Terminal velocity is the constant speed an object reaches when the force of air resistance equals the force of gravity. It depends on weight, shape, and atmospheric density. The drag coefficient is crucial to determine it, and it varies with altitude. Examples include a raindrop at 17 km/h and a skydiver at 124 mph (200 km/h).
Terminal velocity is the term for the speed an object reaches when the drag force, or air resistance, pushing against it equals the force of gravity pulling it downward. An object dropped from a height will initially accelerate due to gravity. The atmosphere, however, exerts a counterforce, or drag, that increases as the object moves faster. After some time, a point is reached where the two opposing forces are equal, and after this, the object’s velocity remains constant unless another force acts upon it: this velocity is known as its velocity. terminal. The final speed depends on the weight of the object, its shape and the density of the atmosphere.
Weight and atmospheric density can vary from place to place. While an object’s mass, which can be defined as the amount of matter it contains, is the same wherever it is found, its weight depends on the strength of the local gravitational field. This doesn’t vary on Earth on a scale that is directly perceptible to humans, but in other places like the Moon or Mars it will be very different. The density of the atmosphere decreases with altitude, so air resistance is greater near the ground than at great altitudes.
Weight and drag
The amount of resistance acting on a falling object depends on the density of the atmosphere and the shape of the object. The higher the density of the atmosphere, the greater the resistance to motion. Over short vertical distances, the density difference will be small and insignificant for most purposes, but for something falling from the upper atmosphere there is a large difference, which complicates terminal velocity calculations.
Resistance also depends a lot on the shape of the falling body. If a piece of heavy material, such as lead, is formed into a bullet-like shape and dropped point downwards from a great height, it will experience relatively low resistance and attain a high terminal velocity. If the same piece of lead is made into a thin disc and dropped so that it is flat to the earth’s surface, it will experience much greater air resistance and reach a much lower terminal velocity in less time.
The amount of downward force on a falling object depends on its weight, which is the interaction of the object’s mass with the force of gravity. The greater the mass, the greater the force and, therefore, the greater the terminal velocity. If the above experiment is conducted using a lightweight material, such as aluminum, the final speeds for both shapes would be lower than for the wire shapes. It’s important to understand, however, that the acceleration due to gravity is the same for all objects; it is the drag factor that causes variations with weight and shape. If the experiment with different shapes of lead and aluminum is performed in a vacuum, all objects will accelerate at the same rate, regardless of weight or shape, because the drag factor due to air has been eliminated.
Calculation
Determining the terminal velocity for an object dropped from a given height can be tricky. Some of the factors, such as mass and acceleration due to gravity, are simple, but you also need to know the drag coefficient, a value that depends crucially on the shape of the object. For many objects, the drag coefficient is determined experimentally, as calculations would be very difficult for complex shapes. Since the density of the atmosphere varies with altitude, this variation must also be taken into account, unless the distance to fall is quite short.
Examples
A raindrop has a terminal velocity of about 17 km/h. Conversely, a large hailstone could reach 27 mph (42 km/h), which is enough to cause injury. A lead bullet fired straight through the air would hit the ground at approximately 68 mph (152 km/h).
A skydiver, facing the ground with limbs splayed to maximize air resistance, will typically have a terminal velocity of about 124 mph (200 km/h). Diving headfirst, with arms and legs tucked in, the same skydiver could reach about 200 mph (320 km/h) or more. Accurate speeds depend on initial altitude, and much higher speeds can be achieved by diving from extreme altitudes, where the atmosphere is much thinner. For objects falling towards the Earth from outside the atmosphere, such as meteorites, the terminal velocity may be less than the initial velocity relative to the Earth. In these cases, the object slows down to its final speed.
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