State the principle of moments.

1. (a)State the principle of moments.[2]
2. (b)A solid plastic cylinder floats in water. It is used to support one end of a horizontal uniform beam AB as shown in [Figure 2.1]. The beam has length 6.0m and weight 1700N. The beam is attached to solid ground with a hinge at end A. The cylinder is floating vertically in the water. The top of the cylinder is attached at its centre to the beam at a horizontal distance of 5.0m from end A. The cylinder applies a vertical force of 1300 N to the beam. A person of weight 660 N stands on the beam at point P. The beam AB is in equilibrium.
3. (b)(i)By taking moments about end A, determine the distance x from A to P. distance = ................................................................m [3][3]
4. (b)(ii)The bottom of the cylinder is submerged in the water to depth y as shown in [Figure 2.2]. The beam is still attached to the cylinder but not shown. The cylinder has mass 11kg and diameter 0.78m. The beam exerts a vertical force of 1300N on the cylinder. The cylinder is in equilibrium. Show that the upthrust acting on the cylinder is 1400 N.[1]
5. (b)(iii)The water has density 990kgm⁻³. Calculate the depth y. y = ................................................................m [2][2]
6. (b)(iv)The person can stand anywhere between A and B. On [Figure 2.3], sketch the variation of the depth of the bottom of the cylinder with the distance of the person from A, for distances between 0 and 6.0 m. Numerical values are not required.[2]

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