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Homework Help: Vector Addition/Components

  1. Sep 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Two force vectors are shown in the figure (not drawn to scale), and the total force vector C is the sum of A and B:C=A+B. If the magnitude of the total force is C = 80 N and its direction is specified by the angle measured from +x axis to be θC = −110˚, find B and φ for the force vector B.
    Capture.jpg
    2. Relevant equations
    Cx= Ax+ Bx
    Cy= Ay+ By
    C= sqrt(Cx^2+Cy^2)?
    tanθc=Cy/Cx?


    3. The attempt at a solution
    Ax=-150cos30=-130
    Ay=150sin30=75
    Cx=80sin(-110)=-75.2
    Cy=80cos(-110)=27.4

    Cx= Ax+ Bx
    -75.2= -130 + B > B= 54.8
    27.4= 75 + B > B=-47.6

    Not sure if I'm doing this right.
     
  2. jcsd
  3. Sep 2, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You mixed up the components here. And be careful with signs.
     
  4. Sep 2, 2010 #3
    ok i got that. now i could use a little hint about what to do next. i'm sure how to get the single magnitude for B.
     
  5. Sep 2, 2010 #4
    Both components of B sould be positive. Try make a drawing and work with reduced angles. 110 is at the second quarter, so work with 30 at the second quarter.
     
  6. Sep 2, 2010 #5
    i meant third quarter
     
  7. Sep 2, 2010 #6
    the components of A and C are Ax=-75sqrt2 Ay=75. Cx=-40 and Cy=-40sqrt2
     
  8. Sep 2, 2010 #7
    Bx=-40-75sqrt2 By=75-40sqrt2 and tanθB= By/Bx and it is at the second quarter. to find the angle subtract from 180, θB.
     
  9. Sep 2, 2010 #8
    what was your final answer by doing your method because it seems different from mine. i got B=182 N and the angle 34.3
     
  10. Sep 2, 2010 #9
    Bx=102 and By=-112. Do we agree so far?
     
  11. Sep 2, 2010 #10
    the way you did it yes. the way i was doing it no.
     
  12. Sep 2, 2010 #11

    Doc Al

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    Staff: Mentor

    Just set up the equations for components:

    Ax + Bx = Cx
    Ay + By = Cy

    And solve for Bx and By. Using the components, you can compute the magnitude.
     
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