uppose such a cable is strung between poles spaced 500 meters apart across a rural landscape. The cables are allowed to sag, following a natural curve called a catenary, increasing their length negligibly over the distance between the poles. 1. What is the total weight in newtons of the mass of the cable held aloft by its supports? 2. A cable tension of 200,000 N results in a sag at the middle of the cable of about 2.5 meters, adding only 0.3% to the length of the cable. Why is the tension so much greater than its weight? 3. What is the speed of a wave along this cable that could develop from wind or vibration in the towers supporting the cable? 4. What are the first three lowest natural frequencies of the cable's vibration created by standing waves between the supports? 5. Based on the physics you know, what factors would affect the choice of how far apart to make the towers?
Suppose such a cable is strung between poles spaced 500 meters apart across a rural landscape. The cables are allowed to sag, following a natural curve called a catenary, increasing their length negligibly over the distance between the poles.
1. What is the total weight in newtons of the mass of the cable held aloft by its supports?
2. A cable tension of 200,000 N results in a sag at the middle of the cable of about 2.5 meters, adding only 0.3% to the length of the cable. Why is the tension so much greater than its weight?
3. What is the speed of a wave along this cable that could develop from wind or vibration in the towers supporting the cable?
4. What are the first three lowest natural frequencies of the cable's vibration created by standing waves between the supports?
5. Based on the physics you know, what factors would affect the choice of how far apart to make the towers?
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