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Question 8: (22 points) Consider a cylindrical buoy with a mass m= 10kg is floating in water as shown in the figure below. It is initially in a state of equilibrium when it is pushed down into the water causing simple harmonic motion. Assume the cylinder has a cross sectional area A=0.04m². Recall the buoyant force is given by FPV s and the density of water is p = 1000 a) (6 points) Find the distance d the bottom edge is submerged while the buoy is in equilibrium. Show your work. Be sure to include units. Fb=pVg = Fg P²= 1₂/² 4cm A=0.04m² P= W Vem mavp P to (1000g/m²) (0.01 m² X(96m/s) 98 N-100N A = I w 0.04 m² = b) (8 points) Now assume the buoy is pushed a distance z further into the water. Find the equation for the resulting acceleration a in terms of given quantities m. A, p, d. 9, and z. Show your work. What direction does the acceleration point? Int=ma 98N= (10₁) a Find an expension for Fart (5) T019 = V/= 0.01 m³ 1000 kg/m² Na More like moss on spring a= 9.8 m/s² c) (8 points) Find the period of oscillations for the buoy. Show your work. Be sure to include units. T= 2+ Nota pradulum (7) 2 6/22)