$v_t$

Definition

$v_t$ is the terminal velocity, which is the maximum velocity an object can reach when falling through a medium, such as air or water. It is the point at which the force of drag on the object equals the force of gravity, resulting in a constant velocity.

5 Must Know Facts For Your Next Test

1. $v_t$ is the velocity at which the net force on an object becomes zero, resulting in a constant velocity.
2. The terminal velocity of an object is dependent on its mass, size, shape, and the medium it is falling through.
3. Objects with a larger surface area-to-mass ratio will reach a higher terminal velocity due to increased drag force.
4. Terminal velocity is an important concept in understanding the motion of objects, such as skydiving, falling raindrops, and the motion of particles in fluids.
5. The time it takes for an object to reach its terminal velocity is determined by the object's initial velocity, the medium's viscosity, and the object's mass and shape.

Review Questions

• Explain how the forces of drag and gravity determine the terminal velocity of an object.
  • The terminal velocity of an object is reached when the force of drag, which opposes the object's motion, becomes equal to the force of gravity acting on the object. As the object falls, the drag force increases until it balances out the gravitational force, resulting in a constant velocity known as the terminal velocity. This occurs because the acceleration of the object decreases as the drag force increases, eventually reaching a point where the net force on the object is zero, and it no longer accelerates.
• Describe how the physical characteristics of an object, such as its mass and surface area, affect its terminal velocity.
  • The terminal velocity of an object is influenced by its physical characteristics, such as its mass and surface area. Objects with a larger surface area-to-mass ratio, such as a skydiver in a spread-eagle position, will experience greater drag forces and reach a higher terminal velocity compared to objects with a smaller surface area-to-mass ratio, such as a skydiver in a streamlined position. Additionally, objects with a greater mass will generally have a lower terminal velocity, as the gravitational force acting on them is stronger, requiring a higher drag force to balance it out.
• Analyze the importance of understanding terminal velocity in the context of rotational variables, such as in the motion of particles in fluids or the behavior of falling objects.
  • Understanding the concept of terminal velocity is crucial in the context of rotational variables, as it allows for the accurate prediction and analysis of the motion of objects and particles in fluids. For example, in the motion of particles in fluids, such as the sedimentation of particles in a centrifuge or the behavior of raindrops, the terminal velocity of the particles determines their settling rate and the overall dynamics of the system. Similarly, in the motion of falling objects, such as skydiving or the motion of falling debris, the terminal velocity is a key factor in determining the object's trajectory and the forces acting on it, which is essential for safety and engineering considerations.

Related terms

Drag Force: The force exerted by a fluid, such as air or water, on an object moving through it, which opposes the object's motion.

Gravitational Force: The attractive force between an object and the Earth, which causes objects to accelerate downwards at a rate of approximately 9.8 m/s^2.

Acceleration Due to Gravity: The rate at which an object's velocity changes due to the Earth's gravitational pull, typically denoted as $g$ and having a value of approximately 9.8 m/s^2.