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Magnitude of a ball's Acceleration

  1. Oct 1, 2014 #1
    1. The problem statement, all variables and given/known data

    A 0.17-kg cue ball rests on the pool table. It's struck by a cue stick applying force F1→ = 13Ni^+21Nj^
    Determine the magnitude of the ball's acceleration.

    2. Relevant equations

    ax = Fnet, x / m
    ay = Fnet, y / m
    a = Fnet / m

    3. The attempt at a solution

    Components of Acceleration:
    ax = 13Ni^ / 0.17kg = 76.47m/s2

    ay = 21Nj^ / 0.17kg = 123.53m/s2

    Magnitude:
    Fnet = √(13Ni^)2 * (21Nj^)2 = 24.7N

    angle θ = tan-1 * (21N / 13N) = 58.24° above the + x-axis (fixed. see replies below)

    Acceleration's Magnitude:
    a = Fnet / m = 24.7N / 0.17kg = 145.29m/s2 or 145m/s2 rounded

    I feel like this should be the answer, or that I'm very close to the answer. Am I missing a step? Did I do something wrong? Am I way off?
     
    Last edited: Oct 1, 2014
  2. jcsd
  3. Oct 1, 2014 #2

    gneill

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    Staff: Mentor

    Hi PhysicsHelp152, Welcome to Physics Forums.

    Your work and results look fine except for the angle. Take another look at which component is which for the arctan function to find the angle w.r.t. the x-axis.
     
  4. Oct 1, 2014 #3
    Is this the correct angle?
    θ = tan-1 * (21N / 13N) = 58.24° (fixed. see replies below)

    Also, the magnitude of the ball's acceleration is indeed 145m/s2?
    I ask because apparently it isn't correct? I answer my questions online and I get 5 tries to get it right. I only have one try left and I already tried 145m/s2.
     
    Last edited: Oct 1, 2014
  5. Oct 1, 2014 #4

    gneill

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    Staff: Mentor

    Yes, that looks better. But don't include the axis unit vectors in the formula: you're taking a ratio of component values, not vector quantities. Besides, the x-component is generally designated by the ##\hat{i}## unit vector, and the y-component by the ##\hat{j}## unit vector, and you seem to have swapped the components of the force vector by using "21Ni^" and "13Nj^".
    Your calculation looks fine. You may be getting hit by significant figures. How many sig figs in the given information?
     
  6. Oct 1, 2014 #5
    There are 2 sig figs in the given information... I think. So my answer should be two sig figs?
    But what would the answer be then?
     
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