In Prob. 3.56, determine the perpendicular distance between a line joining points F and B and the line of action of P.
The perpendicular distance between a line joining points
Answer to Problem 3.65P
The perpendicular distance between a line joining points
Explanation of Solution
Refer the Problem 3.56P
Write the expression for force
The magnitude of the line joining points
The unit vector at line joining points
Here, the unit vector at line joining points
Substitute
Write the equation of the moment of
Here, the moment of force is
Conclusion:
Substitute
Write the expression for force
The magnitude of the line joining points
The unit vector at line joining points
Here, the unit vector at line joining points
Substitute
Write the equation of the moment of
Here, the perpendicular component contribute to the moment of force about the line
Substitute
The relation between perpendicular and parallel component contribute to the moment of force is,
Here, the parallel component of moment is
Rewrite the equation (III) to get
Refer the Problem 3.56
The moment of
Substitute
Write the equation for the moment about a line joining points
Here, the moment about a line joining points
Rewrite the relation in terms of
Refer the Problem 3.56
The value of the moment line joining points
Substitute
Therefore, the perpendicular distance between a line joining points
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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