet.

    To find acceleration, I then isolated for a = Fnet/m = 5.48m/s/s

    However, I'm having a lot of trouble figuring out the direction of the acceleration, and I don't know why! It's simple trig ratios.

    cos(thetha) = F(x)/Fnet = 19.1/19.8
    (theta) = 15.3 degrees
    Its positive because the counterclockwise direction is positive.

    Am I doing it wrong because they are asking for the direction of accleration, and I'm using the direction of Fnet? I don't see how I can use acceleration in the trig ratios though, since acceleration is only in the direction of Fnet... not the components on the x and y axis.
     
  2. jcsd
  3. May 25, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    You don't need Fnet to find the angle. Use tan(theta)=F(y)/F(x). Using the rounded value of Fnet gives you a fairly large error in this case. The direction of the acceleration is the same as that of the force. So you have the angle relative to the x (east-west) axis. Now look at the force vector. Is that 15 degrees clockwise or counterclockwise from east?
     
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