A rectangular block is gradually pushed face-down into a...

A rectangular block is gradually pushed face-down into a liquid. The block has height $d$; on the bottom and top the face area is $A=5.67 \mathrm{~cm}^{2}$. Figure 14-39b gives the apparent weight $W_{\text {app }}$ of the block as a function of the depth $h$ of its lower face. The scale on the vertical axis is set by $W_{s}=0.20 \mathrm{~N}$. What is the density of the liquid?

Key Concepts

Archimedes’ Principle

This principle holds that any object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. It forms the foundation for understanding buoyancy and is critical in determining how the force measured on a submerged object relates to the properties of the fluid.

Buoyant Force

Buoyant force is the upward force exerted by a fluid on a submerged or partially submerged object. It results from the variations in hydrostatic pressure at different depths and is responsible for the reduction in the apparent weight of the object when it is immersed in a liquid.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases with depth and is key to calculating the pressure differences on the surfaces of a submerged object, thereby influencing the magnitude of the buoyant force.

Apparent Weight

The apparent weight of an object in a fluid is the measured weight when the buoyant force is taken into account. It is the actual gravitational weight minus the buoyant force, and analyzing changes in apparent weight helps in determining properties like the density of the fluid.

Fluid Density

Fluid density is the mass per unit volume of a fluid and plays a crucial role in buoyancy. A higher density leads to a larger buoyant force for a given volume displaced, and determining the fluid’s density is essential in problems that involve measuring the buoyant effect on immersed objects.

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