Terminal velocity is the maximum velocity that you can reach during
free-fall. If you imagine yourself falling in gravity, and ignore air
resistance, you would fall with acceleration g,
and your velocity would grow unbounded (well, until special relativity
takes over). This effect is independent of your mass, since
F=ma=mg⇒a=g
Where terminal velocity arises is that air resistance is a velocity dependent force acting against your free fall. If we had, for example, a drag force of FD=KAv2 (K is just a constant to make all the units work out, and depends on the properties of the fluid you're falling through, and A is your surface area along the direction of motion) then the terminal velocity is the velocity at which the forces cancel (i.e., no more acceleration, so the velocity becomes constant):
F=0=mg−KAv2t⇒vt=√mg/KA
So we see that a more massive object can in fact have a larger terminal velocity.
Since the air drag force depends heavily on the size and shape of the object, objects with a large surface area (like a parachute) will have a much lower terminal velocity than objects with a smaller surface area (like a person falling from a plane). The weight of the object does affect the air drag force on the object and, therefore, its terminal velocity.
However, it is not the most important factor. This
explains why a flat piece of paper will fall more slowly than the same
paper after it has been crumpled into a ball. The paper weighs the same,
but the air drag forces have decreased because its surface area and
drag coefficient have changed. This causes the crumpled paper to have a
higher terminal velocity than the flat paper. This also explains why a
parachute can lower your terminal velocity when you jump from an
airplane. The parachute has a very large surface area and drag
coefficient and a relatively small mass, so it experiences much higher
air drag forces than you would without a parachute.
F=ma=mg⇒a=g
Where terminal velocity arises is that air resistance is a velocity dependent force acting against your free fall. If we had, for example, a drag force of FD=KAv2 (K is just a constant to make all the units work out, and depends on the properties of the fluid you're falling through, and A is your surface area along the direction of motion) then the terminal velocity is the velocity at which the forces cancel (i.e., no more acceleration, so the velocity becomes constant):
F=0=mg−KAv2t⇒vt=√mg/KA
So we see that a more massive object can in fact have a larger terminal velocity.
Terminal Velocity
As the object falls, the force of gravity initially causes it to continuously speed up as predicted by Isaac Newton. As it gets faster and faster, the air drag force increases until eventually, the air drag force is exactly equal to the force of gravity, and there is no net force acting on the object. If these two forces are exactly balanced, the object will no longer speed up or slow down but will continue falling at a constant velocity, called the terminal velocity.Since the air drag force depends heavily on the size and shape of the object, objects with a large surface area (like a parachute) will have a much lower terminal velocity than objects with a smaller surface area (like a person falling from a plane). The weight of the object does affect the air drag force on the object and, therefore, its terminal velocity.
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