A 10.0 -kg block of metal measuring 12.0 cm ×10.0 cm ×10.0 cm is suspended from a scale and imme

step 1 Question number 23, the mass is given as m equal to 10 kg and volume is equal to 12 into 10 cm c

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

A 10.0 -kg block of metal measuring $12.0 \mathrm{cm} \times 10.0 \mathrm{cm} \times$ 10.0 $\mathrm{cm}$ is suspended from a scale and immersed in water as shown in Figure $\mathrm{P} 14.22 \mathrm{b}$ . The $12.0-\mathrm{cm}$ dimension is vertical, and the top of the block is 5.00 $\mathrm{cm}$ below the surface of the water. (a) What are the forces acting on the top and on the bottom of the block? (Take $P_{0}=101.30 \mathrm{kPa}$ . (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

Pressure Forces on Submerged Surfaces

The pressure exerted by a fluid acts perpendicular to any surface in contact with it. For an object submerged in a fluid, the forces on the top and bottom surfaces are determined by the hydrostatic pressure at those depths. The difference between these pressures multiplied by the area results in a net upward force, which is equal to the buoyant force. This concept is used to calculate the forces acting on the block and to verify Archimedes' Principle.

Apparent Weight

The apparent weight of an object submerged in a fluid is the effective weight it exhibits when influenced by both gravity and the buoyant force. Since the buoyant force acts upward, it reduces the net force measured by a scale. Calculating the apparent weight involves subtracting the buoyant force from the object's actual weight, which is key in understanding the readings of spring scales in fluid immersion experiments.

Hydrostatic Pressure

Hydrostatic pressure describes how pressure in a fluid increases with depth due to the weight of the overlying fluid. The relationship is given by P = P? + ?gh, where P? is the surface pressure, ? is the fluid density, g is the acceleration due to gravity, and h is the depth below the surface. This concept is crucial when calculating the pressures acting on different surfaces of an immersed object.

Archimedes' Principle

Archimedes' Principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid that the object displaces. This principle is foundational for understanding how and why objects float or sink, and it directly explains the origin of the buoyant force on submerged objects.

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