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What is the magnitude of the total momentum

  1. Feb 26, 2004 #1
    hi, i did the first part of this problem but on
    the second i'm stuck.

    A golf ball with mass 4.5×10^-2 kg is moving
    in the +x-direction with a speed of 8.65 m/s ,
    and a baseball with mass 0.145 kg is moving in
    the -y-direction with a speed of 7.2m/s .
    --What is the magnitude of the total momentum
    of the system that consists of the two balls?
    (i got for this one 1.06 kg*m/s using p=mv for
    each ball and adding them )
    --What is the direction of the total momentum
    of the system that consists of the two balls?
    Express your answer as an angle measured from
    below the x-axis (for this part i tried doing
    arctangent but the answer is not right)

    any help is good, thanks.
     
  2. jcsd
  3. Feb 27, 2004 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Write the two momentum vectors in "component" notation:

    "A golf ball with mass 4.5×10^-2 kg is moving
    in the +x-direction with a speed of 8.65 m/s " so it's momentum is 4.5x10^-2*8.65= 0.38925 in the positive x direction:
    0.38925i+ 0j
    (i is the unit vector in the positive x-direction and j is the unit vector in the positive y-direction.)

    " baseball with mass 0.145 kg is moving in
    the -y-direction with a speed of 7.2m/s" so its momentum is 0.145*7.2=
    1.044 in the negative y direction:
    0i- 1.044j

    The total momentum vector for the system is the sum of those two vectors: 0.38925i- 1.044j

    You can NOT just add the raw values- they are not in the same direction! (and I don't see how you could have gotten "1.06" in any case.)

    The magnitude of the momentum is the "length" of that vector which is, by the Pythagorean theorem, √(0.389252+ 1.0442)= 1.114 kg m/s approximately.

    Yes, you should be able to find the angle using arctan:
    The vector diagram should give you a right triangle with legs of length .38925 and 1.044 (and, of course, hypotenuse of length 1.114).
    The tan(θ)= .38925/1.044= .3728 so θ= 20.5 degrees (make sure your calculator is in "degree mode" if you want angles in degrees).

    Now, check your diagram to see where that angle is! I have intentionally done the "wrong" angle so you will need to determine what the angle is measured from "below the x-axis".
     
  4. Feb 29, 2004 #3
    thans you, i did get the right angle after ur explanation, it was 70 degrees, thanks again! :)
     
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