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 m3 , what was the mass of the raft’s dry wood?
The density of fresh water is 1.00 x 103 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 m3 . What is
the minion’s mass if its apparent weight in sea water is 3.115 x 103 N?
The density of sea water is 1.025 x 103 kg/m3 .
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 m2 . 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/m3 .
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 103 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 .