A thin spherical shell of mass 4.00 kg and diameter 0.200 m is filled with helium (density =0.18

step 1 Question number 66. First of all, let us find the total mass of the shell plus the mass of the h

A thin spherical shell of mass 4.00 kg and diameter 0.200 m...

A thin spherical shell of mass 4.00 $\mathrm{kg}$ and diameter 0.200 $\mathrm{m}$ is filled with helium (density $=0.180 \mathrm{kg} / \mathrm{m}^{3} ) .$ It is then released from rest on the bottom of a pool of water that is 4.00 $\mathrm{m}$ deep. (a) Neglecting frictional effects, show that the shell rises with constant acceleration and determine the value of that acceleration. (b) How long will it take for the top of the shell to reach the water surface?

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Key Concepts

Archimedes' Principle

This principle states that any object, wholly or partially immersed in a fluid, experiences an upward buoyant force equal to the weight of the fluid displaced by the object. It is key to understanding the forces acting on the shell as it rises through the fluid.

Buoyant Force

The buoyant force is the net upward force exerted by the fluid on the submerged object. It is calculated by multiplying the displaced fluid's volume by its density and the acceleration due to gravity, which directly influences the net acceleration of the object.

Newton's Second Law

Newton’s Second Law relates the net force acting on an object to its mass and the resulting acceleration. In problems involving buoyancy, it is used to calculate the net acceleration by subtracting the weight of the object from the buoyant force and then dividing by the object's mass.

Uniform Acceleration in Fluids

When an object experiences constant forces, such as a constant buoyant force and gravitational force, it will move with uniform acceleration. This concept is applied to determine the time evolution of the rising motion, assuming that other resistive forces like friction or drag are negligible.

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