Question

Three objects are placed in water. Cube A (0.5 m on a side) has a mass of 2.0 kg. Cube B (1.2 m on a side) has a mass of 4.0 kg. Cube C (2.0 m on a side) has a mass of 1.0 kg. Which cubes float? Which cube experiences the greatest buoyant force? Which experiences the least buoyant force? Show your work and/or explain your reasoning. (20 pts, 10 for floating, 10 for buoyant force)

Answer 1

here,

for cube A

m1 = 2 kg

the weight , Wa = m1 * g = 19.6 N

the maximum buoyant force , F1 = density of water * a^3 * g

F1 = 1000 * 0.5^3 * 9.81 N = 1226 N

as F1 > Wa

the buoyant force = Wa = 19.6 N

so, the cube will float

b)

for cube B

m2 = 4 kg

the weight , Wa = m2 * g = 39.2 N

the maximum buoyant force , F2 = density of water * a^3 * g

F2 = 1000 * 1.2^3 * 9.81 N = 16952 N

as F2 > Wb

the buoyant force = Wb = 39.2 N

so, the cube will float

for cube C

m3 = 1 kg

the weight , Wb = m3 * g = 9.8 N

the maximum buoyant force , F3 = density of water * a^3 * g

F3 = 1000 * 2^3 * 9.81 N = 78480 N

as F3 > Wc

the buoyant force = Wc = 9.8 N

so, the cube will float

ALL the cubes will float

the cube B will experience greatest buoyant force

the cube C will experience least buoyant force