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Math Help - Magnitude and Direction

  1. #1
    A riddle wrapped in an enigma
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    Magnitude and Direction

    Hey guys,

    This is more for the Physics forum, but there's noone over there.

    Three workers are pulling on ropes attached to a tree stump (S) as shown in the diagram.
    Find the magnitude and direction of the resultant force on the stump.

    Diagram is attached at the bottom.

    A force of 60 Newtons North, a force of 35 Newtons East and a force of 40 Newtons 60 degrees South of East is applied.

    I know the answer is 61 Newtons at a direction of 23 degrees North of East, but I'll be danged if I can get there.

    A little nudge in the right direction would be helpful.

    Magnitude and Direction-stump.jpg
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  2. #2
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    Make a polygon of the forces and then use the trigonometric functions to solve the distance.
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  3. #3
    A riddle wrapped in an enigma
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    Revised drawing:

    Magnitude and Direction-stump1.jpg

    I have two resultant vectors with two different magnitudes with 2 different directions.

    I need these two forces to combine to 61 Newtons somehow. Do I combine those two vectors and find the resultant of these two forces?

    "My mind's going, Dave. I can feel it."
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  4. #4
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    Decompose the force vectors into each of their x- and y-components, then sum the x-components and sum the y-components. The resulting x- and y-components are the components of the resultant force.

    Note the x- and y-components of a force vector \vec A is given by

    x = |\vec A|\cos \theta
    y = |\vec A|\sin \theta

    where |\vec A| is the magnitude of the force vector and \theta is the angle between the force vector and the x-axis.
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  5. #5
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    It is not need to make two result vectors and then find final resultant. Just make a polygon of vectors and use trigonometric. Find what is a polygon of the vectors. This way is better because when you will get 10, 15 vectors, It is not need two make resultant for each two vectors.

    Kind regards
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  6. #6
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    Quote Originally Posted by masters View Post
    Revised drawing:

    Click image for larger version. 

Name:	stump1.jpg 
Views:	25 
Size:	7.3 KB 
ID:	21387

    I have two resultant vectors with two different magnitudes with 2 different directions.

    ...
    If you want to use both resultant forces you would have used the force of 35 N twice!

    Quote Originally Posted by masters View Post
    Hey guys,

    Three workers are pulling on ropes attached to a tree stump (S) as shown in the diagram.
    Find the magnitude and direction of the resultant force on the stump.

    Diagram is attached at the bottom.

    ...
    I assume that you are looking for a more geometric way to solve this question:

    1. I've attached a (nearly exact) drawing. Scale is 1 cm correspond to 10 N.

    2. Calculate the green resultant first using Pythagorean theorem ( \sqrt{4825})

    2. Calculate the green angle: \tan^{-1}\left(\frac{60}{35}\right)\approx 59.744^\circ

    3. Use the greyed triangle and the Cosine rule to calculate the final (red) resultant:

    R = \sqrt{4825 + 1600 - 2 \cdot \sqrt{4825} \cdot 40 \cdot \cos(60.256^\circ)}

    I've got R \approx 60.565\ N

    4. Use Sine rule or Cosine rule to calculate the missing angle.
    Attached Thumbnails Attached Thumbnails Magnitude and Direction-dreikraefte.png  
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