The experimental diving rig is lowered from rest at the ocean’s surface and reaches a maximum depth of $80\,\text{m}$. Initially it accelerates downward at a rate of $0.10\,\text{m/s}^2$ until it reaches a speed of $2.0\,\text{m/s}$, which then remains constant. During the descent, the pressure inside the bell remains constant at $1$ atmosphere. The top of the bell has a cross-sectional area $A = 9.0\,\text{m}^2$. The density of seawater is $1025\,\text{kg/m}^3$.

Question

The experimental diving rig is lowered from rest at the ocean’s surface and reaches a maximum depth of $80\,\text{m}$. Initially it accelerates downward at a rate of $0.10\,\text{m/s}^2$ until it reaches a speed of $2.0\,\text{m/s}$, which then remains constant. During the descent, the pressure inside the bell remains constant at $1$ atmosphere. The top of the bell has a cross-sectional area $A = 9.0\,\text{m}^2$. The density of seawater is $1025\,\text{kg/m}^3$.(a) Calculate the total time it takes the bell to reach the maximum depth of $80\,\text{m}$.
, (b) Calculate the weight of the water on the top of the bell when it is at the maximum depth.
, (c) Calculate the absolute pressure on the top of the bell at the maximum depth.
, (d) On the top of the bell there is a circular hatch of radius $r = 0.25\,\text{m}$. Calculate the minimum force necessary to lift open the hatch of the bell at the maximum depth.
, (e) What could you do to reduce the force necessary to open the hatch at this depth? Justify your answer.
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Jason · Accepted Answer

$\boxed{50\;\text{s}}$
$\boxed{7.23 \times 10^6\;\text{N}}$
$\boxed{9.05 \times 10^5\;\text{Pa}}$
$\boxed{1.58 \times 10^5\;\text{N}}$
Increase the bell&#8217;s internal pressure (or use a pressure equalization system) so that it closely matches the external pressure, thereby reducing the net force on the hatch.

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