Balanced forces, drag and terminal velocity

What you will learn

Air resistance, road vehicles, parachutes and objects falling in liquids.

Specification mapping: B2.7, B2.7.1

Prerequisites: B2.5, B2.6

Physical principles

If the resultant force is zero, acceleration is zero and velocity is constant, including the possibility of rest. A non-zero resultant changes velocity. Resistive drag commonly increases with speed, although its exact dependence varies with flow regime, object shape and fluid properties.

A falling object initially has a downward resultant because weight exceeds upward drag and buoyancy. As speed increases, drag grows and acceleration decreases. Terminal velocity occurs when upward forces balance weight. It is a non-zero steady velocity, not zero motion. In a liquid, upthrust can be substantial and must not be omitted when relevant.

Opening a parachute greatly increases effective drag area. Just after opening at the previous high speed, drag can exceed weight, giving upward acceleration while the person is still moving downwards. Speed decreases until a new lower terminal speed is reached. Eventually drag plus upthrust balances weight again.

A road vehicle reaches steady speed when drive balances rolling and aerodynamic resistance on a level road. Greater speed usually requires greater power to overcome drag. Do not assume a universal drag law or terminal speed without the necessary data. A velocity–time curve approaching a horizontal line has a gradient tending to zero.

Scientific diagram and interpretation

Worked examples and applications

Common misconceptions

Terminal velocity means zero acceleration, not zero velocity. Deceleration after parachute opening can occur while motion is still downwards.

Examination technique

Describe how forces change during each stage and mention upthrust in fluid problems when significant.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.