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The perpendicular distance (d) between rod AB and the line of action of Q.
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Answer to Problem 3.65P
The perpendicular distance (d) between rod AB and the line of action of Q is
Explanation of Solution
Given information:
The length of the vertical rod CD
The length of the rod AB
The force (Q) is 174 lb.
The distance between the points O to B (x) is 32 inch.
The distance between the points O to A (y) is 24 inch.
The vertical height of OA
The vertical height of OH
The horizontal distance between point O and midpoint C
The horizontal distance between midpoint C and point G over x axis
The horizontal distance between point B and midpoint C
The horizontal distance between midpoint C and point G over z axis (h) is 18 inch.
Calculation:
Calculate the position vector of AB using the relation:
Substitute 32 in. for x, 30 in. for
Calculate the unit vector of AB
Substitute
Apply the force Q at the point H.
Calculate the position vector of from point H to point B
Substitute 32 in. for x and 17 in. for
Calculate the position vector of DH using the relation:
Substitute 16 in. for
Calculate the force
Substitute 174 lb for P,
Calculate the position vector at Q
Substitute
Calculate the angle between AB and Q
Substitute
Calculate the moment about AB
Substitute
Calculate the perpendicular distance (d) between rod AB and the line of action of Q:
Take moment about AB:
Substitute 174 lb for Q and
Thus, the perpendicular distance (d) between rod AB and the line of action of Q is
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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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