Terminal velocity

Terminal Velocity Experiment For Schools, Teachers, and Students

Terminal velocity is the constant maximum velocity attained by a falling object when the downward gravitational force is balanced by the upward drag force and buoyant force. At this point, the net force acting on the object is zero, and it falls at a steady speed.

Theory

1. Forces Acting on the Object
   • The downward force is the gravitational force:
     Fg = mg
     where:
     • m: Mass of the object (kg)
     • g: Acceleration due to gravity (m/s²)
   • The upward forces include:
     • Drag force:
       Fd = (1/2) C ρ A v²
       where:
       • C: Drag coefficient (dimensionless)
       • ρ: Density of the fluid (kg/m³)
       • A: Cross-sectional area of the object (m²)
       • v: Velocity of the object (m/s)
     • Buoyant force:
       Fb = ρf V g
       where:
       • ρf: Density of the fluid (kg/m³)
       • V: Volume of the object (m³)
2. Terminal Velocity Condition
   When the object reaches terminal velocity (vt):
   Fg = Fd + Fb

   Simplifying for vt (ignoring buoyant force if negligible):
   vt = sqrt(2mg / C ρ A)

3. Key Concepts
   • Terminal velocity depends on the object’s mass, cross-sectional area, drag coefficient, and the density of the fluid.
   • Heavier objects with smaller cross-sectional areas attain higher terminal velocities.

Applications of Terminal Velocity

1. Skydiving
   A skydiver reaches terminal velocity during free fall, which can be controlled by changing body position (e.g., spread arms and legs to increase drag).
2. Rain Drops
   Raindrops attain terminal velocity, which prevents them from becoming harmful upon impact.
3. Industrial Processes
   Terminal velocity is used in particle settling tanks to separate particles based on size and density.
4. Parachuting
   Parachutes increase drag to reduce the terminal velocity, ensuring a safe landing.

Examples

1. Falling Objects in Air
   A dense sphere falls faster through the air, attaining a higher terminal velocity compared to a lightweight, porous object like a feather.
2. Raindrop Size Effects
   Larger raindrops attain higher terminal velocities due to their greater mass and lower drag-to-weight ratio.
3. Particle Sedimentation
   In sedimentation tanks, smaller particles with lower terminal velocities take longer to settle compared to larger, denser particles.

Real-Life Uses

• Designing skydiving and parachuting equipment to ensure safe terminal velocities.
• Optimizing industrial processes like filtration, sedimentation, and particle separation.
• Predicting motion of objects through fluids, including spacecraft re-entry through the atmosphere.
• Studying fluid dynamics in biological systems, such as blood flow and cell sedimentation.

Observations

• Terminal velocity increases with the object’s mass and decreases with the fluid’s density.
• Larger cross-sectional areas lead to lower terminal velocities due to increased drag.
• Smooth, streamlined shapes attain higher terminal velocities by minimizing drag.
• In denser fluids, such as water, terminal velocities are significantly lower than in air.