THEORY
In your high school physics classes, you learned all about various forces that act on matter. Ex:
- gravitational force
- electromagnetic force
- friction
- tension
Here I will introduce another force that is commonly overlooked. How many times have you been a trajectory problem with the comment "ignore air resistance"? Have you ever wondered what would happen if it is not ignored?
![](https://static.wixstatic.com/media/1c3841_eb8976820a24bb31e63887699d063fab.jpg/v1/fill/w_389,h_259,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/1c3841_eb8976820a24bb31e63887699d063fab.jpg)
Drag force is caused by the movement of an object through a medium. It is included in the F(net) calculation just like any other force.
Drag is given by the formula:
![](https://static.wixstatic.com/media/1c3841_43e9cdc9abcb5fc76ceed57f041f2cbc.jpg/v1/fill/w_335,h_240,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/1c3841_43e9cdc9abcb5fc76ceed57f041f2cbc.jpg)
![](https://static.wixstatic.com/media/1c3841_1bbe971e541811e2fcff4b6a5c850885.png/v1/fill/w_229,h_439,al_c,lg_1,q_85,enc_auto/1c3841_1bbe971e541811e2fcff4b6a5c850885.png)
where:
F(D) = drag force (N)
ρ = density of the medium (kg/m^3)
A = impact area of the object (m^2)
C(D) = coefficient of drag
v = velocity (m/s)
Some common drag coefficients are listed here:
Notice that the smallest drag coefficient is the 'streamlined' body. Where have you seen this shape before?
Some animals have evolved to be shaped similarly to the "streamlined body" because it is the most aerodynamic. This shape is also used in planes, submarines, and other transportation as a way to minimize the amount of energy needed to overcome drag.
![](https://static.wixstatic.com/media/1c3841_bf7a5f1e38e9357a4470d2fc67674623.png/v1/fill/w_253,h_144,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/1c3841_bf7a5f1e38e9357a4470d2fc67674623.png)
![](https://static.wixstatic.com/media/1c3841_b41cbdfb963bb05ac8bb62f9909b98ce.jpg/v1/fill/w_213,h_144,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/1c3841_b41cbdfb963bb05ac8bb62f9909b98ce.jpg)
![](https://static.wixstatic.com/media/1c3841_9e132148912d10ad8b60057e612f976c.jpg/v1/fill/w_234,h_144,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/1c3841_9e132148912d10ad8b60057e612f976c.jpg)
Photo credits:
Car: http://ffden-2.phys.uaf.edu/212_spring2011.web.dir/Jared_Boerger/Aerodynamics.html
Table of Drag Coefficients: http://en.wikipedia.org/wiki/Drag_coefficient
Bird, Submarine, Whale: clip art