The gate shown in Figure 5 has a mass of 225 kg/m normal to the screen/page and is normal to the page. It is supported by a counterweight made of concrete (Specific gravity = 2.5). If θ = 30o, determine the minimum mass (in air) of the counterweight per unit length of the gate (into the page) required to keep the gate in equilibrium as shown. Neglect the weight of the arm required to hold the counterweight.

1. Bellow Fig illustrates a cylinder having diameter of 1.8 m and height 1.2 m. The mass of the cylinder is 1019.3 kg which is floating vertically in salty water of density 1025 kg/m³. If an object weighing 2 kN is placed on the top of the cylinder, calculate the maximum height of centre of gravity (z) for the object to keep the cylinder in a state of stable equilibrium. Z 2 kN 0.45m . G₁ G 1.8m 1.2m p=10;

Gate AB in the given image is semicircular, hinged at B, and held by a horizontal force P at A. If a = 5 m, and b = 3 m, what force P is required for equilibrium? Water b B P Gate: Side view

The figure below shows a container filled with a liquid of density p up to a height of 4R. The container is of unit width into the plane of the screen and AB is half a parabola with a height of kR and a base of R. Determine the magnitude and direction of the vertical component Fy of the hydrostatic force acting on the curved surface AB if k = 2, R = 0.5 m, p = 1000 kg/m³ and the gravitational acceleration g = 9.81 m/s². Note that Fy is positive if it acts upwards and is negative if it acts downwards. Geometric properties of a half-parabola are also given below. Fy= 1. [-6.7362, -6.3438 kN. 4R h ထမ 35 b Liquid Р X Half-Parabola BR KR A = 3bh 1xc=²bh³ |yxc=hb³ |yy,c=²7/531 2 h63