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Calculating 3-Way Vectors

  1. May 15, 2016 #1
    1. The problem statement, all variables and given/known data

    upload_2016-5-15_18-24-22.png

    2. Relevant equations


    3. The attempt at a solution

    I can't remember what this method of calculation this is as it's been a while since I've done this.

    upload_2016-5-15_18-25-55.png


    Could someone explain to me what I've done wrong in my calculations?

    The answer was 13.8N at 80 degrees.

    upload_2016-5-15_18-28-37.png
     
  2. jcsd
  3. May 15, 2016 #2

    Simon Bridge

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    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You are asked to do it graphically. The method you are looking for is "head to tail".
    What you did was resolve the vectors into components, add the components... this approach is prone to compounding mistakes.
    You probably have rounding errors due to irrational numbers, check your arithmetic too
    i.e. the value for y in (2) is incorrect.

    ... notice
    - for (2) and (3) the triangles are similar - in the technical sense: the 90-60-30 triangle has sides of ratios 1:2:√3
    - force B and force C are 90deg to each other.
     
  4. May 15, 2016 #3

    jedishrfu

    Staff: Mentor

    Look at how you computed y in the second vector is it really sqrt(7^2 - 3.5^2) = 2?

    does 2^2 + 3.5^2 =?= 7^2? thats a simple check you could have done.

    Also if you're going to use sin and cos why are you bothering with pythagoras? it takes longer to compute and its not elegant in this case.

    The third vector y value is 15/2 = 7.5 an exact number which again shows why using Pythagoras causes a rounding problem that didn't need to be there.

    You should KNOW that sin 60 = sqrt(3)/2 and cos 60 = 1/2 and you should know that sqrt(3) = 1.732...

    Hope this helps.

    Take care.
     
    Last edited: May 15, 2016
  5. May 15, 2016 #4
    Thanks Simon and jedishrfu. It turns out it was the wrong calculation in (2) as you guys spotted.

    Need to triple check my work next time :smile:
     
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