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Vector Resultant problem

  1. Aug 11, 2003 #1
    I should slap myself for not picking out what I did wrong but...

    500 N are acting 140 degrees, 150 N are acting at 90 degrees and 420 N are acting at 60 degrees. Find the resultant.

    the Resultant = (Rx^2 + Ry^2)^(1/2)

    The angle of the resultant = arctan(Fy/Fx)

    Correct?

    Well, Fx = -500cos40 + 150cos90 + 420cos60 = -173.02222

    Fy = 500sin40 + 150sin90 + 420sin60 = 835.12447.

    Resultant = ((8.35.12447)^2 + (-173.02222)^2)^(1/2) = 852.85964 N

    angle of resultant = arctan(Fy/Fx) = arctan(835.12447/-173.02222) =
    78.29.

    The answers in the back of the book say 853 N and 101.7 degrees.

    I have the resultant correct but not the angle. If I had both wrong, I wouldn't question it, but one right and one wrong makes me question it. What went wrong?
     
  2. jcsd
  3. Aug 11, 2003 #2
    Nothing, you are right. The angle you calculated is with respect to the resultant, which has an x-component along the negative x-axis. So, your resultant angle is 180 - 78.29 = 101.71 (since we take the angles starting along the positive x-axis)
     
  4. Aug 11, 2003 #3
    Okay, that's good that I'm not going crazy but...

    my calculator needs to be changed because I got a slightly higher value for for the resultant angle.
     
  5. Aug 11, 2003 #4

    enigma

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    You were in the second quadrant.

    atan is only defined for the first and fourth quadrants. You can either do a quadrant check or see if there is a function to take it into account (like atan2 in Matlab).
     
  6. Aug 12, 2003 #5
    Yes, but I still need either a new calculator or a new light bulb (I'm sure I misread the figure in the first place)
     
  7. Aug 14, 2003 #6

    HallsofIvy

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    There's a little screw in the back to adjust answers slightly!:smile:
     
  8. Aug 14, 2003 #7
    lol. It's really a good calculator but then I'm thinking about the conditions I worked that problem in. It was 3 in the morning, dark except for that faint blue-glow from my office lamp, and freaking cold (which I had to admit, I enjoyed). You know how solar powered calculators are in faint light...

    So I'm assuming it was a midread figure due to bad lighting.

    About that screw, do TI-89's have it? If there's any calculator I want to trample, it's that one. :smile:
     
  9. Aug 14, 2003 #8

    enigma

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    AAH Blasphemy!

    I love my TI-89! You can teach them to do anything.

    Mine came able to sit up, roll over, and fetch, and I've even taught it to make a mean cup of coffee.
     
  10. Aug 14, 2003 #9
    Blasphemy? Blasphemy is when you talk bad about Led Zeppelin.

    But what I said about the TI-89... I meant every word of it! :smile:

    Actually, I haven't gone beyond simple operations and simple graphing so maybe I'm just ignorant of its potential.

    Would you mind sharing with us a few good (and useful) things you've acquired from you TI-89?
     
  11. Aug 15, 2003 #10

    HallsofIvy

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    Considering all the hours I spent calculating eigenvalues BY HAND, the TI-89 is a miracle!

    (For doing basic things like evaluating functions or solving equations, a more basic calculator is easier to use.)
     
  12. Aug 16, 2003 #11
    I have to admit, they can take some of the grunt out of grunt work but I've wanted to smash mine into [al]0 pieces because the time I actually need it to work, it does nothing.

    You might think I'm weird but I've put away the calculator and I prefer to do most calculations by hand or mind.

    I'm not trying to sound arrogant but I want to exercise the mind God blessed me with.

    But don't get me wrong. If I have to calculate arctan(0.314573) in a hurry, forget Taylor Series. I'll use the calculator. :smile:
     
    Last edited: Aug 16, 2003
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