Determine the magnitude of the resultant force


Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis.

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Solution:

Draw the components as follows. (Note that the diagrams are not to scale)

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Draw the vector components tail to tail as follows.

q3-2

Use cosine law to figure out the resultant force F_{R}

F_{R}=\sqrt{600^2+800^2-(2)(600)(800)(\cos60^0)}

 

F_{R}=721.1N

 

Use sine law to figure out angle counter clockwise from the x-axis

\frac{600}{\sin\theta} = \frac{721.1}{\sin60^0}

 

\theta = 46.1^0

 

Subtract \theta from 90^0 to get the angle between x-axis and the resultant force.

\phi = 90^0-46.1^0 = 43.9^0

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