Originally Posted by tommo
Everyone and everything's terminal velocity is the same.
The problem is that in the normal world the size of something and shape, say if it's flat and fairly light, like a piece of plastic. It has the wind resistance. But something fairly round or thin has barely any
But yeah, terminal velocity doesn't change.
I politely disagree with that (while assuming you were being serious in that post). Consider sky divers who go into vertical diving positions to fall faster, and then spin to their stomachs, increasing their area, and wind resistance, to slow their falling speed. There is a change in terminal velocity depending on the distribution of area an object has when falling through a fluid with any density, such as air.
Terminal velocity is the speed when the forces of gravity, drag, and buoyancy (usually buoyancy can be neglected) are balanced, giving no net acceleration, thus a constant speed. Drag increases linearly in proportion to the projected area in the direction of travel, so as you increase the area of an object (such as by rotating, or extending arms from and to certain positions), you increase the drag. As drag always acts opposite the direction of motion, an increase in drag results in a decrease in terminal velocity, assuming the volume of the object, and gravity remain constant. Drag also increases in proportion to velocity squared, the drag coefficient (which depends entirely on the shape of the object), and on the density of the fluid (air is a fluid) in which the object is moving.
In a vacuum, by definition, there is no fluid, which means zero density. This drops the drag factor out of the terminal velocity equation, as well as the buoyancy factor (buoyancy force = volume*density of fluid*acceleration of gravity), leaving only the force due to gravity. With no forces opposing the gravitational force, all objects accelerate at the acceleration of gravity continuously until impacting something (assuming they are dropped from rest), thus giving all objects the same speed.
The force of gravity depends on the mass of the object, with heavier objects falling with greater force than lighter ones. This means that 2 objects with the same size and shape but of different masses, will have different terminal velocities. The heavier object will fall with a faster terminal velocity than the lighter one due to the greater force of gravity acting on it, opposite their equal drag forces. (Note: in a vacuum, there is no terminal velocity, and it is assumed that when talking about terminal velocities, we are also talking about things moving through fluids.)
Also, any imperfections in either object that cause turbulence in the flow traveling over the object would also decrease their terminal velocity, as turbulence increases drag.
The speed at which an object falls, can be determined by summing all the forces acting on that object, and then dividing by the object's mass to find its acceleration. Then integrate the acceleration to get velocity. At terminal velocity, the sum of all forces acting on an object is zero. Net Force = mass*acceleration, and if there is an acceleration, the velocity is not constant, which is the criteria for terminal velocity. So for the acceleration to be zero, the net force must be zero. As objects increase their falling speed, the force due to drag increases proportionally to the square of the falling speed, and eventually increases to the point where it balances the force due to gravity, which does not change in most practical scenarios. If an object were falling from the outer limits of our atmosphere, to sea level, there are slight variations in gravitational acceleration at those distances.
For everyone, and everything's terminal velocity to be the same, everyone and everything would have to have the same physical properties, be falling through identical fluids, and falling in an area with the same local gravity. If you meant, "a very small percentage of people and things have the same terminal velocity." then you would indeed be correct, but "everyone and everything", is too general and does not apply to terminal velocity.
In case anyone is wondering where buoyancy comes into terminal velocities: A piece of styrofoam submerged in water, has a terminal velocity as it floats up towards the surface. The dominating force is the buoyancy force, not the gravitational force. Also, helium filled balloons floating upwards in the atmosphere reach a terminal velocity, also dominated by the buoyancy force. - Just two of countless examples where the terminal velocity is different, thus negating the assumption that "everyone and everything have the same terminal velocity."
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