![]() It's because there are two wires, each having this same 80-degree angle, the total force parallel to the pole is going to be two times this component, and this component is the adjacent leg of this triangle here, or this part is the perpendicular component of the tension. This component here, in other words, in red here, I'm drawing the force of tension parallel component. ![]() The total force parallel to the pole is going to be the component of the tension that is directed along the pole. We've looked up the Young's modulus and we're given the initial length of 15 meters, and the area is pi times the radius of the pole squared, but the radius is half the diameter, and we end up with pi times diameter squared over 4. It's the initial length, and it's Young's modulus, and it's area. To figure out the change in length of the pole or its compression, in other words, we need to know what the total force is that's parallel to the pole. I'm just trying to emphasize this 80-degree angle that's here. Now we look at just one of the wires on the side. The diameter of the pole is 18 centimeters, it has a length of 15 meters, and the tension in each of these wires is 4.00 times 10 to the 4 newtons. That's 5 times 10 to the 9 newtons per square meter. For the sheer modulus, we look across to here and take half of 10. We look in Table 5.3 for hardwood and see that it's Young's modulus is 15 times 10 to the 9 newtons per meter squared, so half of that is seven and a half times 10 to the 9. ![]() We're told that the pole has half the strength of hardwood. For the compression, we'll need to know what Young's modulus is and for the amount of bending over, we'll need to know the sheer modulus. Then part B asked us how much do these two power lines bend the pole over. For parts A and B of the question, we're going to ask how much do these power lines compress the pole which happens because of this 80-degree angle, some component of this tension that is directed downwards. This guy-wire is part of part C in this question, but initially we imagined that there's no guy-wire connected to the ground. The lines are at an angle of 80 degrees with respect to the pole. A power pole has two power lines connected to it and there's a 90-degree angle here between these power lines. This is College Physics Answers with Shaun Dychko.
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