A 300-N force is applied at A as shown. Determine (a) the moment of the 300-N force about D, (b) the magnitude and sense of the horizontal force applied at C that creates the same moment about D, (c) the smallest force applied at C that creates the same moment about D.
(a)
Moment of
Answer to Problem 3.5P
Moment of
Explanation of Solution
Refer Figure 1.
Write an expression to calculate the force vector acting at point A
Here,
Write an expression to calculate the position vector along line connecting A and D.
Here,
Write an expression to calculate the moment about point D.
Here,
Substitute equation (I) and (II) in equation (III) to rewrite equation (III).
Conclusion:
Substitute
Therefore, the of
(b)
The magnitude and sense of horizontal force applies at C that creates the same moment about D.
Answer to Problem 3.5P
The magnitude and sense of horizontal force applies at C that creates the same moment about D is
Explanation of Solution
Refer Figure 2.
Write an expression to calculate the position vector along line connecting C and D.
Here,
Write an expression to calculate the moment about point D.
Here,
Write an expression to calculate the force acting at point C.
Here,
Substitute equation (V) and (VII) in equation (VI) to rewrite equation (VI).
Write an expression to determine the magnitude of the moment about D.
Here,
Rearrange the equation (IX) to determine the magnitude of force acting at point C.
Conclusion:
Substitute
Therefore, the magnitude and sense of horizontal force applies at C that creates the same moment about D is
(c)
The smallest force applied at C that creates the same moment about D.
Answer to Problem 3.5P
The smallest force applied at C that create the same moment about D is
Explanation of Solution
Refer Figure 3.
For minimum force, the force vector
Write an expression to calculate the smallest magnitude of force vector
Here,
Write an expression to calculate the length of DB.
Substitute equation (XII) in (XI) to rewrite the equation (XI).
Write an expression to calculate the angel
Write an expression to calculate the direction of force.
Substitute equation (XIV) in (XV) to rewrite find (XV).
Conclusion:
Substitute
Write an expression to calculate the angel
Write an expression to calculate the direction of force.
Substitute equation (XIV) in (XV) to rewrite find (XV).
Substitute
Therefore, the smallest force applied at C that create the same moment about D is
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics, 11th Edition
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L