Knowing that α = 35°, determine the resultant of the three forces shown.
Fig. P2.35
The resultant of the three forces shown in figure P2.35.
Answer to Problem 2.35P
The resultant of three forces shown in the figure P2.35 is
Explanation of Solution
Refer figure P3.35.
The figure shows three forces of magnitude
Since these forces are making an angle with the axis of cylinder, they can be resolved into x and y components.
Write the equation to find the x component of
Here,
Write the equation to find the y component of
Here,
Similarly write the equation to find the x component of the
Here,
Write the equation to find the y component of
Here,
Write the equation to find the x component of the
Here,
Write the equation to find the y component of
Here,
Express a consolidated form of the x and y components of the three forces as shown in figure 1.
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.
Write the general expression of a vector with
Express the vectors
Write the equation to find the tangent of angle
Here,
Rewrite equation
Write the equation to find the y component of the resultant force vector.
Here,
Rewrite equation
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the resultant of the three forces shown in figure P2.35 is
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics 11th Edition
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