Terminal velocity

Terminal velocity

Graph of velocity versus time of a skydiver reaching a terminal velocity

Stokes sphere

Settling velocity quartz

Terminal velocity is a concept in physics and fluid dynamics that describes the maximum speed an object falling through a fluid (such as air or water) can achieve when the resistance of the medium prevents further acceleration. This occurs when the force of gravity pulling the object downward is balanced by the drag force acting upward against the object, causing no net acceleration. Terminal velocity depends on several factors, including the mass, shape, and surface area of the falling object, as well as the density and viscosity of the fluid it is falling through.

Overview

When an object first starts to fall, it accelerates due to gravity. However, as its speed increases, the drag force (air resistance or fluid resistance) also increases. Eventually, this drag force will equal the gravitational force in magnitude but act in the opposite direction, causing the acceleration to cease. At this point, the object continues to fall at a constant speed, known as its terminal velocity.

Factors Affecting Terminal Velocity

Several key factors influence an object's terminal velocity:

• Mass: Heavier objects tend to have higher terminal velocities because they have a greater force of gravity acting on them.
• Cross-sectional area: Objects with a larger cross-sectional area facing the direction of motion experience greater air resistance, leading to a lower terminal velocity.
• Shape: The aerodynamics of an object's shape can significantly affect its drag coefficient. Streamlined shapes reduce air resistance and can increase terminal velocity.
• Density of the fluid: Objects fall faster in less dense fluids because there is less resistance against them.
• Viscosity of the fluid: Higher viscosity fluids exert more drag, reducing terminal velocity.

Mathematical Description

The terminal velocity of an object can be calculated using the equation:

\[ V_t = \sqrt{\frac{2mg}{\rho A C_d}} \]

where:

• \(V_t\) is the terminal velocity,
• \(m\) is the mass of the falling object,
• \(g\) is the acceleration due to gravity,
• \(\rho\) is the density of the fluid through which the object is falling,
• \(A\) is the cross-sectional area of the object, and
• \(C_d\) is the drag coefficient, which depends on the shape of the object and the nature of the fluid flow around it.

Applications and Examples

Terminal velocity is a concept with various applications and examples in real life:

• Skydiving: Skydivers reach terminal velocity after a few seconds of free fall, which is why they appear to be floating relative to each other when in free fall.
• Raindrops: Raindrops reach terminal velocity as they fall, which prevents them from becoming too large and damaging when they hit the ground.
• Spacecraft re-entry: Engineers must consider terminal velocity when designing spacecraft to ensure they can withstand the heat generated by air resistance during re-entry into the Earth's atmosphere.

See Also

• Drag (physics)
• Free fall
• Gravity
• Fluid dynamics

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