A sphere of radius 1.0 cm is dropped into a glass cylinder...

A sphere of radius $1.0 \mathrm{cm}$ is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is $12.0 \mathrm{g}$ and the density of the liquid is $1200 \mathrm{kg} / \mathrm{m}^{3} .$ The sphere reaches a terminal speed of $0.15 \mathrm{m} / \mathrm{s} .$ What is the viscosity of the liquid?

Key Concepts

Stokes' Law

Stokes' Law describes the drag force experienced by a spherical object moving at low Reynolds numbers through a viscous fluid. This law is fundamental for relating the viscous drag force to the viscosity of the liquid, the object's radius, and its velocity, allowing one to solve for the fluid's viscosity when other quantities are known.

Terminal Velocity

Terminal velocity is the constant speed achieved by an object when the net force acting on it becomes zero during its fall through a fluid. At terminal velocity, the downward gravitational force is balanced by the upward buoyant and drag forces, which is critical in setting up the force balance needed to calculate properties such as fluid viscosity.

Buoyancy

Buoyancy is the upward force exerted by a fluid that opposes the weight of an object immersed in it. This force, determined by the fluid density and the volume of the displaced fluid, is essential for accurately describing the net force on a falling sphere and establishing the conditions necessary for terminal velocity.

Viscosity

Viscosity is a measure of a fluid's resistance to deformation or flow. It quantifies the internal friction within the fluid and is a key parameter in determining the drag force on objects moving through the fluid, particularly under flow conditions described by Stokes' Law.

Force Equilibrium

Force equilibrium refers to the condition where all forces acting on an object sum to zero, resulting in no acceleration. In the context of a sphere reaching terminal velocity in a viscous fluid, the gravitational, buoyant, and viscous drag forces balance perfectly, an equilibrium that can be utilized to solve for the viscosity of the liquid.

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