Unit $3$ section $4$ problems $$ density and pressure relations

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Suppose your refrigerator $(1\mathrm{.}0$ m by $0\mathrm{.}60$ m by $0\mathrm{.}75$ m$)$ only contains a dozen

$$ eggs $(44$ g each$).$ Compare the mass of air contained in the fridge to the mass of

$$ the eggs.

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$2.$ Compare the pressure exerted on the skin of a balloon if you press with a force of $$

$2\mathrm{.}1$ N using your finger $($A$=1\mathrm{.}0$ x $10-4$ m$2)$ and a needle $($A$=2\mathrm{.}5$ x $10-7$ m$2).$ If the$$

$$ balloon pops with a pressure of $3\mathrm{.}0$ x $105$ Pa$,$ find the force needed to pop the$$

$$ balloon with the needle.

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The Titanic was found lying at the bottom of the North Atlantic at a depth of $2\mathrm{.}5$

$$ miles. What is the pressure $($in atm$)$ at this depth?

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A cubical box $20\mathrm{.}00$ cm on a side is completely immersed in a fluid. The pressure

$$ at the top of the box is $105\mathrm{.}0$ kPa and at the bottom of the box is $106\mathrm{.}8$ kPa. What

$$ is the density of the fluid?$$ What is the depth of the fluid at the top of the box?

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To inspect a $14,500\mathrm{.}0$ N car, it is raised with a hydraulic lift. If the radius of the small$$ piston is $4\mathrm{.}0$ cm and the radius of the large piston is $17$ cm$,$ find the force that must be exerted on the small piston to lift the car.

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A piece of wood with a density of $706$ kg$/$m$3$ and volume of $8\mathrm{.}00$ x $10-6$ m$3$ is tied with a string to the bottom of a water$-$filled beaker. Find the tension in the string.

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What percentage of an iceberg projects above the surface of seawater?

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Water travels through a $9\mathrm{.}6$ cm diameter fire hose at a rate of $1\mathrm{.}3$ m$/$s$.$ At the end of the hose, the water flows out through a nozzle with diameter $2\mathrm{.}5$ cm$.$ What is the speed of the water coming out of the nozzle?

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During a windstorm, a $35\mathrm{.}5$ m$/$s wind blows across the flat roof of a home. Find the pressure difference between the air inside the home and just above the roof.