5.4.14 Terminal Velocity

• What is the definition of terminal velocity?

  Terminal velocity is the constant speed that a freely falling object reaches when the resistance of the medium prevents further acceleration.
• What happens to a falling object at terminal velocity?

  The object stops accelerating and continues to fall at a steady speed.
• What forces are balanced when an object reaches terminal velocity?

  The force of gravity pulling the object downwards is balanced by the air resistance pushing it upwards.
• What are the steps to achieve terminal velocity?

  1. Initial acceleration due to gravity.

  2. Increasing air resistance as speed increases.

  3. Air resistance equals the force of gravity, net force becomes zero.

  4. Object falls at a constant speed (terminal velocity).
• How does the mass of an object affect its terminal velocity?

  Heavier objects generally have a higher terminal velocity due to greater gravitational force.
• How does surface area influence terminal velocity?

  Objects with a larger surface area experience more air resistance, resulting in a lower terminal velocity.
• What is the effect of an object's shape on its terminal velocity?

  Streamlined shapes encounter less air resistance and can reach a higher terminal velocity compared to less streamlined shapes.
• How does the density of the medium affect terminal velocity?

  The denser the medium, the higher the air resistance, which can affect terminal velocity.
• What are two examples of terminal velocity?

  1. Skydiver: Accelerates until air resistance balances gravitational pull, then falls at terminal velocity.

  2. Raindrop: Falls until air resistance balances gravitational force, then falls at terminal velocity.
• What is the formula for the force of gravity acting on an object?

  The force of gravity is calculated as \( F_g = mg \), where \( m \) is mass and \( g \) is acceleration due to gravity.
• What is the formula for drag force (air resistance)?

  The drag force is calculated as \( F_d = \frac{1}{2} \rho v^2 C_d A \), where \( \rho \) is fluid density, \( v \) is velocity, \( C_d \) is drag coefficient, and \( A \) is cross-sectional area.
• What equation represents the balance of forces at terminal velocity?


  At terminal velocity, \( mg = \frac{1}{2} \rho v^2 C_d A \).
• How can terminal velocity be calculated for an object in a fluid?

  Terminal velocity can be calculated using the formula \( v = \sqrt{\frac{2mg}{\rho C_d A}} \).
• What is the summary of terminal velocity?

  • Terminal velocity is the constant speed at which a falling object stops accelerating.
  • Achieved when the force of gravity is balanced by air resistance.
  • Affected by mass, surface area, shape, and density of the medium.
  • Important for understanding the behavior of objects in free fall.
• Why is understanding terminal velocity important in physics?

  It helps explain the behavior of objects in free fall and the impact of forces such as air resistance.