Explanation Given information : The mass of the block D is 4kg. The mass of the block E is 6kg. The distance x value is 2 m. Assumption: Consider the point F in between the point B and C . Draw a free body diagram of the cord and its distances as shown below in Figure 1. Draw the free body diagram of the forces acting on cord as shown below in Figure 2. Determine the length of the cord AB using the formula. l A B = l B F 2 + l A F 2 (I) Here, the length of the point BF is l B F and the length of the point CF is l C F . Determine the length of the cord AC using the formula. l A C = l A F 2 + l C F 2 (II) Here, the length of the point BE is l B E . Determine the weight of the block D . W D = m D g (III) Here, the mass of block D is m D and the acceleration due to gravity is g . Determine the weight of the block E . W E = m E g (IV) Here, the mass of block E is m E . Determine the tension force F and the sag s by applying the Equation of equilibrium. Along the horizontal direction : ∑ F x = 0 W E sin ϕ A C − W D sin θ A B = 0 W E sin ϕ A C = W D sin θ A B (V) Here, the angle of cord AC is ϕ A C and the angle of cord AB is θ A B . Along the vertical direction : ∑ F y = 0 W E cos ϕ A C − W D cos θ A B − F = 0 (VI) Conclusion : Substitute 4 m for l B F and s for l A F in Equation (I). l A B = 4 2 + s 2 = 16 + s 2 Substitute s for l A F and 2 m for l C F in Equation (II). l A C = s 2 + 2 2 = s 2 + 4 Substitute 4 kg for m D and 9.81 m / s 2 for g in Equation (III). W D = 4 × 9.81 = 39.24 kg ⋅ m s 2 × 1 N 1 kg ⋅ m / s 2 = 39.24 N Substitute 6 kg for m E and 9.81 m / s 2 for g in Equation (IV). W D = 6 × 9.81 = 58.86 kg ⋅ m s 2 × 1 N 1 kg ⋅ m / s 2 = 58.86 N Determine the cos θ A B value. cos θ A B = l A F l A B Substitute s for l A F and 16 + s 2 for l A B . cos θ A B = s 16 + s 2 Determine the cos ϕ A C value. cos ϕ A C = l A F l A C Substitute s for l A F and s 2 + 4 m for l A C

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 3.3, Problem 31P

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The force F and sag s for equilibrium.

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Chapter 3.3, Problem 30P

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Chapter 3 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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The force F and sag s for equilibrium.

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Chapter 3 Solutions