Concept explainers
To Find:The tension in the backstay and the normal force that the deck exerts on the mast.
Answer to Problem 17P
The tension in thee backstay is
The normal force exerted by the deck on the mast is
Explanation of Solution
Given data:
Free body diagram for the given situation is as follows:
Formula used:
Apply the condition of translational and
Calculation:
Apply the condition of rotational equilibrium to the mast. The net torque due to tension by the wires is equal to zero and is represented as:
Torque due to the left side of the pole is given as
Torque due to right side of the pole is given as
Since the torque due to right side of the wire is in clock wise direction, it is negative.
Thus, the torque of horizontal components according to the condition of rotational equilibrium is given as
Here,
Substitute
From the figure, angle of forestay is obtained as follows:
Here,
Substitute
Determine the tension in the backstay as below.
Substitute the
Therefore, the tension in the backstay is
Torque due to the left side of the pole is given as,
Torque due to right side of the pole is given as,
Since the torque due to right side of the wire is in clock wise direction, it is negative.
Thus, the net torque of vertical components according to the condition of rotational equilibrium is given as,
Here,
Re-arrange the above equation for
Substitute
Conclusion:
The normal force exerted by the deck on the mast is
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Chapter 12 Solutions
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