Six wooden blocks (mass m ) float in a barrel of water. The...

Six wooden blocks (mass $m$ ) float in a barrel of water. The blocks are not all made from the same type of wood. The bottom of each block is submerged to a depth $d$ below the water surface. Rank the blocks in order of the buoyant force on them, largest to smallest. (a) $m=20 \mathrm{g}, d=2.5 \mathrm{cm}$ (b) $m=20 \mathrm{g}, d=2 \mathrm{cm}$ (c) $m=25 \mathrm{g}, d=2 \mathrm{cm}$ (d) $m=25 \mathrm{g}, d=2.5 \mathrm{cm}$ (e) $m=10 \mathrm{g}, d=2 \mathrm{cm}$ (f) $m=10 \mathrm{g}, d=1 \mathrm{cm}$

Six wooden blocks (mass $m$ ) float in a barrel of water. The blocks are not all made from the same type of wood. The bottom of each block is submerged to a depth $d$ below the water surface. Rank the blocks in order of the buoyant force on them, largest to smallest.
(a) $m=20 \mathrm{g}, d=2.5 \mathrm{cm}$
(b) $m=20 \mathrm{g}, d=2 \mathrm{cm}$
(c) $m=25 \mathrm{g}, d=2 \mathrm{cm}$
(d) $m=25 \mathrm{g}, d=2.5 \mathrm{cm}$
(e) $m=10 \mathrm{g}, d=2 \mathrm{cm}$
(f) $m=10 \mathrm{g}, d=1 \mathrm{cm}$

Key Concepts

Archimedes' Principle

Archimedes' principle is the foundational concept in buoyancy, stating that any object immersed in a fluid experiences an upward force (buoyant force) equal to the weight of the fluid it displaces. This idea explains why objects float, sink, or remain neutrally buoyant based on the amount of fluid displaced relative to their own weight.

Buoyant Force and Equilibrium

For objects floating in a fluid, the buoyant force exactly counterbalances the object's gravitational weight, establishing a state of static equilibrium. Since the buoyant force on a floating object is equal to its weight, comparing the mass of objects directly relates to their buoyant force, with heavier objects experiencing a larger upward force provided they are floating.

Density and Submerged Volume

An object's density relative to the fluid determines the fraction of its volume that must be submerged to support its weight. A less dense object will float with a smaller submerged volume, whereas a denser object must displace a larger volume of fluid (and thus be more submerged) to generate enough buoyant force to counteract its greater weight.

Relationship Between Mass, Volume, and Buoyancy

The interconnection between an object's mass, its volume, and the buoyant force is critical in analyzing floating bodies. In equilibrium, an object's weight (determined by its mass) is balanced by the weight of the displaced fluid, so a higher mass necessitates a larger displaced volume, directly linking mass to the magnitude of the buoyant force.

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