A 10.0-kg block of metal measuring 12.0 cm by 10.0 cm by...

A 10.0-kg block of metal measuring $12.0 \mathrm{~cm}$ by $10.0 \mathrm{~cm}$ by $10.0 \mathrm{~cm}$ is suspended from a scale and immersed in water as shown in Figure P14.11b. The 12.0 -cm dimension is vertical, and the top of the block is $5.00 \mathrm{~cm}$ below the surface of the water. (a) What are the magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water? (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the gravitational force. It increases linearly with depth, as given by the relationship p = p? + ?gh, where p? is the atmospheric pressure at the surface and h is the depth below the fluid’s surface. This concept is fundamental for understanding pressure differences on submerged objects.

Buoyant Force (Archimedes’ Principle)

The buoyant force is the upward force that a fluid exerts on a submerged object. According to Archimedes’ Principle, this force is equal to the weight of the fluid that the object displaces. This concept explains why objects seem lighter when submerged and is key for calculating the net force acting on them in a fluid.

Pressure Force Differences

The difference in hydrostatic pressure acting on different surfaces of a submerged object leads to net forces. The pressure is higher at greater depths, which results in a larger upward force on the bottom surface than the downward force on the top surface. The net effect of this pressure difference is the buoyant force.

Apparent Weight

The apparent weight of a submerged object is the reading on a scale, which is lower than the object's true weight due to the upward buoyant force. It is calculated as the actual weight minus the buoyant force, illustrating how immersion in a fluid reduces the effective weight measured by a supporting device.

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