Concept explainers
In the What If? section of Example 12.2, let d represent the distance in meters between the person and the hinge at the left end of the beam. (a) Show that the cable tension is given by T = 93.9d + 125, with T in newtons. (b) Show that the direction angle θ of the hinge force is described by
(c) Show that the magnitude of the hinge force is given by
(d) Describe how the changes in T, θ, and R as d increases differ from one another.
(a)
The cable tension is
Answer to Problem 12.66CP
The cable tension is given by,
Explanation of Solution
The weight of the person is
The diagram for the given condition is shown below.
Figure (1)
Apply the rotational equilibrium equation and take the torque about hinge support.
Here,
Rearrange the equation (1) for
Substitute,
Conculasion:
Therefore, the cable tension will be
(b)
The direction angle is
Answer to Problem 12.66CP
The direction angle will be
Explanation of Solution
Apply the equilibrium condition for the horizontal forces.
Apply the equilibrium equation for the vertical forces.
Here,
Divide equation (4) by equation (3).
Substitute,
Conculasion:
Therefore, The direction angle will be
(c)
The magnitude of the hinge force is
Answer to Problem 12.66CP
The magnitude of the hinge force will be
Explanation of Solution
Square on both side of equation(2) and equation(3) and then add them.
Substitute,
Conclusion:
Therefore, the magnitude of the hinge force is
(d)
The changes in
Answer to Problem 12.66CP
Explanation of Solution
Conclusion:
Therefore,
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Chapter 12 Solutions
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