Background

The relationship between the velocity of an object is directly related to its momentum, as shown by the equation P=MV; as velocity increases on the object, the momentum obviously will increase as well. This law of momentum is based on the law of inertia, where an object at rest/moving will stay at rest/moving at the same speed unless acted upon by an outside force. However, it is obvious enough that an object will not remain moving at a constant speed for a long sustained period of time; this is due mainly to the force of friction that the air provides, decelerating (or possibly even accelerating) the object in motion. This applies especially to the movement of a bullet, despite its aerodynamic shape, since the mass is very small in opposition to win currents. As this increases or decreases the velocity of the bullet, this in turn increases or decreases the momentum of the object. When the bullet hits another object, the law of momentum conservation states that this momentum will not be lost, but instead transferred to the object that was hit. To test this theory, there are many variables that could be adjusted to change the velocity (and therefore the momentum) of the bullet; testing in an indoor vs. an outdoor environment may produce different results, with less wind movement indoors than outdoors. Mass of the bullet could also be adjusted, to slow the bullet but hold a constant momentum. However, I find that the most interesting of these variables may be the use of distance as the variable. By using distance as a variable, I should be able to test the effect that the air friction will have on the bullet. By adjusting the distance, I should be able to increase the amount of air friction by increasing the distance.


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.