3.2 Non-uniform motion
- Syllabus
- 9702–2028–2029
- Topic
- 3.2
- Level
- AS
Learning objectives
3.2.1Frictional forces and viscous/drag forces including air resistance (no• show a qualitative understanding of frictional forces and viscous/drag forces including air resistance (no treatment of the coefficients of friction and viscosity is required, and a simple model of drag force increasing• As speed increases is sufficient)3.2.2The motion of objects in a uniform gravitational field with air resistance• describe and explain qualitatively the motion of objects in a uniform gravitational field with air resistance3.2.3Objects moving against a resistive force may reach a terminal (constant)• understand that objects moving against a resistive force may reach a terminal (constant) velocity
Friction and drag resist relative motion
| Resistive force | Where it acts | Direction | Required model |
|---|---|---|---|
| Friction | between touching surfaces | opposes relative sliding or the tendency to slide | qualitative only |
| Viscous/drag force, including air resistance | on an object moving relative to a fluid | opposite to the relative velocity | zero with no relative motion; increases as speed increases |
A changing drag force makes the resultant force change, so acceleration need not be constant. For example, as a falling object speeds up, upward air resistance increases while weight remains downward.
Do not assume every resistive force has a fixed size, and do not introduce coefficient formulae here: this syllabus requires qualitative friction and only the simple drag-increases-with-speed model.
Air resistance makes acceleration change during a fall
For an object released from rest, weight acts downward and air resistance is initially zero. The downward resultant gives acceleration g at the instant of release.
As downward speed increases, upward air resistance increases. Weight stays constant, so the downward resultant decreases; therefore downward acceleration decreases even while velocity continues to increase.
For an object moving upward, both weight and air resistance act downward. As the object slows, air resistance decreases; at the highest point its speed and air resistance are momentarily zero, but weight and downward acceleration remain.
Air resistance changes the resultant force; it does not switch gravity off. Constant-g equations without drag do not describe the whole motion in air.
Terminal velocity occurs when the resultant force becomes zero
Terminal velocity is a constant, usually non-zero velocity reached when resistive forces balance the other forces, so resultant force and acceleration are zero.
For an object falling through air: it first accelerates downward; increasing speed produces increasing upward drag; the downward resultant and acceleration decrease; when drag equals weight, velocity becomes constant.
In a liquid, upthrust may also act upward. At terminal velocity the complete force balance is weight = drag + upthrust, not necessarily weight = drag alone.
Terminal velocity is not zero velocity and does not mean forces disappear. Its value depends on the object and fluid conditions, so different objects need not share the same terminal speed.