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Limit to Impact Velocity
Name: Rafael C.
Status: educator
Age: 30s
Location: N/A
Country: N/A
Date: 7/13/2004
Question:
If there is no friction, will the terminal velocity of
a falling object reach a specific limit?
In other words, is there a chance (hypothetically) that a falling
object will never reach a terminal velocity if there is no drag present?
Replies:
Yes. If there is no drag, the object will just keep accelerating.
Tim Mooney
Rafael,
If there is nothing to work against gravity, no air resistance or drag, then
the object will continue to accelerate until it collides with the ground.
So long as the object is close enough to the surface of the Earth, the
acceleration will be a constant 9.8m/s^2 throughout the fall. Gravity will
be the only force on the object, so gravity will determine the acceleration.
Terminal velocity only happens because drag is proportional to speed. As a
falling object speeds up, air resistance increases. If the fall lasts long
enough, the air resistance gets just as large as gravity, but in the
opposite direction. At this time, net force and acceleration are zero.
Velocity is constant.
Ken Mellendorf
Math, Science, Engineering
Illinois Central College
Sounds like you understand it correctly, Rafael.
With no friction there is no terminal velocity.
"Terminal velocity" is a effect of drag-producing fluid media such as air or water.
The drag force increases with speed until it is almost equal to the weight of the object,
so then there is almost no further acceleration, so the object falls at a steady speed
from then on.
In a vacuum there is no drag, let alone drag which increases with speed.
So in a vacuum there is no "terminal velocity" effect.
Our moon has no atmosphere. High vacuum right down to the surface.
A feather dropped on the moon from 100 miles above the surface would keep on
accelerating at
1/6 of earth-gravity (earth: 9.8m/sec2 or 32ft/sec/sec or 22mph/sec, moon: 1.6m/sec2
or 5.3ft/sec/sec or 3.6mph/sec)
until it hit the surface at about 1600 miles per hour.
I do not think that is quite enough to vaporize the feather, so maybe we should drop
it from a little higher than that.
If a black hole has no matter near it to provide gas, it can be surrounded by high
vacuum,
and an unlikely object falling straight "down" into it should reach light speed at the
event horizon radius.
If you wish to try thinking of light speed as the terminal velocity of empty space,
I think you will gain some perspective from that.
As an object approaches light speed relative to an observer, it requires increasingly
more energy to accelerate it 1 mph faster.
A bit like air drag requires steeply increasing force as velocity increases.
But the energy used pushing air drag is lost, while the energy used to push a mass
faster in vacuum is stored as momentum,
and is all available to be given back.
A high-speed object in a vacuum can coast forever, while an object in air slows down
when the pushing stops.
Jim Swenson
In the absence of friction but the presence of a gravitational field the
object will continue to accelerate. It should be noted, however, that
there is no such thing as a perfect vacuum so there will always be some
friction.
Greg Bradburn
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Update: June 2012
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