Concept explainers
A traffic-signal pole may be supported in the three ways show part c, the tension in cable BC is known to be 1950 N. Determ the reactions for each type of support shown.
Fig. P4.50
The reaction forces acting on the support.
Answer to Problem 4.50P
The reaction forces acting on the support in figure (a) are
Explanation of Solution
The free body diagram of the traffic signal pole (a) and its support is given in the figure 1.
The free body diagram of the traffic signal pole (b) and its support is given in the figure 2.
The free body diagram of the traffic signal pole (c) and its support is given in the figure 3.
Write the equation to find the moment of force.
Here,
Write the equation to find the total moment about the point
Write the equations for equilibrium for the free body diagram.
Here,
Write the equation for the Pythagoras theorem to find the side
Write the equation to find the angle of orientation of the reaction force on
Write the expression to find the vector
Write the equation to find the angle of orientation of the components of
Conclusion:
Refer figure P4.50(a) and figure 1.
Substitute
Solve equation (I) using the figure 1.
Here,
Substitute
Solve equation (II) using figure 1.
Here,
Substitute
Solve equation (III) using figure 1.
Here,
Substitute
Substitute
Substitute
Substitute
Refer figure P4.50(b) and figure 2.
Solve equation (I) using the figure 2.
Here,
Substitute
Solve equation (II) using figure 2.
Solve equation (III) using figure 2.
Substitute
Substitute
Substitute
Refer figure P4.50(c) and figure 3.
Solve equation (I) using the figure 3.
Here,
Substitute
Solve equation (II) using figure 3.
Here,
Substitute
Solve equation (III) using figure 1.
Here,
Substitute
Substitute
Substitute
Substitute
Therefore, the reaction forces acting on the support in figure (a) are
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