Concept explainers
(a)
The resultant force.
(a)
Answer to Problem 3.139P
The resultant force is
Explanation of Solution
Write the equation of the distance between AC.
Here, the distance between AC is
Write the equation of the distance between BD.
Here, the distance between BD is
Write the equation of the momentum about AC.
Here, the momentum about AC is
Write the equation of the momentum about BD.
Here, the momentum about BD is
Write the equation of resultant force.
Here, the resultant force is
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
The magnitude of the resultant force,
Thus, the resultant force is
(b)
The pitch of the wrench.
(b)
Answer to Problem 3.139P
The pitch of the wrench is
Explanation of Solution
Write the equation of pitch of the wrench.
Here, the pitch of the wrench is
Since, the
Here, the constant is
Write the expression for the constant is,
Write the equation of momentum.
Here, the momentum is
Rewrite the expression for the momentum of the wrench is,
Conclusion:
Substitute,
Substitute,
Thus, the pitch of the wrench is
(c)
The point at which the axis of wrench intersects the yz-plane.
(c)
Answer to Problem 3.139P
The axis of wrench intersects the yz-plane at
Explanation of Solution
The diagram for the force-couple system is given below:
Refer fig 1,
Write the equation for the force couple system for the wrench.
Here, the momentum is
Write the expression for the momentum at which the wrench intersects the xz-plane.
Here, the position vector is
Write the expression for the position vector is,
Here, the coordinates are
Conclusion:
Substitute,
Substitute,
Substitute,
Comparing the coefficients of the y and z components both sides,
Therefore, the axis of wrench intersects the yz-plane at
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics
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