Drag force is the resistive force a fluid, such as air or water, exerts on an object moving through it. This cheat sheet helps students connect free-body diagrams, velocity, net force, and acceleration for falling objects. It is especially useful for understanding why objects do not keep speeding up forever when they fall through air.
These ideas appear in mechanics, motion graphs, and real-world applications such as skydiving, parachutes, and vehicle design.
The most important idea is that drag force usually increases as speed increases. At low speeds, drag is often modeled as , while at higher speeds it is commonly modeled as . Terminal velocity occurs when drag balances weight, so the net force is and acceleration is .
A clear force diagram shows weight downward and drag upward for a falling object.
Key Facts
- Drag force acts opposite the direction of an object's motion through a fluid.
- For slow motion through a fluid, drag can be modeled as , where is a drag constant and is speed.
- For faster motion through air, drag is often modeled as , where is fluid density, is drag coefficient, and is cross-sectional area.
- The weight of a falling object is , where is mass and is gravitational field strength.
- Terminal velocity occurs when , so and .
- If downward is positive for a falling object, the net force can be written as .
- Increasing area or drag coefficient increases drag force and lowers terminal velocity.
- For quadratic drag at terminal velocity, .
Vocabulary
- Drag force
- A resistive force exerted by a fluid that acts opposite an object's motion through the fluid.
- Terminal velocity
- The constant speed reached when drag force equals weight and the net force is zero.
- Free-body diagram
- A simplified diagram showing all external forces acting on one object.
- Drag coefficient
- A dimensionless value that describes how strongly an object's shape resists motion through a fluid.
- Cross-sectional area
- The effective area of an object facing the direction of motion through a fluid.
- Net force
- The vector sum of all forces on an object, given by .
Common Mistakes to Avoid
- Forgetting that drag acts opposite motion is wrong because drag changes direction if the object's velocity changes direction.
- Treating terminal velocity as zero velocity is wrong because terminal velocity means constant nonzero speed with .
- Using without squaring the speed is wrong because quadratic drag depends on , not just .
- Assuming heavier objects always fall faster is wrong because terminal velocity also depends on , , and the fluid density .
- Drawing only weight in a falling-object free-body diagram with air resistance is wrong because drag must be included when air resistance is significant.
Practice Questions
- 1 A skydiver has mass . What is the skydiver's weight if ?
- 2 An object moving through air has , , , and . Calculate the drag force using .
- 3 A falling object has and experiences upward. If downward is positive and , find and .
- 4 Explain why opening a parachute decreases a skydiver's terminal velocity even though the skydiver's mass stays the same.
Understanding Drag Force & Terminal Velocity
A falling object has changing motion because the forces change during the fall. Just after release, its speed is small, so air resistance is small. Gravity then produces a downward net force.
Force equals mass times acceleration, so the object accelerates downward. As its speed grows, the air pushes back more strongly. The downward net force becomes smaller over time.
This means the object is still moving downward and gaining speed, but its acceleration is decreasing. Students often confuse decreasing acceleration with slowing down.
They are different. An object can speed up while its acceleration gets closer to zero.
Motion graphs show this process clearly. On a velocity versus time graph, the slope represents acceleration. Early in a fall, the graph rises steeply.
Later, it bends and becomes flatter as acceleration falls. Once the speed becomes constant, the graph is horizontal. On a position versus time graph, the slope is the velocity.
The curve becomes steeper at first, then settles into a straight line when the speed is constant. A force versus time graph can show the upward air force increasing until it matches the downward weight. Reading all three graph types helps connect forces to observed motion.
Terminal speed depends on more than an object's mass. A heavier object has greater weight, so it generally needs a larger air force before its motion settles. If its shape and size stay the same, this usually gives it a higher terminal speed.
But mass alone does not decide the outcome. A crumpled sheet of paper falls much faster than the same sheet spread flat because its exposed area is smaller. A feather can have a low terminal speed because its weight is small compared with the air force on its broad shape.
Air density matters too. An object falls differently in water, where the fluid is much denser than air.
Real falling situations often have stages. A skydiver first falls with a relatively small area facing the air. Opening a parachute greatly increases the area, causing a large upward air force.
For a short time, that force can be greater than weight. The net force is then upward even though the diver is still moving downward. The diver slows down until reaching a new, lower constant speed.
In free body diagrams, draw only forces acting on the chosen object. Do not draw velocity or acceleration as forces. Keep arrow directions separate from the chosen positive direction, and use the signs in calculations consistently.