(a) Explanation The free-body diagram is shown in figure 1. The free-body diagram includes the weight of the panels, the reactions at A and F and the force exerted by the wire. To eliminate the reactions at A and F, the sum of moments of the forces about the line A F must be set to zero. Σ M → A F = 0 λ ^ A F ⋅ ( r → G 1 / A × P → ) + λ ^ A F ⋅ ( r → G 2 / A × P → ) + λ ^ A F ⋅ ( r → B / A × T → ) = 0 (I) Here, Σ M A F is the sum of the moments of forces along AF, λ ^ A F is the unit vector along AF, T → is the tension, r → G 1 / A , r → G 2 / A and r → B / A are position vectors and P → is the load. Write the expression of λ ^ A F . λ ^ A F = 1 3 ( 2 i ^ − j ^ − 2 k ^ ) (II) Write the expressions of the position vectors. r → G 1 / A = 2 i ^ − j ^ r → G 2 / A = 4 i ^ − j ^ − 2 k ^ r → B / A = 4 i ^ (III) Write the expression of the weight. P → = − 12 j ^ (IV) Put equations (II), (III) and (IV) in equation (I) and use determinants. | 2 − 1 − 2 2 − 1 0 0 − 12 0 | 1 3 + | 2 − 1 − 2 4 − 1 − 2 0 − 12 0 | 1 3 + λ ^ A F ⋅ ( r → B / A × T → ) = 0 48 3 + 48 3 + λ ^ A F ⋅ ( r → B / A × T → ) = 0 λ ^ A F ⋅ ( r → B / A × T → ) = − 32 T → ⋅ ( λ ^ A F × r → B / A ) = − 32 (V) Equation (V) shows that the projection of T → on the vector ( λ ^ A F × r → B / A ) is constant (b) To determine The value of the minimum tension.

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Author: BEER

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Chapter 4.3, Problem 4.140P

(a)

To determine

The location of the H in the xy plane for the tension in the wire to be minimum.

(b)

To determine

The value of the minimum tension.

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Chapter 4.3, Problem 4.139P

Chapter 4.3, Problem 4.141P

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The location of the H in the x y plane for the tension in the wire to be minimum.

Solution Summary: The free-body diagram includes the weight of the panels, the reactions at A and F and the force exerted by the wire.

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The location of the H in the xy plane for the tension in the wire to be minimum.

The value of the minimum tension.

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Chapter 4 Solutions