The buoy in the photograph can be modeled as a circular cylinder of diameter d and mass m. If the buoy is pushed down in the water, which has density ρ, it will oscillate vertically. Consider d = 1.2 m, m = 1060 kg, and surface seawater, which has a density of ρ = 1027 kg/m3.       NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.     Determine the frequency of oscillation. (Round the final answer to four decimal places.)   The frequency of oscillation is  Hz.

Using the following dimensional scales x' = x/l; y' = y/l; u' = u/U; v' = v/U; p' = p/(pU²); B' = B/(pU²/1); 0 = (T-T.)/AT; Re = UL/v; Pr = v/a; Sc = v/Dab, show that the governing equations can be written in the following non-dimensional form: continuity: x-motion: y-motion: Energy: Species a: du' ax' u +3y= 0 u' du' ax' Əx' +v' du' Əy' +v'. == ay' 30 u' +v'. Əx' ƏWA ax' де dy! +v' aw A Əy' др' ax' (0²u' a²u' + + 2/12 (3²1/²/² + 0²1/²1) + Bx Reax¹² dy' = ap' -1 (2²0² + 3²1/²) + By + ay' Reax¹² dyr² 1 a²0 a²0 dyr² Re Prax¹² + 1 ResTWA +2 J²WA ax¹2 ay ¹2

Q3. As shown on the right in image below, the force Facting on the box varies with displacement s, and the coefficient in the image, C = 14. Determine the work done by force Fto the box when the box has displaced s = 1.9 m. Please pay attention: the numbers may change since they are randomized. Negative sign must be included if the work done is negative. Your answer must include 2 places after the decimal point, and proper SI unit. F (N) F 5 3 S 4 C s (m) 1 2

1. Find the mass and the center of mass of the cone below assuming constant density po 2. R Same cone geometry as above, but the density p(2) is known to be a linear function of 2, where z is the vertical coordinate measured upward from the base. If the density at z = 0 is Po, find the function p(2) if the center of mass is at z = h/3. Calculate the mass of this cone. [Hint: assume p(z) = po(1+kz/h), where k is an unknown constant to be determined.]

A three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length 200mm and has a thickness of 20mm. Plywood has a density of 0.3 g/cm^3. For the purposes of finding the platform weight, W, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts M1, M2, and M3 were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. Co • F: (-75,-75) F₂: (85, -75) • F3: (15,85) -17.4319 MAT 1.338758 3.18886 7 Top View A coordinate system has been defined, such that middle of the…

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A 45 grams (0.045 kg) golf ball of diameter equal to 43 mm fell into a 2m deep lake. Neglect inertia at the moment of impact. Assume viscosity of 1.12x10-3 Ns/m2 , water density of 1,000 kg/m3 and Cd=0.5. Sphere volume equals 4π r³ /3. 1. How long will it take from the moment it hits the surface until it gets to the bottom? 2. If one estimates the Cd with Cd=24/Re formula, the settling velocity would be unrealistically large. Why?

Q3. In the image shown below, according to the provided datum line, determine the gravitational potential energy of the 5.9-kg block. The radius r = 2.6 m and the angle 0 = 29°. Negative sign must be included if the energy is negative. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper SI unit. Take g = 9.81 m/s². Your Answer: Answer Ө units Datum

Find the center of mass of a uniform slice of pizza with radius R and angular width \theta Express your answer in terms of the variables R and \theta .

Question 2. A fluid of density p is contained in a cylinder of radius R as shown in the Figure below. The cylinder and the fluid are both spinning at an angular velocity w. Due to the spin, the difference in elevation of the fluid's free surface between the rim of the cylinder and its centre is h. Taking the acceleration due to gravity as g, answer the following, while showing all your work: (a) If h is thought to be a function of the other parameters in the problem (R, p, g, and w), generate all the non-dimensional parameters in the problem without choosing the acceleration due to gravity as a repeating variable. (b) Show that at least one of the non-dimensional parameters can be recast as the Froude number for the problem. Additionally, show the functional relationship between the independent and dependent non-dimensional parameters. (c) Through an experimental design of your choice, explain how and with how many experiments, you would determine the functional form of the…