Know that friction (drag) acts on an object moving through a gas (e.g. air resistance)

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1.5.1 Effects of Forces

Learning Objective

Know that friction (drag) acts on an object moving through a gas (air resistance) – and also through a liquid – and understand the factors that influence its magnitude.

1. Solid (surface) friction

  • Definition: A resistive force that arises when two solid surfaces are in contact and move (or try to move) relative to each other.
  • Key features
    • Acts opposite to the direction of motion.
    • Magnitude is (approximately) independent of speed (kinetic friction).
    • Proportional to the normal reaction:
      Ff = μ N, where μ is the coefficient of friction and N is the normal force.
    • Produces heating of the contacting surfaces (e.g. a block sliding down a rough ramp becomes warm).

2. Drag (air or fluid resistance)

Drag is a type of friction that occurs when a solid object moves through a fluid – either a gas (air) or a liquid (water, oil). It always opposes the motion, but unlike surface friction it does not depend on a normal reaction.

2.1 Drag in a gas (air resistance)

Typical IGCSE examples: sky‑diver falling, paper parachute, falling ball.

2.2 Drag in a liquid (fluid resistance)

Typical IGCSE examples: swimmer moving through water, boat cruising on a lake, stone dropped into oil. Because liquids are much denser than air, the drag forces are considerably larger for the same speed and area.

3. Factors that Influence Drag (ordered as in the syllabus)

Factor (syllabus order) How it influences drag Typical IGCSE example
Speed of the object (v) At low speeds drag ≈ k v (linear). At higher speeds drag ≈ ½ Cd ρ A v² (quadratic). Drag therefore rises rapidly with speed. A sky‑diver accelerates until the upward drag equals his weight (terminal velocity).
Cross‑sectional area (A) Larger area presents more fluid to push aside, giving a larger drag force. A flat sheet of paper falls slower than a rolled‑up sheet of the same mass.
Shape (drag coefficient Cd) Streamlined shapes have low Cd → less drag; blunt shapes have high Cd → more drag. Airplane wings are shaped to minimise drag.
Density of the fluid (ρ) Denser fluids exert a larger drag for the same speed and area. Moving through water (ρ≈1000 kg m⁻³) feels much more resistance than moving through air (ρ≈1.2 kg m⁻³).
Viscosity of the fluid Viscosity is the internal “thickness” of a fluid; higher viscosity gives a greater frictional component of drag, especially at low speeds. A stone falls more slowly in honey than in water.

4. Mathematical Description of Drag (IGCSE level)

Two approximations are used in the syllabus, each appropriate for a different speed regime.

  1. Linear (low‑speed) approximation – when the speed is small, drag is roughly proportional to speed:

    $$F_{d}=k\,v$$

    k is a constant that depends on the object's shape, area and the fluid’s properties. This form is valid for very slow motion (e.g. a gently falling feather).

  2. Quadratic (high‑speed) approximation – for faster motion, drag varies with the square of the speed:

    $$F_{d}= \frac{1}{2}\,C_{d}\,\rho\,A\,v^{2}$$

    • Cd – drag coefficient (dimensionless, shape‑dependent)
    • ρ – density of the fluid (kg m⁻³)
    • A – cross‑sectional area perpendicular to the motion (m²)
    • v – speed of the object relative to the fluid (m s⁻¹)

    This form is used for objects such as sky‑divers, projectiles, or cars moving quickly through air.

5. Comparison of Drag with Surface Friction

Aspect Surface (solid) friction Drag (air or fluid resistance)
Medium Two solid surfaces in contact Solid object moving through a fluid (gas or liquid)
Direction Opposes relative motion of the surfaces Opposes the motion of the object through the fluid
Dependence on speed Largely independent of speed (kinetic friction) Strongly dependent on speed (linear at low v, quadratic at high v)
Dependence on normal reaction Proportional to normal force ( Ff=μN ) Does **not** depend on a normal reaction
Other influencing factors Nature of the two surfaces (roughness, material) Cross‑sectional area, shape (Cd), fluid density, viscosity
Typical observable effect Heating of the contact surfaces Energy loss from the moving object (slower fall, reduced range)

6. Practical Implications for IGCSE Experiments

  • When measuring the acceleration of a falling object, air resistance reduces the observed acceleration compared with the theoretical value g.
  • In a “paper parachute” experiment, increasing the parachute’s area or using a more porous material raises drag and therefore slows the descent.
  • Ballistic trajectory calculations that ignore drag over‑estimate the range; the real range is shorter because drag continuously removes kinetic energy.
  • In a water‑tank experiment (e.g., a toy car moving through water), the much larger fluid density and viscosity give a visibly larger drag force than in air.
Suggested diagram: a falling object with two arrows – weight mg downwards and drag force Fd upwards – the length of the drag arrow increasing with speed.

7. Summary Checklist (AO1‑AO3)

  • Drag always opposes the motion of an object through a fluid (gas or liquid).
  • Low‑speed drag ≈ k v; high‑speed drag ≈ ½ Cd ρ A v².
  • Key factors: speed, cross‑sectional area, shape (drag coefficient), fluid density, and viscosity.
  • Surface friction acts between solids, is largely speed‑independent, is proportional to the normal reaction (Ff=μN), and produces heating.
  • Be able to apply the drag equations to simple IGCSE problems (e.g., calculate terminal velocity, compare two objects, predict the effect of changing area or shape).

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