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Air Resistance problem
Name: D. F.
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 2000-2001
Question:
a .060kg tennis ball and a 4.55kg bowling ball sitting on
a ladder at 3.1m above the ground they fall off simutaneously which will
hit the ground first and why?
Replies:
Assuming that they are falling in air and not in a vacuum, the bowling ball
will almost certainly hit the ground first. The reason is that their
acceleration toward the ground is determined by the forces acting on them
divided by their masses. The force due to gravity is exactly proportionate
to their masses, so if that were the only force acting on them, both balls
would fall at exactly the same rate. However, gravity isn't the only force.
Once the balls are moving through the air, they experience a force from wind
resistance as well. This force will oppose the downward motions of the
balls. The overall acceleration of each ball will be governed by the sum of
the forces from gravity and wind resistance, divided by the mass of the
ball.
The force acting on a ball from wind resistance depends on its airspeed, its
shapes, and its size. Because the bowling ball is bigger than the tennis
ball, it will experience more force from wind resistance. However, when
this force is added to the gravitational force (since these forces act in
opposite directions, you could also say that you're subtracting the force of
wind resistance from the gravitational force), it will change the total
force acting on the bowling ball by only a small fraction. However, when
you do the same subtraction for the tennis ball, the wind resistance will be
a larger fraction of the total force. In other words, wind resistance will
interfere with the tennis ball's fall more than with the bowning ball's
drop. So, the bowling ball lands first.
Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
According to Newton's law of gravitation, neglecting the resistance of
air, both will hit the ground at the same time. Newton's law of gravitation
states that the acceleration due to gravity is a constant, call it "g". This
acceleration is a constant regardless of the mass of the object. This means
that the speed that the falling objects, call it "s", is the acceleration
"times" the time of fall, that is:
s = g*t. That is the speed increases linearly with time with a slope of "g".
This, in turn, means that the position of the object, call it "x", at some
time "t" is:
x = 1/2*(g*t^2). These formulas are derived from Calculus.
Without worrying about the mathematics, the important point is that the
position of the falling objects depends only on "g" which is a constant, and
the duration of fall "t". The mass of the object does not enter into
equation.
Note that this is a "law" that is a statement of observations. It does not
depend upon any "theory" about "how" or "why". It only states the results of
many observations.
Vince Calder
Mr. Fluke,
This can be done without mathematics. First, look at the problem in a
vacuum: no air. Both balls feel exactly the same acceleration. Both start
at exactly the same velocity (zero). Their motions will be identical. They
will reach the ground at exactly the same time.
Now, include the air. As they begin to speed up, air resistance will affect
the motion of the tennis ball much more than that of the bowling ball. To
verify this, place a bowling ball and tennis ball on a table. Blow on both
as hard as you can. You can get the tennis ball moving. You have no effect
on the bowling ball. Both balls are slowed, but the tennis ball is slowed
more. The tennis ball will therefore take more time than the bowling ball
to reach the ground. The greater the height of the ladder, the more
noticeable the effect will be.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012
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