This relationship is given by Stokes’ law. Then we find that the drag force is proportional just to the velocity. The above quadratic dependence of air drag upon velocity does not hold if the object is very small, is going very slow, or is in a denser medium than air. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.” Divide an animal’s length, breadth, and height each by ten its weight is reduced to a thousandth, but its surface only to a hundredth. For the resistance presented to movement by the air is proportional to the surface of the moving object. A rat is killed, a man is broken, and a horse splashes. You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. “To the mouse and any smaller animal, presents practically no dangers. Haldane, titled “On Being the Right Size.” The following interesting quote on animal size and terminal velocity is from a 1928 essay by a British biologist, J. You do not reach a terminal velocity in such a short distance, but the squirrel does. However, a small squirrel does this all the time, without getting hurt. If you fall from a 5-m-high branch of a tree, you will likely get hurt-possibly fracturing a bone. The size of the object that is falling through air presents another interesting application of air drag. Let’s see how this works out more quantitatively.įind the terminal velocity of a 50-kg skydiver falling in spread-eagle fashion. Since F D F D is proportional to the speed squared, a heavier skydiver must go faster for F D F D to equal his weight. At this point, the person’s velocity remains constant and we say that the person has reached his terminal velocity ( v T ). A zero net force means that there is no acceleration, as shown by Newton’s second law. However, as the person’s velocity increases, the magnitude of the drag force increases until the magnitude of the drag force is equal to the gravitational force, thus producing a net force of zero. The downward force of gravity remains constant regardless of the velocity at which the person is moving. The two forces acting on him are the force of gravity and the drag force (ignoring the small buoyant force). For instance, consider a skydiver falling through air under the influence of gravity. Some interesting situations connected to Newton’s second law occur when considering the effects of drag forces upon a moving object. (credit: NASA/Kathy Barnstorff) Terminal Velocity Smoother “skin” and more compression forces on a swimmer’s body provide at least 10 % 10 % less drag. When taking into account other factors, this relationship becomesįigure 6.31 Body suits, such as this LZR Racer Suit, have been credited with aiding in many world records after their release in 2008. We can write this relationship mathematically as F D ∝ v 2. For most large objects such as cyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force F D F D is proportional to the square of the speed of the object. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. Like friction, the drag force always opposes the motion of an object. You feel a smaller drag force when you tilt your hand so only the side goes through the air-you have decreased the area of your hand that faces the direction of motion. The faster you move your hand, the harder it is to move. You might also feel it if you move your hand during a strong wind. You feel the drag force when you move your hand through water. Determine an object’s terminal velocity given its massĪnother interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid).Describe applications of the drag force.By the end of this section, you will be able to:

Drag coefficient