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Stage Design A cable is used to support an actor as he swings onto the stage. Now suppose the tension in the cable is 920 N as the actor reaches the lowest point. What diameter should an 11-m-long steel cable have if we do not want it to stretch more than 0.50 cm under these conditions? R Yi Actor Sandbag SOLUTION Conceptualize Look back at the Example "A Grand Entrance," where we analyzed a cable used to support an actor as he swung onto the stage. We ignored any stretching of the cable there, but we wish to address this phenomenon in this example. Categorize We perform a simple calculation involving the equation F A Y = AL Li so we categorize this example as -Select--- v problem. Solve the Young's modulus equation for the cross-sectional area of the cable: FL; A = YAL Assuming the cross section is circular, find the diameter of the cable from d = 2r and A = ar (Use the following as necessary: F, Y, L;, AL, and n.): FL; A d = 2r = 21 = 2 V 元 Substitute numerical values. (Enter your answer in mm to at least 2 decimal places.): d = mm To provide a large margin of safety, you would probably use a flexible cable made up of many smaller wires having a total cross- sectional area substantially --Select--- than our calculated value. EXERCISE Suppose we choose to use a cable as described in the example to meet the minimal diameter requirement (to cut cost). We are told that such cable will break when extended by more than 0.62 cm, what is the maximum tension (in N) the cable can tolerate without breaking? Hint N

Stage Design A cable is used to support an actor as he swings onto the stage. Now suppose the tension in the cable is 920 N as the actor reaches the lowest point. What diameter should an 11-m-long steel cable have if we do not want it to stretch more than 0.50 cm under these conditions? R Yi Actor Sandbag SOLUTION Conceptualize Look back at the Example "A Grand Entrance," where we analyzed a cable used to support an actor as he swung onto the stage. We ignored any stretching of the cable there, but we wish to address this phenomenon in this example. Categorize We perform a simple calculation involving the equation F A Y = AL Li so we categorize this example as -Select--- v problem. Solve the Young's modulus equation for the cross-sectional area of the cable: FL; A = YAL Assuming the cross section is circular, find the diameter of the cable from d = 2r and A = ar (Use the following as necessary: F, Y, L;, AL, and n.): FL; A d = 2r = 21 = 2 V 元 Substitute numerical values. (Enter your answer in mm to at least 2 decimal places.): d = mm To provide a large margin of safety, you would probably use a flexible cable made up of many smaller wires having a total cross- sectional area substantially --Select--- than our calculated value. EXERCISE Suppose we choose to use a cable as described in the example to meet the minimal diameter requirement (to cut cost). We are told that such cable will break when extended by more than 0.62 cm, what is the maximum tension (in N) the cable can tolerate without breaking? Hint N

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Stage Design A cable is used to support an actor as he swings onto the stage. Now suppose the tension in the cable is 920 N as the actor reaches the lowest point. What diameter should an 11-m-long steel cable have if we do not want it to stretch more than 0.50 cm under these conditions? R. Actor Sandbag SOLUTION Conceptualize Look back at the Example "A Grand Entrance," where we analyzed a cable used to support an actor as he swung onto the stage. We ignored any stretching of the cable there, but we wish to address this phenomenon in this example. Categorize We perform a simple calculation involving the equation F A Y = AL Li so we categorize this example as --Select--- v problem. Solve the Young's modulus equation for the cross-sectional area of the cable: FL; A = YAL Assuming the cross section is circular, find the diameter of the cable from d = 2r and A = ar (Use the following as necessary: F, Y, Li, AL, and r.): FL A d = 2r = 2 - = 2 Substitute numerical values. (Enter your answer in mm to at least 2 decimal places.): mm To provide a large margin of safety, you would probably use a flexible cable made up of many smaller wires having a total cross- sectional area substantially -Select--- than our calculated value. EXERCISE Suppose we choose to use a cable as described in the example to meet the minimal diameter requirement (to cut cost). We are told that such cable will break when extended by more than 0.62 cm, what is the maximum tension (in N) the cable can tolerate without breaking? Hint N Need Help? Read It
Transcribed Image Text:Stage Design A cable is used to support an actor as he swings onto the stage. Now suppose the tension in the cable is 920 N as the actor reaches the lowest point. What diameter should an 11-m-long steel cable have if we do not want it to stretch more than 0.50 cm under these conditions? R. Actor Sandbag SOLUTION Conceptualize Look back at the Example "A Grand Entrance," where we analyzed a cable used to support an actor as he swung onto the stage. We ignored any stretching of the cable there, but we wish to address this phenomenon in this example. Categorize We perform a simple calculation involving the equation F A Y = AL Li so we categorize this example as --Select--- v problem. Solve the Young's modulus equation for the cross-sectional area of the cable: FL; A = YAL Assuming the cross section is circular, find the diameter of the cable from d = 2r and A = ar (Use the following as necessary: F, Y, Li, AL, and r.): FL A d = 2r = 2 - = 2 Substitute numerical values. (Enter your answer in mm to at least 2 decimal places.): mm To provide a large margin of safety, you would probably use a flexible cable made up of many smaller wires having a total cross- sectional area substantially -Select--- than our calculated value. EXERCISE Suppose we choose to use a cable as described in the example to meet the minimal diameter requirement (to cut cost). We are told that such cable will break when extended by more than 0.62 cm, what is the maximum tension (in N) the cable can tolerate without breaking? Hint N Need Help? Read It
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