Drag & Terminal Velocity
Drag & Terminal Velocity
Kinematics described how a falling object moves. Dynamics now explains why its acceleration changes when air resistance is present.
Drag changes when speed changes
- Drag is a resistive force from a fluid, such as air or water. It points opposite to the object's velocity.
- For the simple model required here, drag increases as speed increases. The exact equation depends on the object and the fluid; no coefficient of drag or viscosity is required by this syllabus.
- Friction between solid surfaces also resists relative motion, but it does not have to follow the same speed relationship as fluid drag.
velocity downwarddrag upwardDirection rule: drag opposes motion relative to the fluid. Size rule: faster relative motion through the same fluid gives more drag.
From release to terminal velocity
Follow the same object. Its weight is constant, but its speed and drag change.
- Just released: speed is zero, so drag is zero. Weight is the only significant force and acceleration is close to downward.
- Speed increasing: drag grows upward. The downward resultant becomes smaller, so acceleration decreases. The object still speeds up while weight is larger than drag.
- Terminal velocity: drag equals weight when upthrust is negligible. The resultant force and acceleration are zero, so the object continues downward at constant velocity.
Definition
1 markWhat is meant by terminal velocity?
Model answer: The constant velocity reached when the resultant force is zero.
Common mistake
What a parachute changes
- Opening a parachute suddenly increases area, so drag becomes larger than weight. The resultant force is upward while velocity is downward, so the skydiver slows down.
- As the skydiver slows, drag decreases. A new balance is reached when drag again equals weight. This gives a new, much lower terminal velocity.
Worked example
Parachute opens: force direction first
A skydiver and equipment have total mass 68 kg. Just after the parachute opens, total drag is 1800 N upward and upthrust is negligible. Find the acceleration. (9702/22/M/J/24 Q2(b))
- Weight is downward.
- Taking upward as positive, the resultant is upward.
- upward.
| Change while other factors stay fixed | Effect on terminal speed | Reason |
|---|---|---|
| larger mass / weight, same shape and area | higher | more drag is needed to balance weight |
| larger area, same mass | lower | the same speed produces more drag |
| denser fluid, same object | lower | the same speed produces more drag |
If mass and area both change, the information may be insufficient. Compare one factor at a time before predicting the terminal speed.
Show worked answer
As speed increases, upward drag increases. Weight stays constant, so the downward resultant force decreases. Since acceleration is caused by the resultant force, the acceleration decreases.