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Can somebody help translate this question? 2D Kinematics.

  1. Sep 27, 2011 #1
    I'm having difficult understanding the question, can somebody help me? The question is:

    "The velocity of a 3 kg particle is given by v = (3ti + 6(t^2)j )m/s, with time t in seconds. At the instant the net force on the particle has a magnitude of 35 N, what are the direction (relative to the positive direction of the x axis) of (a) the net force and (b) the particle's direction of travel?

    Answer:
    (a) 75.099403312170 Units ° (degrees)
    (b) 61.978933315223 Units ° (degrees)"


    My initial approach was to find t when the magnitude of the particle is 35N to get the components of the triangle.

    Velocity and Acceleration
    v = 3ti + 6(t^2)j
    a = 3 + 12t

    Time
    F = ma
    35 = 3(3+12t)
    35 = 9 + 36t
    26 = 36t
    .72 = t

    Since, I thought I was to find the angle created by the velocity vector, I found the y-comp. (opp.) and x-comp. (adj.).
    y-comp. = 6(t^2) = 6(.72^2) = 3.13
    x-comp. = 3t = 3(.72) = 2.27

    tan(theta) = opp./adj. = 3.13/2.27
    theta = arctan(3.13/2.27) = arctan(1.44) = 55.27

    However, 55.27 isn't the angle... for anything! Did I misinterpret the question? What is the difference between the two angles they are asking me to find, what are they asking of my specifically? If somebody can help me I would deeply appreciate it.

    Thank you for taking the time to read my question.
     
  2. jcsd
  3. Sep 27, 2011 #2

    PeterO

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    Homework Helper

    The velocity had an i and j component. 3ti + 6t2j

    Should the acceleration also have had an i and j component.
     
  4. Sep 27, 2011 #3
    Yes... however, I'm still quite oblivious to how that will help :/. I just assumed that the i and j component represented the x and y component of the slope for the velocity. How will i and j help in the equation for acceleration?

    Velocity and Acceleration
    v = 3ti + 6(t^2)j
    a = 3i + 12tj

    Time
    F = ma
    35 = 3(3i+12tj)
    35 = 9i + 36tj
    ..? help?
     
  5. Sep 27, 2011 #4

    PeterO

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    Homework Helper

    because the directions i & j are perpendicular, I expect you would be working with Pythagorus.

    (35/3)2 = 32 + (12t)2

    That will let you find t, so then substitute into velocity and acceleration expressions to find the directions and magnitudes.
     
  6. Sep 27, 2011 #5

    gneill

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    Staff: Mentor

    When you want to find the magnitude of the acceleration the components add in quadrature (that is, square root of the sum of the squares).
     
  7. Sep 27, 2011 #6
    Thank you so much! I really appreciate your help. :)
     
  8. Sep 28, 2011 #7
    So I solved a, but I don't know how to do part b. Anyone can help me out ?
     
  9. Sep 28, 2011 #8

    SammyS

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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The direction of the velocity is the direction of travel.
     
  10. Sep 28, 2011 #9
    Thank you !
     
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