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D11 B X P A a a D E 8 За щи A step-ladder has two sides AB and AC, each of length 4a, smoothly hinged at A and connected by a light taut rope DE, where AD = AE = a. The side AC is light, and the side AB is of weight W and is assumed to be uniform. A man of weight 4W stands at a point P on AB, where BP = x, and the system is in equilibrium with B and C on a smooth horizontal floor and the sides at an angle to the vertical. Find the reaction at C and the tension in the rope. Given also that DE is an elastic rope of natural length +a and modulus W, show that the condition for equilibrium is x=1a (8 cos 0-cot 0 - 1). Show that the maximum value of x for which equilibrium is possible is just over 2a.

D11 B X P A a a D E 8 За щи A step-ladder has two sides AB and AC, each of length 4a, smoothly hinged at A and connected by a light taut rope DE, where AD = AE = a. The side AC is light, and the side AB is of weight W and is assumed to be uniform. A man of weight 4W stands at a point P on AB, where BP = x, and the system is in equilibrium with B and C on a smooth horizontal floor and the sides at an angle to the vertical. Find the reaction at C and the tension in the rope. Given also that DE is an elastic rope of natural length +a and modulus W, show that the condition for equilibrium is x=1a (8 cos 0-cot 0 - 1). Show that the maximum value of x for which equilibrium is possible is just over 2a.

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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D11 B X P A a a D E 8 За щи A step-ladder has two sides AB and AC, each of length 4a, smoothly hinged at A and connected by a light taut rope DE, where AD = AE = a. The side AC is light, and the side AB is of weight W and is assumed to be uniform. A man of weight 4W stands at a point P on AB, where BP = x, and the system is in equilibrium with B and C on a smooth horizontal floor and the sides at an angle to the vertical. Find the reaction at C and the tension in the rope. Given also that DE is an elastic rope of natural length +a and modulus W, show that the condition for equilibrium is x=1a (8 cos 0-cot 0 - 1). Show that the maximum value of x for which equilibrium is possible is just over 2a.
Transcribed Image Text:D11 B X P A a a D E 8 За щи A step-ladder has two sides AB and AC, each of length 4a, smoothly hinged at A and connected by a light taut rope DE, where AD = AE = a. The side AC is light, and the side AB is of weight W and is assumed to be uniform. A man of weight 4W stands at a point P on AB, where BP = x, and the system is in equilibrium with B and C on a smooth horizontal floor and the sides at an angle to the vertical. Find the reaction at C and the tension in the rope. Given also that DE is an elastic rope of natural length +a and modulus W, show that the condition for equilibrium is x=1a (8 cos 0-cot 0 - 1). Show that the maximum value of x for which equilibrium is possible is just over 2a.
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