Knowing that the tension in cable BC is 725 N, determine the resultant of the three forces exerted at point B of beam AB.
Fig. P2.36
The resultant of the three forces shown in figure P2.36.
Answer to Problem 2.36P
The resultant of three forces shown in the figure P2.36 is
Explanation of Solution
Figure 1 below shows the three forces acting on point A and their directions.
The figure shows three forces of magnitude
Since these forces make an angle with the axis, they can be resolved into x and y components.
The tension in the wire BC is
Write the equation to find the x component of
Here,
Substitute
Write the equation to find the y component of the tension in the wire.
Here,
Substitute
Similarly write the equation to find the x component of the
Here,
Substitute
Write the equation to find the y component of
Here,
Substitute
Write the equation to find the x component of the
Here,
Substitute
Write the equation to find the y component of
Here,
Substitute
Let
Write the equation to find the resultant of all the three x components.
Here,
Write the equation to find the resultant of all the three y components.
Here,
Write the general expression of a vector with
Express the vectors
Write the equation to find the resultant of vectors
Here,
Write the equation to find the tangent of angle
Here,
Rewrite equation
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the resultant of the three forces acting at point B shown in figure P2.36 is
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