Why does terminal velocity exist

If the mass of an object remains constant, the motion of the object can be described by Newton's second law of motion, force F equals mass m times acceleration a :. Weight and drag are forces which are vector quantities. The net external force F is then equal to the difference of the weight W and the drag D. The magnitude of the drag is given by the drag equation. Drag D depends on a drag coefficient Cd , the atmospheric density r , the square of the air velocity V , and some reference area A of the object.

On the figure at the top, the density is expressed by the Greek symbol "rho". The symbol looks like a script "p". This is the standard symbol used by aeronautical engineers. We are using "r" in the text for ease of translation by interpretive software. Drag increases with the square of the speed. So as an object falls, we quickly reach conditions where the drag becomes equal to the weight, if the weight is small.

When drag is equal to weight, there is no net external force on the object and the vertical acceleration goes to zero. With no acceleration, the object falls at a constant velocity as described by Newton's first law of motion. The constant vertical velocity is called the terminal velocity. Typical values of the drag coefficient are given on a separate slide. This page shows an interactive Java calculator which solves the equations for the terminal velocity of a falling object.

The chemistry of the atmosphere and the gravitational constant of a planet affects the terminal velocity. You select the planet using the choice button at the top left. You can perform the calculations in English Imperial or metric units. You must specify the weight or mass of your object. You can choose to input either the weight on Earth, the local weight on the planet, or the mass of the object. Then you must specify the cross sectional area and the drag coefficient.

Finally you must specify the atmospheric density. We have included models of the atmospheric density variation with altitude for Earth and Mars in the calculator. Asked 8 years, 3 months ago. Active 1 year, 1 month ago. Viewed 2k times. Improve this question. Or have you managed to drill a hole to the centre of the earth and sustained a vacuum in such a hole?

Add a comment. Active Oldest Votes. In most cases, air resistance drag force is the velocity dependent force. Out of curiosity, why does terminal velocity work in a vacuum too?

Improve this answer. But because of the terminal velocity, they can't approach this level of speed. The question is that what is the velocity dependent force that results in a net acceleration of 0, if it's not the air resistance? And it works in vacuum, because if the thing is pulled down, at one point it make Boom! You wouldn't need a resistive force for "terminal velocity" because there isn't acceleration very little due to gravity over great distances.

In this scenario, the acceleration is little, if not none, so the velocity is constant rather than terminal. If it came close enough to a planet earth for gravitational force to "change" the velocity, then it will accelerate more and keep going until BOOM.

A body can keep accelerating while never reaching the speed of light. See Rindler coordinates. Show 1 more comment. Akash 2 2 bronze badges. See image: The 'total mass of fluid displaced' includes the fluid directly fallen through and the fluid indirectly displaced by the rock accelerating the fluid fallen through away from it. Nick Landell Nick Landell 6 6 bronze badges.

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