A diver is located 63 m below the surface of the ocean (the density of seawater is 1025 kg/m^3). To raise a treasure chest that she discovered, the diver inflates a plastic, spherical buoy with her compressed air tanks. The radius of the inflated buoy is 0.41 m. If the treasure has a mass of 215 kg, what is the acceleration of the buoy and the treasure chest when they are tethered together and released? The chest is 22 cm × 53 cm × 11 cm in size. Neglect the tether’s mass and the mass of the buoy (and air in it) because these are much smaller than the mass of the treasure chest. Neglect the tether’s volume as well. The effect of “water resistance” can also be neglected when the buoy is just released (it will become non-negligible as the speed increases, but you only have to calculate the initial acceleration).
When the buoy and the treasure reach the surface and come to rest, what fraction of the volume of the buoy is submerged? The buoy expands to 0.82 m in radius when it reaches the surface due to the reduction in the external pressure acting on the buoy.
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