A worker tries to move a rock by applying a 360-N force to a steel bar as shown, (a) Replace that force with an equivalent force-couple system at D. (b) Two workers attempt to move the same rock by applying a vertical force at A and another force at D. Determine these two forces if they are to be equivalent to the single force of Part a.
(a)
An equivalent force-couple system applied at D to replace the force at B.
Answer to Problem 3.85P
Thus the force-couple system at D to replace the force at B is
Explanation of Solution
Refer Fig P3.85.
Write the expression of the force at D in component form.
Here
Write an expression of the vector connecting point B and D.
Here
Write an expression for the couple at D.
Here
Conclusion:
Substitute
Substitute
Substitute the value of
Thus the force-couple system at D to replace the force at B is
(b)
Two forces at A and D to replace the force in section (a).
Answer to Problem 3.85P
Thus the vertical force at A is
Explanation of Solution
Refer Fig P3.85.
Write the expression of couple at D.
Here
Write the expression of the
Here
Write the expression connecting the forces at A, D and B with the force in the section (a).
Here
Conclusion:
Substitute
Substitute
Solve the above equation to get
Substitute
Write the expression for the magnitude of
Write the expression for the angle made by
Thus the vertical force at A is
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Chapter 3 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics
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