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Vector Addiction

  1. Aug 29, 2010 #1
    1. The problem statement, all variables and given/known data

    In the drawing below, what is the vector sum of forces vector A + vector B + vector C if each grid square is 12 N on a side?
    p2-10.gif


    I have been working at this problem for awhile now and the webassign keeps saying i have the wrong answer. I have one more shot at getting the answer correct. I have two problems like this one and cant seem to figure it out. I know that vector B = 48N, vector C = 24N, and using the pythagorean theorem i found vector A = 60N. Adding all of them up the sum is 132N, that is not correct. Im not sure exactly what to do. I also found the vectors that make up Ax = 36 and Ay = 48. Do i need these to solve the question. Is vector B supposed to be subtracted since it goes in the -y direction, as well as vector C going in the -x direction.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 29, 2010 #2

    rock.freak667

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    Consider the two directions separately. In the x-direction you have

    Ax=36N and C= -24N (Remember, vectors have direction, I chose right as positive)


    So what is the resultant of these two?


    Then do the same for the y-direction.

    Then the Pythagorean theorem will get you A+B+C
     
  4. Aug 29, 2010 #3
    The resultant of Ax and C = 12N. That is my x direction. the y component ends up being 0, Ay = 48N and B = -48N. Im not sure where to go from here using the pythagorean theorem.
     
  5. Aug 29, 2010 #4

    rock.freak667

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    Right well in that case, the resultant force = R

    So you have Rx= +12 N and Ry=0 N. So your resultant is just Rx. Also remember, to put the direction in your final answer.
     
  6. Aug 29, 2010 #5
    Re: Vector Addition

    So i figured out the answer to my first two problems, now im on the third and final one. Can anyone explain to me what the component method of adding vectors is. It differs from the vector sum in a certain way and i can't really distinguish that. My next problem i have solved for all x directions and y directions but the answer doesn't seem to be correct. Here is my 3rd question and the values i have calculated

    Use the component method to find the vector sum D + E + F. Each grid square is 3 N on a side.

    2-p-010-alt.gif

    My x directions are:
    Vector F = 6N
    Vector Ex= 6N
    Vector Dx = -9N

    x = 5N

    My Y directions are:
    Vector F = 0
    Vector Ey = -12N
    Vector Dy= -12N

    y = -24N

    The picture i drew makes the shape into a trapezoid. I thought that adding up just the x vectors would find the resultant, obviously that did not work. I guess what i will try next is solving for vector D and vector E, using the pythagorean theorem.

    vector d2 = dx2 + dy2
    vector e2 = ex2 + ey2

    That comes out to equal

    vector d2 = 81 + 144
    vector d2 = 225
    vector d = 15

    vector e2 = 36 + 144
    vector e2 = 180
    vector e = 13.4

    Will my answer be vector d = 15, vector e = 13.4, and vector f = 6 all added together.

    Which equals 34.4N, is this the correct answer?


    Thanks for all the help everyone
     
    Last edited: Aug 29, 2010
  7. Aug 29, 2010 #6

    rock.freak667

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    Re: Vector Addition

    Your directions of Dx and Dy should be positive.

    But once you have that, the parts in red, are the resultant forces in the x and y directions. So the magnitude of the resultant is just resultant = √(x2+y2)
     
  8. Aug 29, 2010 #7
    I'm not sure I follow why those two should be positive...drawing my arrows from head to tail those both would be negative as well as Ex would be negative while Ey would be positive...could u explain why those would be positive? if they are positive then my answer would be 21N, since y would equal 0
     
  9. Aug 29, 2010 #8

    rock.freak667

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    Vectors pointing towards the east are positive in x and towards the north are positive for y.

    So the components of E would be Ex pointing towards the east and Ey pointing towards the South (away from North).

    Hence the directions of D should be changed, else how you have it, your picture would show D pointing in the opposite direction.
     
  10. Aug 29, 2010 #9
    Awesome, thank you so much...21N is the correct answer. THANK YOU for the great explanation i understand how to do this now!!!!!!!!
     
  11. Aug 30, 2010 #10
    Re: Vector Addition

    Have you try graphical method? I am pretty sure the question is intentionally desighned for you to use graphical method.
     
  12. Aug 30, 2010 #11
    it says to use the compenent method to find the vector sum. What is the graphical method?
     
  13. Aug 30, 2010 #12
    It is to simply move the position of vectors on the so that they are connected head-to-tail.
    The vector sum is the vector drawn by joinning the free ends. The magnitude can be found by
    counting the square grids it occupies.
    Sorry for my bad English btw... if you dont know what i am talking, i can try to draw you a solution.
     
  14. Aug 30, 2010 #13
    Oh, thats actually what i did and it forms a trapezoid, that way is extremely simple...thanks for the explanation
     
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