12.4. Archimedes’ Law http://www.ck12.orgFIGURE 12.15
mlogg=mwaterg→mlog=mwater→ρlogVlog=ρwaterVwater→
Vwater=
ρlog
ρwaterVlogThe volume of the log isVlog= (πr^2 )L→( 3. 14 )( 0. 150 m)^2 ( 7. 60 m) = 0. 5369 m^3 → 0. 537 m^3.Vwater=ρρwaterlogVlog=
(^420) mkg 3
(^1000) mkg 3 (^0.^537 m
(^3) ) = 0. 2255 → 0. 226 m 3
The atmosphere is also able to exert a buoyant force, otherwise hot air balloons would not rise.
See the link below to learn more.
http://phet.colorado.edu/en/simulation/balloons-and-buoyancy
Check Your Understanding
True or False: Steel cannot float because it is denser than water.
Answer: False. Large ships are usually made of steel and other comparatively dense materials. It is true that a solid
block of material with a density greater than water will sink. But if the block is molded into the shape of a boat
(hollowed out), it will be able to displace a greater volume of water than when it was a solid block. The result is that
the hollowed block will be able to displace a volume of water equal to its weight before sinking. It will float.
Illustrative Example 3
Let’s return to King Hiero’s problem now that we have an understanding of Archimedes’ principle. Recall that the
king commissioned the goldsmith to craft a crown of gold from a specific amount of gold given to him by the king.
The king then became suspicious that the goldsmith had replaced some of the gold with a cheaper metal, perhaps