Buoyant Force - Section 9A

**1. **
The heaviest pig ever raised had a mass
of 1158 kg. Suppose you placed

this pig on a raft made of dry wood. The raft completely submerged in

water so that the raft’s top surface was just level with the surface of the

lake. If the raft’s volume was 3.40 m^{3}
, what was the mass of the raft’s dry wood?

The density of fresh water is
1.00 x
10^{3} kg/m 3 .

**2. ***
La Belle, *
one of four ships that Robert La Salle
used to establish a French

colony late in the seventeenth century, sank off the coast of Texas. The

ship’s well-preserved remains were discovered and excavated in the

1990s. Among those remains was a small bronze cannon, called a

minion. Suppose the minion’s total
volume is 4.14 x10 ^{-2} m^{3} . What is

the
minion’s mass if its
apparent weight in sea water is 3.115 x 10^{3} N?

The density of sea water
is 1.025 x 10^{3} kg/m^{3} .

**3. **
William Smith built a small submarine
capable of diving as deep as

30.0 m. The submarine’s volume can be
approximated by that of a cylinder with a length of 3.00 m and a
cross-sectional area of 0.500 m^{2} . Suppose this submarine dives
in a freshwater river and then moves out to sea, which naturally consists
of salt water. What mass of fresh water must be added to the ballast to
keep the submarine submerged? The density of fresh water is 1.000 x10 ^{
3} kg/m ^{3} , and the density of sea water is 1.025 x10 3
kg/m^{3} .

**4. **
The largest iceberg ever observed had an
area of 3.10 x 10 ^{4} km ^{2} , which is larger than the
area of Belgium. If the top and bottom surfaces of the ice-berg were flat
and the thickness of the submerged part was 0.84 km, how large was the
buoyant force acting on the iceberg? The density of sea water equals 1.025
x 10^{3} kg/m ^{3} .

**5. **
A cannon built in 1868 in Russia could
fire a cannonball with a mass of

4.80 x
10 ^{2} kg and a radius
of 0.250 m. When suspended from a scale

and submerged in water, a cannonball of this type has an apparent weight of

4.07 x 10 ^{3} N. How large is
the buoyant force acting on the cannonball?

The density of fresh water is 1.00 x
10 ^{3} kg/m ^{3}
.

**6. **
The tallest iceberg ever measured stood
167 m above the water. Suppose

that both the top and the bottom of this
iceberg were flat and the thickness of the submerged part was estimated to
be 1.50 km. Calculate the density of the ice. The density of sea water
equals 1.025 x 10 ^{3} kg/m ^{3}

**7. **
The Russian submarines of the “Typhoon”
class are the largest submarines in the world. They have a length of 1.70
x 10 ^{2} m and an average diameter of 13.9 m. When submerged,
they displace 2.65 x 10 ^{7} kg of sea water. Assume that these
submarines have a simple cylindrical shape. If a “Typhoon”-class submarine
has taken on enough ballast that it descends with a net acceleration of
2.00 m/s ^{2} , what is the submarine’s density during its
descent?

**8. **
To keep Robert La Salle’s ship *La
Belle *well preserved, shipbuilders are re-constructing the ship in a
large tank filled with fresh water. Polyethylene

glycol, or PEG, will then be slowly added to the water until a 30 percent

PEG solution is formed. Suppose *La
Belle *displaces 6.00 m ^{3} of liquid

when submerged. If the ship’s apparent weight decreases by 800 N as the

PEG concentration increases from 0 to 30 percent, what is the density of

the final PEG solution? The density of
fresh water is 1.00 x 10 ^{3} kg/m ^{3} .