(b) Below what speed does a 3.0-mm-diameter ball bearing in 20°C air experience linear drag?

Key Concepts

Linear Drag Force

Linear drag force, also known as viscous drag, is the resistance experienced by an object moving through a fluid. It is proportional to the object's velocity and is described by Stokes' law for small, spherical objects in a viscous medium. The drag force can be calculated using the formula F_d = 6πμrv, where F_d is the drag force, μ is the dynamic viscosity of the fluid, r is the radius of the sphere, and v is the velocity.

Reynolds Number

The Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. It is calculated as Re = (ρvD)/μ, where ρ is the fluid density, v is the velocity, D is the characteristic length (diameter for spheres), and μ is the dynamic viscosity. A low Reynolds number indicates laminar flow, where drag is dominated by viscous forces, while a high Reynolds number indicates turbulent flow.

Critical Speed

Critical speed refers to the velocity below which an object experiences predominantly linear drag and above which other forces, such as inertial forces, become significant. For small spheres in a viscous fluid, this speed can be determined by analyzing the balance between gravitational and drag forces. Understanding critical speed is essential for predicting the motion of objects in fluids, particularly in applications like ball bearings in air.