Question

connecting buoyancy with displacement
metal | density (g/cm³)
aluminum | 2.64
cork | 0.24
iron | 7.50
lead | 11.34
wax | 0.72
which material will displace a volume of water?
which material will displace a volume of water less than its own volume?
which material will displace a volume of water equal to its own volume?
which material will displace a volume of water greater than its own volume?

Explanation:

• Which material will displace a volume of water? All materials (Aluminum, Cork, Iron, Lead, Wax) will displace water as per Archimedes' principle when submerged.
• Which material will displace a volume of water less than its own volume? Cork and Wax. Since their densities ($0.24\ g/cm^{3}$ for Cork and $0.72\ g/cm^{3}$ for Wax) are less than water's density ($1\ g/cm^{3}$), they float. When floating, the volume of water displaced is equal to the volume of the part of the object submerged, which is less than the total volume of the object.
• Which material will displace a volume of water equal to its own volume? Aluminum, Iron, Lead. Their densities ($2.64\ g/cm^{3}$ for Aluminum, $7.50\ g/cm^{3}$ for Iron, $11.34\ g/cm^{3}$ for Lead) are greater than water's density ($1\ g/cm^{3}$). So they sink, and the volume of water displaced is equal to their own volume (Archimedes' principle: $F_{b}=

ho_{fluid}gV_{displaced}$, when fully submerged $V_{displaced} = V_{object}$).

• Which material will displace a volume of water greater than its own volume? None of the given materials. According to Archimedes' principle, the maximum volume of water displaced by an object is equal to its own volume (when fully submerged). There is no physical situation among these materials (with normal - state water) where the displaced water volume is greater than the object's volume.

Answer:

• All materials (Aluminum, Cork, Iron, Lead, Wax) will displace water.
• Cork and Wax will displace a volume of water less than their own volume.
• Aluminum, Iron, Lead will displace a volume of water equal to their own volume.
• None of the given materials will displace a volume of water greater than their own volume.