CIE AS/A Level Physics Unit : 3.2 Non-uniform motion Study Notes - 2025-2027 Syllabus
CIE AS/A Level Physics Unit : 3.2 Non-uniform motion Study Notes
CIE AS/A Level Physics Unit : 3.2 Non-uniform motion Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics Study Notes syllabus with Candidates should be able to:
- 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)
- describe and explain qualitatively the motion of objects in a uniform gravitational field with air resistance
- understand that objects moving against a resistive force may reach a terminal (constant) velocity
Frictional Forces and Viscous (Drag) Forces
Frictional and drag (viscous) forces are resistive forces that oppose the relative motion of surfaces or objects through a fluid. They always act in the direction opposite to motion and convert some mechanical energy into thermal energy.
1. Frictional Forces (Solid–Solid Contact)
Nature of Friction:
Friction is a resistive force that arises when two solid surfaces are in contact and there is an attempt to move one relative to the other. It acts parallel to the surfaces and opposes motion.
- Static friction: The frictional force that prevents motion between two surfaces at rest. It increases with applied force up to a maximum value.
- Kinetic (sliding) friction: The frictional force that acts when two surfaces slide past each other. It is usually smaller than the maximum static friction.
Key Characteristics:
- Friction acts opposite to the direction of motion or attempted motion.
- It depends on the nature of the surfaces in contact and the normal reaction between them.
- It converts mechanical energy into heat, reducing the efficiency of systems.
- No detailed formula or coefficient is required for this level — a qualitative understanding suffices.
Example
A block pushed along a rough horizontal surface slows down even after the pushing force is removed. Explain this observation in terms of frictional forces.
▶️ Answer / Explanation
The rough surface exerts a frictional force opposite to the motion of the block. Once the external push is removed, this frictional force is unbalanced and causes a deceleration, bringing the block to rest. The mechanical energy of motion is transformed into heat due to friction.
2. Viscous or Drag Forces (Fluid Resistance)
Nature of Drag Forces:
When an object moves through a fluid (liquid or gas), it experiences a resistive force called drag or viscous force. This force acts in the direction opposite to the object’s velocity.
Key Characteristics:
- Drag arises due to friction between the object’s surface and the surrounding fluid layers.
- It depends on the speed, shape, and surface area of the moving object, and the fluid’s properties (density and viscosity).
- At low speeds, drag is small and increases roughly in proportion to speed.
- At higher speeds, drag increases rapidly — approximately as the square of the speed.
- Air resistance is a common example of drag in gases.
Qualitative Model of Drag Force vs. Speed:
- At low speeds: \( \mathrm{F_{drag} \propto v} \)
- At high speeds: \( \mathrm{F_{drag} \propto v^2} \)
This means drag increases as speed increases — the faster an object moves, the stronger the resistive force becomes.
Example
A ball is dropped from a height. Initially, it accelerates rapidly, but after some time it falls at a constant velocity. Explain this behaviour in terms of drag and weight.
▶️ Answer / Explanation
At the start, the ball’s speed is low and air resistance is small, so its weight \( \mathrm{(mg)} \) produces a net downward acceleration. As the ball speeds up, air resistance increases until it equals the weight. At this point, the resultant force becomes zero, and the ball falls with a constant terminal velocity.
3. Combined Effects of Friction and Drag
- Both friction and drag oppose motion and dissipate mechanical energy as heat.
- Friction acts between solid surfaces; drag acts on objects moving through fluids (air or liquid).
- Friction is nearly constant for a given surface; drag depends strongly on speed.
- Reducing friction and drag improves efficiency — e.g. lubrication, streamlining vehicle shapes, using smooth surfaces.
Summary Table:
| Type of Force | Acts Between | Direction | Dependence | Effect |
|---|---|---|---|---|
| Frictional Force | Solid–solid contact | Opposite to motion or attempted motion | Surface texture and normal force | Resists motion; converts work into heat |
| Viscous / Drag Force | Object–fluid interaction | Opposite to velocity direction | Increases with speed (∝ \( \mathrm{v} \) or \( \mathrm{v^2} \)) | Resists motion; can lead to terminal velocity |
Key Takeaways:
- Friction and drag are both resistive forces that oppose motion.
- Friction occurs between solids, while drag acts in fluids.
- Drag increases with speed; friction is relatively independent of speed.
- Both forces dissipate mechanical energy as heat and limit motion efficiency.
Example
A car travels along a straight, level road at a constant speed. Identify the main resistive forces acting on the car and explain how these forces affect the car’s motion and energy use.
▶️ Answer / Explanation
The two main resistive forces acting on the car are:
- Frictional force — acts between the tyres and the road surface, opposing the car’s motion.
- Air resistance (drag) — acts on the body of the car due to its motion through air, increasing with speed.
To maintain constant speed, the engine must provide a forward driving force equal in magnitude to the total resistive forces. The work done by the engine is continuously converted into heat energy through friction and into kinetic energy of air particles due to drag. Streamlined car designs reduce drag, while tyre tread and lubrication help minimize friction.
Motion of Objects in a Uniform Gravitational Field with Air Resistance
A uniform gravitational field is one in which the acceleration due to gravity, \( \mathrm{g} \), is constant in magnitude and direction at all points. When objects move through such a field, they experience two main forces: the weight (downward) and the air resistance (upward, opposing motion).
Forces Acting on a Falling Object:
- Weight ( \( \mathrm{W = mg} \) ): Acts vertically downward and remains constant throughout the fall.
- Air resistance (drag): Acts upward, opposing motion, and increases with speed.
Qualitative Description of Motion:
The motion of an object falling in air can be divided into three stages:
- Initial stage (start of fall):
- Speed is very low → air resistance is negligible.
- Resultant force ≈ weight → large downward acceleration ≈ \( \mathrm{g} \).
- Intermediate stage:
- As the object speeds up, air resistance increases.
- The resultant force (and therefore acceleration) decreases.
- The object continues to gain speed, but more slowly.
- Final stage (steady motion):
- Air resistance grows until it equals the weight.
- Resultant force = 0 → acceleration = 0.
- The object falls with constant speed — called terminal velocity.
Velocity–Time Graph for a Falling Object with Air Resistance:
- Initially, the graph is steep (high acceleration).
- The slope gradually decreases as drag increases.
- The curve eventually levels off when terminal velocity is reached.
The terminal velocity corresponds to the horizontal part of the graph, where velocity remains constant.
Energy Consideration:
- As the object falls, gravitational potential energy decreases.
- This energy is converted into kinetic energy and heat (due to air resistance).
- At terminal velocity, all gravitational energy lost per second is converted into heat energy in the air — kinetic energy no longer increases.
Example
A small steel ball and a feather are dropped simultaneously from the same height in air. Explain why they reach the ground at different times.
▶️ Answer / Explanation
The feather experiences a much larger air resistance relative to its weight, so its acceleration decreases rapidly and it reaches a much lower terminal velocity. The steel ball has a much greater weight and smaller relative air resistance, so it continues accelerating longer and falls faster. Hence, they reach the ground at different times.
Terminal (Constant) Velocity
Terminal velocity is the constant speed reached by an object moving through a fluid (such as air or water) when the resistive forces acting on it exactly balance the driving force (usually weight).
At terminal velocity:
\( \mathrm{Resultant\ Force = 0 \ \Rightarrow \ Acceleration = 0.} \)
Conditions for Terminal Velocity:
- The object moves through a fluid or gas that exerts drag (air resistance or viscous force).
- The drag force increases with speed.
- Eventually, the drag becomes equal in magnitude and opposite to the driving force (e.g., weight).
- No further acceleration occurs; the object continues at constant speed — the terminal velocity.
Forces Acting at Terminal Velocity:
| Force | Symbol | Direction | At Terminal Velocity |
|---|---|---|---|
| Weight | \( \mathrm{W = mg} \) | Downward | Balanced by drag |
| Air resistance / Drag | \( \mathrm{F_d} \) | Upward | \( \mathrm{F_d = W} \) |
Key Features of Terminal Velocity:
- Occurs when the object’s acceleration becomes zero.
- Velocity remains constant (no further increase).
- Depends on the shape, surface area, density, and mass of the object, as well as the density and viscosity of the fluid.
- Streamlined shapes have higher terminal velocities because they experience less drag.
Application Examples:
- A skydiver accelerating and then reaching constant speed during free fall.
- Rain droplets falling at steady speed through the atmosphere.
- An air bubble rising at constant speed in water.
Motion with Air Resistance and Terminal Velocity:
| Stage | Forces | Resultant Force | Acceleration | Velocity |
|---|---|---|---|---|
| Start of motion | Weight > air resistance | Downward | Maximum (≈ \( \mathrm{g} \)) | Increasing |
| During motion | Weight > air resistance (increasing) | Decreasing | Decreasing | Still increasing |
| Terminal velocity | Weight = air resistance | Zero | Zero | Constant |
Key Takeaways:
- Air resistance increases with speed and eventually balances the weight of a falling object.
- When the forces balance, the object stops accelerating — terminal velocity is reached.
- Heavier or more streamlined objects reach higher terminal velocities.
Example
Describe the motion of a skydiver from the moment they jump from a plane until they reach terminal velocity.
▶️ Answer / Explanation
At the start of the fall, air resistance is small, and the skydiver accelerates downwards under gravity. As speed increases, air resistance grows, reducing the resultant force and acceleration. Eventually, air resistance equals the weight of the skydiver, so the resultant force becomes zero and acceleration stops. The skydiver then continues to fall at a constant terminal velocity.