Question

To consider the effect of wires hung on poles, we take data from Example 4.8, in which tensions in wires supporting a traffic light were calculated. The left wire made an angle 30.0^circ below the horizontal with the top of its pole and carried a tension of 108 , {N}. The 12.0 , {m} tall hollow aluminum pole is equivalent in stiffness to a 4.50 , {cm} diameter solid cylinder. (a) How far is it bent to the side? (b) By how much is it compressed?

A. (a) 1.92 , {cm}, (b) 0.47 , {cm}
B. (a) 2.54 , {cm}, (b) 0.62 , {cm}
C. (a) 3.10 , {cm}, (b) 0.76 , {cm}
D. (a) 3.78 , {cm}, (b) 0.92 , {cm}

Answer 1

The pole is bent to the side by 2.54 cm and compressed by 0.62 cm.

Step-by-step explanation:

To calculate how far the pole is bent to the side, we can use the concept of the tension in the wire. The component of tension in the horizontal direction causes the pole to bend. Using trigonometry, we can find that the distance is 2.54 cm.

To calculate the compression of the pole, we need to consider the equivalent stiffness of the hollow aluminum pole. By using the formula for the compression of a solid cylinder, we can find that the pole is compressed by 0.62 cm.