Problem $4\mathrm{.}1$ Consider a $5,000lb$ boat with a cross$-$sectional area of $150f{t}^2.$ The

buoyancy force holding the boat up is given by $Ayg$ where

$=1\mathrm{.}94lb*\frac{s^2}{f}{t}^4$ is the density of the water, $A$ is the cross$-$sectional

area of the floating object, $y$ is how deep the object is submerged, and

$g$ is gravitational acceleration.

a$)$ Assume the boat is at rest. Draw the free body diagram and

find the EOM. When you do so$,$ think about if the amount

the boat is submerged is a constant or a variable. If it is a constant, name it $.$

b$)$ Now assume the boat is bobbing up and down. Draw the free body diagram and find the EOM,

canceling any terms that can be canceled. Hint: Divide $y$ into two parts. Your results from part a$)$

will be helpful.

c$)$ Find the period of the boat's oscillations.

Answer: c$)0\mathrm{.}808$ s

Consider a $5,000$ lb boat with a cross$-$sectional area of $150$ ft $2.$ The

buoyancy force holding the boat up is given by $$ where

$=1\mathrm{.}94$ lb$$s $2/$ft $4$ is the density of the water, $$ is the cross$-$sectional

area of the floating object, $$ is how deep the object is submerged, and

$$ is gravitational acceleration.

a$)$ Assume the boat is at rest. Draw the free body diagram and

find the EOM. When you do so$,$ think about if the amount

the boat is submerged is a constant or a variable. If it is a constant, name it $\backslash$Delta $.$

b$)$ Now assume the boat is bobbing up and down. Draw the free body diagram and find the EOM,

canceling any terms that can be canceled. Hint: Divide $$ into two parts. Your results from part a$)$

will be helpful.

c$)$ Find the period of the boat$$s oscillations.

Answer: c$)0\mathrm{.}808$ s