A vertical solid cylinder of uniform cross-sectional area A floats in water. The cylinder is partially...

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A vertical solid cylinder of uniform cross-sectional area A floats in water. The cylinder is partially submerged. When the cylinder floats at rest, a mark is aligned with the water surface. The cylinder is pushed vertically downwards so that the mark is a distance x below the water surface. water surface cylinder floating at rest mark cylinder pushed downwards x At time t = 0 the cylinder is released. The resultant vertical force F on the cylinder is related to the displacement x of the mark by F = -pAgx where p is the density of water. 3a. Outline why the cylinder performs simple harmonic motion when released. |F|-x [1 mark] 3b. The mass of the cylinder is 118 kg and the cross-sectional area of the [2 marks] cylinder is 2. 29 10-1 m. The density of water is 1.03 10 kg m3. Show that the angular frequency of oscillation of the cylinder is about 4.4 rad s F = -4x 2 F = - mwx .-P. Agx= -mwx PAg = W m 1 1030 x 0.229 9.81 9 of 61 = 118 W = 4.43 rad s' The cylinder was initially pushed down a distance x = 0.250 m. 3c. Determine the maximum kinetic energy Ekmax of the cylinder. Fumax when 24=0 Eu = 1mv [2 marks] A vertical solid cylinder of uniform cross-sectional area A floats in water. The cylinder is partially submerged. When the cylinder floats at rest, a mark is aligned with the water surface. The cylinder is pushed vertically downwards so that the mark is a distance x below the water surface. water surface cylinder floating at rest mark cylinder pushed downwards x At time t = 0 the cylinder is released. The resultant vertical force F on the cylinder is related to the displacement x of the mark by F = -pAgx where p is the density of water. 3a. Outline why the cylinder performs simple harmonic motion when released. |F|-x [1 mark] 3b. The mass of the cylinder is 118 kg and the cross-sectional area of the [2 marks] cylinder is 2. 29 10-1 m. The density of water is 1.03 10 kg m3. Show that the angular frequency of oscillation of the cylinder is about 4.4 rad s F = -4x 2 F = - mwx .-P. Agx= -mwx PAg = W m 1 1030 x 0.229 9.81 9 of 61 = 118 W = 4.43 rad s' The cylinder was initially pushed down a distance x = 0.250 m. 3c. Determine the maximum kinetic energy Ekmax of the cylinder. Fumax when 24=0 Eu = 1mv [2 marks]