3 (b) 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 [Figure 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.

1. (a)State what is meant by the centre of gravity of a body.[1]
2. (b)(i)Calculate the vertical component of the tension in the wire.[1]
3. (b)(ii)Explain why the force on the sign at B does not have a moment about point A.[1]
4. (b)(iii)By taking moments about point A, show that the weight W of the sign is 150N.[2]
5. (b)(iv)Calculate the total vertical force exerted by the wall on the sign at points A and B.[1]
6. (c)The sign in (b) is held together by nuts and bolts. One of the nuts falls vertically from rest through a distance of 4.8m to the pavement below. The nut lands on the pavement with a speed of 9.2ms⁻¹. Determine, for the nut falling from the sign to the pavement, the ratio change in gravitational potential energy / final kinetic energy[4]

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