Determine the magnitude of the resultant force 2


Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x axis.

Determine the magnitude of the resultant force

Solution:

Draw the components as follows.

Determine the magnitude of the resultant force

(Remember to use the angle theorems with parallel lines)

Draw the vector components tail to tail as follows.

Determine the magnitude of the resultant force

Use cosine law to figure out F_{R}

F_{R} =\sqrt{6000^{2}+2000^{2}-(2)(6000)(2000)(\cos(105^{0}))}

 

F_{R} =6798N

 

Use sine law to figure out \theta

 

\frac{6798N}{\sin105^0}=\frac{6000N}{\sin\theta}

 

\theta = 58.5^0

 

To find the angle clockwise from the x-axis, add 58.5^0 + 45^0 = 103.5^0

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