Statement of Problem
The purpose of this inquiry is to find the relationship between the
distance between the pellet gun and the target block, and loss of momentum due
to air friction.
Review of Literature
As Tom Benson from the Glenn Research Center of NASA explains, a moving object
moving through air will always encounter a “drag” force. This drag
is directly related to the velocity of the object; as velocity increases, drag
increases on the object. Relating this situation to a bullet, which moves at
incredible speeds, the air resistance on that object plays a very major factor
in determining its final speed as well as momentum.
Mathew Mosdell makes note of a particular mathematician, the first man to invent
a ballistic pendulum, Benjamin Robins. By firing a musket at different ranges,
Robins was able to discover the effects of air resistance on the ball fired,
as Mosdell confirms. At one point, Mosdell noted that the air resistance actually
caused 85 times greater influence than that of gravity, playing an incredible
factor in the final velocity of the bullet.
Similarly, Tom Henderson explains the affects of air resistance on a free falling
object, noting that eventually the object will fall to a terminal velocity eventually,
as air resistance counterbalances completely to the acceleration of gravity.
This process of reaching terminal velocity takes time, even though this time
may be very small and may even be negligible. However, this suggests that the
force of air resistance is constantly slowing the acceleration of an object
while moving in the air. When this idea is applied to a moving bullet, this
suggests that the bullet will be constantly be decelerated while moving in the
air, continuously losing velocity. This would suggest that the relationship
between the momentum lost due to air friction, and the distance between the
target and rifle, is a linear relationship. As the distance increases, the amount
of momentum lost also increases.
Hypothesis
As the distance between the muzzle of the air gun and the target increases,
the amount of momentum lost due to air friction will also increase at a exponential
rate.