Problem 5 Stability Small floating devices such as kayaks are marginally stable to lateral perturbations. We are inter- ested in designing a submerged kayak for a target user weighing mp = 60 kg. When seated in the kayak, the entire kayak is submerged just under the waterline (Fig 5) and the center of gravity of the user is at G. For your calculations, consider the kayak to be a cylinder with a radius of rk and of uniform density Pk. The kayak has a depth of dk. mp 5 NG D Pk TK d Ps r Figure 5: Cylindrical kayak with a one-sided stabilizer float. hc = 0.5 m, r = 1m, dk = 3m, ds 0.5 m. = To stabilize the kayak, a one-sided cylindrical stabilizer float of density ps, depth ds and radius rs is considered. The stabilizer float is exactly half submerged with the user on board. (1) Determine the density of the kayak PR and the stabilizer float p, so that the system floats in the given configuration (Fig 5). Assume the connector of length d has negligible mass. (2) Find the dimensions of stabilizer float attachment (d and rs) such that the system is stable to small lateral perturbations (rotation about the point C) in both directions. Hint: Calculate all moments about point O. To determine the stabilizer float parameters, consider the maximum and minimum contribution from the buoyancy forces of the stabilizer float as the kayak undergoes small rotation about point C.

A pontoon boat floats on two cylindrical pontoons (assume the ends are flat). Each pontoon is 6m long. The mass of the boat, pontoons, and gear (without any passengers) is 1950 kg. If exactly half of the pontoon volume was submerged without any passengers on the boat, what is the maximum volume of water that can be displaced to support the weight of passengers? The density of freshwater is 1000 kg/m³ . End view of pontoons: Waterline Pontoon D/2 is submerged

(a) A rectangular, fully enclosed tank 2.4m long, 1.4m wide and 0.8m high is constructed of sheet metal weighing 443.6 kg-f (force). The tank floats in sea water of density 1025kg/m³ with its 0.8m sides vertical. If the centre of gravity is at the geometric centre of the vessel, calculate the metacentric height and comment on the stability of the tank. (b) A hydrometer is an instrument used for measuring the relative density of liquids based on the concept of buoyancy. A particular hydrometer is 80 cm in length. When placed in pure water, 50cm of the hydrometer is submerged and it reads 1.000 as shown in Figure 1. i) Calculate the density of the hydrometer? ii) When placed in Alcohol, 65 cm of the hydrometer is submerged beneath the alcohol. Calculate the density of alcohol? iii) Determine the reading of the hydrometer when it is in the alcohol? iy What will happen when this hydrometer place in Pentane (p-625 kgm): Fluid surface 1.00 Hydrometer- 80 cm 50cm Figure 1: A hydrometer

A flotation buoy has mass 806 kg, volume 1.43 m, and is attached to the sea floor by a cable in such a way that the buoy is completely submerged. Calculate the magnitude of the tension in the cable, given the density of sea water is 1025 kg/m³. T=_ %3D

The following questions consider the stability of a floating iceberg.  Approximate the iceberg as a perfect cylinder of uniform density,  If the iceberg has a diameter of 3 meters and a length of 0.5 meters find the location of the metacenter as measured from the bottom of the iceberg. Take the density of sea water to be 1030 kg/m3 and the density of the ice to be 920 kg/m3.

1- Panel BC in the figure is circular. Compute (a) the hydrostatic force of the water on the panel; (b) its center of pressure; and (c) the moment of this force about point B. Given and unknowns: Assumptions: Schematic: Governing Equation(s): Analysis and Results: Water at 20°C C 50° B 3 m 3 m 3 m

what is the answer for number 4?a and b

The tank shown in Figure a is accelerated to the right. Calculate the acceleration ܽax needed to cause the free surface, shown inFigure b, to touch point A. Also find ܲPB, and the total force acting on the bottom of the tank if the tank width is 1m.

Q2/ If 70% of body weight is distributed below the superior surface of the L5 intervertebral disc and the area of the superior surface of the disc is 25 cm2, how much pressure exerted on the dise is attributable to body mass for a 90 kg man?

A float sensor for the determination of the level of water in a vessel has a cylindrical float of mass 2.0 kg, cross-sectional area 20 cm= and a length of 1 5 in. It floats vertically in the water and presses upwards against a beam attached to its upward end. What will be the minimum and maximum up thrust forces exerted by the float on the beam? Suggest a means by which the deformation of the beam under the action of the   force could be monitored