6.9:
Drag Force and Terminal Speed
Drag force is an undesirable force that opposes the motion of an object through a fluid like air or water.
For smaller, slowly moving objects, the drag force is proportional to the object's speed.
For larger and faster-moving objects, the drag force depends on the square of the object's speed, the fluid density, the object's cross-sectional area, and the drag coefficient.
As a result of drag force, an object falling freely in a fluid does not exhibit constant acceleration.
Applying Newton's second law, the forces acting on the object are gravitational and drag, ignoring the buoyant force.
As the object falls, its speed increases, and as a result, the drag force also increases until it balances the gravitational force, resulting in zero net force and acceleration.
The highest constant speed at this point is called the terminal speed, which depends on the object's mass, shape, and surface area and the density of the fluid it is falling through.
For this reason, heavier objects have a higher terminal speed and fall faster.
6.9:
Drag Force and Terminal Speed
An interesting force in everyday life is the force of drag on an object when it is moving in a fluid. Like friction, the drag force always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects, such as cyclists, cars, and baseballs, that are not moving too slowly, the magnitude of the drag force is proportional to the square of the speed of the object.
Athletes, as well as car designers, seek to reduce the drag force to lower their race times. The aerodynamic shaping of an automobile can reduce the drag force and so increase a car's gas mileage. At highway speeds, over 50% of the power of a car is used to overcome air drag. The most fuel-efficient cruising speed is about 70–80 km/h. For this reason, during the 1970s oil crisis in the United States, maximum speeds on highways were set at about 90 km/h
While falling under the influence of gravitational force, the maximum velocity achieved by any object is called the terminal velocity. For example, a skydiver with a mass of 75 kg achieves a terminal velocity of about 350 km/h while traveling in a pike (head first) position, minimizing the area and the drag. In a spread-eagle position, that terminal velocity may decrease to about 200 km/h as the area increases. This terminal velocity becomes much smaller after the parachute opens.
The effect of size of the object that is falling through the air presents another interesting aspect of air drag. If a person falls from a 5 meter high tree branch, they will likely get hurt and possibly fracture a bone. However, small squirrels do this all the time without getting hurt. This is because the person does not reach terminal velocity in such a short distance but the squirrel does.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 1. [Web version], pages 94–95. Retrieved from https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed