(a) Explanation The free body diagram is shown in figure 1. Sum of the moments of the forces about the point A must be zero. Σ M A = 0 (I) Here, Σ M A is the sum of the moments of forces about the point A. Write the expression for the sum of the moments about the point A. Σ M A = ( B cos 60 ° ) × ( A B ) − ( B sin 60 ° ) × h − ( 150 N ) × ( A G ) Here, B is the magnitude of the reaction at the point B. Substitute 500 mm for A B and 250 mm for A G in equation (I) and rewrite the equation to find B . Σ M A = ( B cos 60 ° ) × ( 500 mm ( 1 m 1000 mm ) ) − ( B sin 60 ° ) × h − ( 150 N ) × ( 250 mm ( 1 m 1000 mm ) ) = 0 ( B cos 60 ° ) ( 0.5 m ) − ( B sin 60 ° ) × h − ( 150 N ) ( 0.25 m ) = 0 B = 37.5 0.25 − 0.866 h (II) Substitute 0 for h in equation (II) to find the value of reaction at the point B. B = 37.5 0.25 = 150.0 N The x component of the net force must be equal to zero. Σ F x = 0 (III) Here, Σ F x is the x component of the net force. Write the equation for the x component of the net force. Σ F x = A x − B sin 60 ° Here, A x is the magnitude of the x component of the reaction at the point A. Put the above equation in equation (III). A x − B sin 60 ° = 0 A x = B sin 60 ° (IV) Substitute 150 N for B in equation (IV) to find the value of the x component of the magnitude of the reaction at the point A. A x = ( 150 N ) sin 60 ° = 129.9 N Write the expression for the x component of the reaction at the point A. A → x = 129 (b) To determine The reactions at A and B when h = 200 mm .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 4, Problem 4.144RP

(a)

To determine

The reactions at A and B when h=0 .

(b)

To determine

The reactions at A and B when h=200 mm .

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Chapter 4, Problem 4.143RP

Chapter 4, Problem 4.145RP

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The reactions at A and B when h = 0 .

Solution Summary: The free body diagram is shown in figure 1. Sum of the moments of forces about the point A must be zero.

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The reactions at A and B when h=0 .

The reactions at A and B when h=200 mm .

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Chapter 4 Solutions