Math Problem Statement

A uniform square sign with sides of length 0.68 m is fixed at its corner points A and B to a wall. The sign is also supported by a wire CD, as shown in Fig. 3.1. The sign has weight W and centre of gravity at point E. The sign is held in a vertical plane with side BC horizontal. The wire is at an angle of 35° to side BC. The tension in the wire is 54 N. The force exerted on the sign at B is only in the vertical direction. (i) Calculate the vertical component of the tension in the wire. (ii) Explain why the force on the sign at B does not have a moment about point A.

Solution

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Math Problem Analysis

Mathematical Concepts

Statics
Forces
Trigonometry

Formulas

Tension vertical component = T * sin(θ)

Theorems

Moment of Force
Equilibrium Conditions

Suitable Grade Level

Grades 11-12