Important Topic of Physics: Terminal Velocity

# Terminal Velocity

## Introduction:

Terminal velocity is the constant speed attained by an object falling freely through a gas or liquid. A typical terminal velocity for a parachutist who waits too long to open the chute is about 150 miles (240 kilometres) per hour. Raindrops have a much lower terminal velocity, and a mist of tiny oil droplets has an even lower terminal velocity. When an object is dropped from rest, its speed increases until it reaches terminal velocity; when an object is forced to move faster than its terminal velocity, it slows down to this constant velocity upon release.

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Terminal velocity is reached when the speed of a moving object no longer increases or decreases; the object’s acceleration (or deceleration) is zero. Because the force of air resistance is proportional to the speed of the falling object, air resistance increases for an object that is accelerating after being dropped from rest until terminal velocity is reached. At terminal velocity, air resistance equals the weight of the falling object in magnitude. Because the two forces are oppositely directed, the total force on the object is zero, and the object’s speed has become constant.

The terminal velocity of a body moving through a viscous fluid is its maximum velocity. It is attained when the medium’s force of resistance equals and opposes the force of gravity. As the velocity increases, so does the retarding force, and there will come a point when the force of gravity equals the resistance force. After that point, velocity ceases to increase, and this velocity is referred to as terminal velocity.

## Overview:

When a body falls through a viscous fluid, it causes relative motion between the layers. As a result, the body is subjected to a viscous force that tends to slow its movement. The viscous force (F=6πηr v) increases as the velocity of the body increases. A stage is reached when the body’s weight equals the sum of the upthrust and viscous force. The body then experiences no net force and begins to move at a constant velocity. So, here’s the idea of Terminal Velocity.

The highest velocity attained by an object falling through a fluid is defined as terminal velocity. When the sum of drag force and buoyancy equals the downward gravity force acting on the object, it is observed. The object’s acceleration is zero because the net force acting on it is zero.

### Terminal velocity speed:

The maximum velocity (speed) attained by an object as it falls through a fluid is referred to as terminal velocity (air is the most common example). It occurs when the sum of the drag force (Fd) and buoyancy (B) acting on the object equals the downward force of gravity (FG).

Terminal velocity is the constant speed attained by an object falling freely through a gas or liquid. A typical terminal velocity for a parachutist who waits too long to open the chute is about 150 miles (240 kilometres) per hour. The terminal velocity speed varies with the weight of the falling object, its surface area, and what it is falling through. A feather, for example, has a small weight but a large surface area in the air as it falls. As a result, its terminal velocity speed is much slower than that of a rock of the same weight. This is why an ant can fall off a tall building and land unharmed, whereas you would die in a similar fall. Remember that this process occurs in any gas or fluid. So terminal velocity is the rate at which a rock sinks when dropped in water.

Joseph Kittinger holds the world skydiving speed record, falling at a speed of 988 km/h by properly orienting his body and jumping at high altitude, where there is less wind resistance. The Earth’s gravity pulls on you with a constant acceleration of 9.81 metres per second. You’ll fall 9.81 meters/second faster every second if there’s no wind resistance. 9.81 metres per second in the first second, 19.62 metres per second in the second second, and so on.

Drag is the opposing force of the atmosphere. And the drag force increases roughly proportionally to the square of the speed. So, doubling your speed results in a squaring of the drag force. Because the drag force increases much faster than the constant acceleration, you eventually achieve a perfect balance between gravity and the drag force of whatever you’re moving through.

### Terminal velocity meaning:

The maximum velocity (speed) attained by an object as it falls through a fluid is referred to as terminal velocity (air is the most common example). It occurs when the sum of the drag force (Fd) and buoyancy (B) acting on the object equals the downward force of gravity (FG). Because the object’s net force is zero, it has no acceleration.

An object is moving at its terminal velocity in fluid dynamics if its speed is constant due to the restraining force exerted by the fluid through which it is moving. As an object’s speed increases, so does the drag force acting on it, which is also affected by the substance it is passing through (for example air or water).

The force or drag of resistance will equal the gravitational pull on the object at some speed (buoyancy is considered below). At this point, the object ceases to accelerate and continues to fall at a constant speed known as the terminal velocity (also called settling velocity).

An object moving downward faster than the terminal velocity will slow down until it reaches the terminal velocity (for example, because it was thrown downwards, fell from a thinner part of the atmosphere, or changed shape).

Drag is proportional to the projected area, which is represented in this case by the object’s cross-section or silhouette in a horizontal plane. A parachute with a large projected area relative to its mass has a lower terminal velocity than a dart with a small projected area relative to its mass.

In general, for the same shape and material, an object’s terminal velocity increases with size. This is due to the fact that the downward force (weight) is proportional to the cube of the linear dimension, whereas air resistance is proportional to the cross-section area, which increases only as the square of the linear dimension.

### Terminal Velocity Formula:

As an object’s speed increases, so does the drag force acting on it, which is also affected by the substance it is passing through (for example air or water). The drag or force of resistance will equal the gravitational pull on the object at some speed (buoyancy is considered below). At this point, the object ceases to accelerate and continues to fall at a constant speed known as the terminal velocity (also called settling velocity).

In the case of raindrops, it is initially due to gravity that they accelerate. As the velocity increases, so does the retarding force. Finally, when the sum of the viscous and buoyant forces equals the force due to gravity, the net force equals zero, as does the acceleration. The raindrop then falls at a constant rate. Thus, the equation gives the terminal velocity v t in equilibrium.

v t=2 a 2 (ρ-σ)g / 9η

ρ and σ are sphere and fluid mass densities.

Question 1: When does terminal velocity exist?

Answer: The acceleration (or deceleration) of a moving object is zero when its speed is no longer increasing or decreasing.

Question 2: What is terminal velocity?

Answer: The highest velocity attained by an object falling through a fluid is defined as terminal velocity.

Question 3: How does terminal velocity work?

Answer: Terminal velocity is the constant speed attained by an object falling freely through a gas or liquid. When an object is dropped from rest, its speed increases until it reaches terminal velocity; when an object is forced to move faster than its terminal velocity, it slows down to this constant velocity upon release.

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