When an object falls through air, gravity pulls it downward while air resistance pushes upward against its motion. This air resistance is called drag, and it grows as the object moves faster. Drag matters for skydiving, sports, vehicle design, falling raindrops, and spacecraft reentry.
Terminal velocity is the steady falling speed reached when the upward drag force balances the downward weight.
At low speeds, drag may be modeled as roughly proportional to speed, but for many everyday falling objects in air, drag is better modeled as proportional to speed squared. As the object speeds up, drag increases until the net force becomes zero. With zero net force, acceleration becomes zero, so the object continues falling at constant velocity.
A velocity time graph rises steeply at first, then gradually levels off toward the terminal velocity.
Understanding Physics: Drag and Terminal Velocity
Drag comes from the way air must move around an object. Air is pushed aside at the front, then flows around the sides. This creates pressure differences.
Some air rubs against the surface because air has viscosity. Behind many objects, the flow breaks into a messy wake full of swirling air. Making that wake takes energy from the moving object.
A streamlined shape keeps the airflow smoother and makes a smaller wake. This is why a cycling helmet, a racing car, and a bird's body have curved shapes.
The drag coefficient is a number that describes how strongly a particular shape resists airflow. It depends on shape, surface texture, and the object's orientation.
Size changes drag in an important way. A broad flat object meets more air than a narrow object facing the same direction. Its effective front area is larger, so it slows more strongly.
Turning a sheet of paper from edge-first to face-first changes its fall dramatically. Mass matters too, but not in the simple sense that heavy objects always fall faster. A heavy object with a large area may have a low steady speed.
A compact object of the same mass may move much faster. If two objects have similar shape and material, making one larger increases its mass faster than its front area.
That larger object can therefore have a higher terminal speed. This helps explain why a hailstone falls much faster than a tiny raindrop.
The approach to terminal velocity is gradual. At release, an object has little or no drag because it is not yet moving through the air quickly. Its acceleration is close to the usual gravitational acceleration.
As speed builds, the upward effect of drag becomes more important. The acceleration gets smaller each moment. On a velocity time graph, the curve becomes flatter rather than suddenly forming a sharp corner.
A skydiver experiences a clear version of this process. After leaving the aircraft, the diver gains speed. When the parachute opens, the front area increases greatly.
Drag becomes much larger than weight for a short time, so the diver slows down. A new, much lower terminal speed is then reached.
Real situations are rarely perfectly steady. Wind changes the speed of an object relative to the air, which is the speed that controls drag. A falling object can tumble or rotate, changing its area and drag coefficient as it falls.
Air density is lower at high altitude, so the same object usually has a higher terminal speed there. Near the ground, denser air produces more drag. Very small particles, such as dust or mist droplets, can be in a low speed regime where drag is closer to being proportional to speed rather than speed squared.
In experiments, students should check whether the drop distance is long enough for the speed to level out. They should use repeated trials, measure distance carefully, and note whether wind or tumbling could affect the result.
Key Facts
- Weight acts downward: W = mg.
- Quadratic drag can be modeled as Fd = 1/2 rho Cd A v^2.
- Terminal velocity occurs when Fd = W.
- For quadratic drag, terminal speed is vt = sqrt(2mg / (rho Cd A)).
- Net force during falling is Fnet = mg - Fd if downward is positive.
- Acceleration decreases as speed increases because a = Fnet / m.
Vocabulary
- Drag force
- Drag force is the resistive force from a fluid, such as air, that acts opposite an object's motion.
- Terminal velocity
- Terminal velocity is the constant speed reached when drag force equals the object's weight.
- Weight
- Weight is the gravitational force on an object, calculated by W = mg.
- Cross-sectional area
- Cross-sectional area is the area of an object facing the airflow, which affects how much drag it experiences.
- Drag coefficient
- The drag coefficient is a dimensionless number that describes how strongly an object's shape resists motion through a fluid.
Common Mistakes to Avoid
- Treating drag as constant is wrong because drag usually increases as speed increases, especially in air at typical falling speeds.
- Saying terminal velocity means no forces act is wrong because weight and drag still act, but they balance so the net force is zero.
- Using mass instead of weight in the force balance is wrong because drag must be compared to W = mg, not just m.
- Forgetting the direction of drag is wrong because drag always acts opposite the object's motion, so for a falling object it points upward.
Practice Questions
- 1 A 70 kg skydiver falls before opening a parachute. What is the skydiver's weight? Use g = 9.8 m/s^2.
- 2 A falling ball has mass 0.50 kg and experiences 3.0 N of upward drag at one instant. Taking downward as positive, find the net force and acceleration. Use g = 9.8 m/s^2.
- 3 A skydiver opens a parachute, greatly increasing cross-sectional area. Explain how this changes drag, acceleration, and the new terminal velocity.