Mechanics: Terminal Velocity

Mechanics: Terminal Velocity

Definition of Terminal Velocity in Mechanics

  • Terminal velocity is the maximum constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.
  • This velocity is achieved when the force due to gravity (weight) equals the resistance, usually air resistance, acting upward on the object.

Factors Influencing Terminal Velocity

  • The size of the object: larger objects face a greater air resistance.
  • The shape of the object: streamlined objects encounter less air resistance.
  • The mass of the object: heavier objects have a higher terminal velocity.
  • The density of the medium: a denser medium (e.g., water) offers greater resistance and leads to a lower terminal velocity.

Mathematical Formula for Terminal Velocity

  • When the gravitational force (mg) equals the drag force (1/2 ρ C A v²), the object will move at a constant speed, or terminal velocity, where:
    • m is the mass of the object
    • g is the acceleration due to gravity
    • p (rho) is the density of the fluid
    • C is the drag coefficient
    • A is the surface area of the object in contact with the fluid
    • v is the speed of the object.

Parachuting and Terminal Velocity

  • Parachuting is a common example of terminal velocity. After jumping from the plane, the skydiver accelerates for some time. Once the air resistance equals their weight, they will have reached their terminal velocity.
  • The deployment of a parachute increases the skydiver’s air resistance dramatically. This reduces their terminal velocity, allowing them to land safely.

Role of Terminal Velocity in Fluid Mechanics

  • Knowing the terminal velocity is crucial for designing objects that move through fluids, whether they be cars, aeroplanes, or undersea vehicles.
  • Controlling and predicting terminal velocity is a key objective in many real-world situations, such as estimating the speed of raindrops or when designing parachutes.

Importance of Units

  • Be mindful of the units you are working with and ensure to convert them appropriately. For instance, if mass is measured in kilograms and the acceleration due to gravity in m/s², the force will be measured in Newtons.
  • Additionally, when calculating velocity, ensure your answer is in an appropriate velocity unit, such as metres per second (m/s).