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- Show that for a "broken in" clutch, the maximum torque transfer through the clutch occurs when the inner radius of the clutch "r" is equal to the outer radius of the clutch "ro" divided by the "√3" (i.e. r₁ = 12). Start with equation 18.6 (i.e. T = (π)(Pmax)(µ)(N)(ro²ri — r₁³)). Treat "r" as the independent variable, "T" as the dependent variable, and the remaining parameters as "constants" (Note: Essentially, the torque "T" is a cubic function (3rd degree polynomial) of the inner radius "r"). "Maximize" this "cubic function" over a realistic domain using differential calculus. Be sure to show the "critical point" r₁ = 1/3 corresponds to a "relative maximum" (Hint: This can be done by using either the 1st derivative test or the 2nd derivative test).

- Show that for a "broken in" clutch, the maximum torque transfer through the clutch occurs when the inner radius of the clutch "r" is equal to the outer radius of the clutch "ro" divided by the "√3" (i.e. r₁ = 12). Start with equation 18.6 (i.e. T = (π)(Pmax)(µ)(N)(ro²ri — r₁³)). Treat "r" as the independent variable, "T" as the dependent variable, and the remaining parameters as "constants" (Note: Essentially, the torque "T" is a cubic function (3rd degree polynomial) of the inner radius "r"). "Maximize" this "cubic function" over a realistic domain using differential calculus. Be sure to show the "critical point" r₁ = 1/3 corresponds to a "relative maximum" (Hint: This can be done by using either the 1st derivative test or the 2nd derivative test).

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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- Show that for a "broken in" clutch, the maximum torque transfer through the clutch occurs when the inner radius of the clutch "r" is equal to the outer radius of the clutch "ro" divided by the "√3" (i.e. r₁ = 12). Start with equation 18.6 (i.e. T = (π)(Pmax)(µ)(N)(ro²ri — r₁³)). Treat "r" as the independent variable, "T" as the dependent variable, and the remaining parameters as "constants" (Note: Essentially, the torque "T" is a cubic function (3rd degree polynomial) of the inner radius "r"). "Maximize" this "cubic function" over a realistic domain using differential calculus. Be sure to show the "critical point" r₁ = 1/3 corresponds to a "relative maximum" (Hint: This can be done by using either the 1st derivative test or the 2nd derivative test).
Transcribed Image Text:- Show that for a "broken in" clutch, the maximum torque transfer through the clutch occurs when the inner radius of the clutch "r" is equal to the outer radius of the clutch "ro" divided by the "√3" (i.e. r₁ = 12). Start with equation 18.6 (i.e. T = (π)(Pmax)(µ)(N)(ro²ri — r₁³)). Treat "r" as the independent variable, "T" as the dependent variable, and the remaining parameters as "constants" (Note: Essentially, the torque "T" is a cubic function (3rd degree polynomial) of the inner radius "r"). "Maximize" this "cubic function" over a realistic domain using differential calculus. Be sure to show the "critical point" r₁ = 1/3 corresponds to a "relative maximum" (Hint: This can be done by using either the 1st derivative test or the 2nd derivative test).
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