FRICTION

Friction — Complete Lesson (Edwin Ogie Library)

Static & kinetic friction, coefficient of limiting friction, viscosity & terminal velocity, Stoke's law — worked examples, calculators, and CBT quiz.

Introduction & Objectives

Learning objectives

1. Differentiate between static and dynamic (kinetic) friction.
2. Determine the coefficient of limiting friction experimentally and by calculation.
3. Compare the advantages and disadvantages of friction.
4. Suggest practical ways to reduce friction in machines and everyday life.
5. Analyze factors affecting viscosity and terminal velocity.
6. Apply Stoke's law to calculate drag and terminal velocity for small spheres in viscous fluids.

Friction is the resistive force that acts between surfaces in contact and opposes relative motion (or the tendency to move). It is essential to many everyday activities (walking, driving) and engineering applications, but also causes energy losses and wear.

Key idea: Friction depends on the nature of surfaces and the normal force — not directly on contact area for rigid bodies in common cases.

1. Static vs Kinetic (Dynamic) Friction — Explanation & Worked Example

Static friction acts on objects at rest. It adjusts to match the applied tangential force up to a maximum value called the limiting (maximum static) friction F_max. When the applied force exceeds F_max, motion begins.

Kinetic (dynamic) friction acts on objects already in motion. Its magnitude is usually slightly less than the maximum static friction.

Worked example — Identifying static vs kinetic friction

Scenario: A 10.0 kg box sits on a horizontal floor. You push gently; nothing moves until your push reaches 35 N, after which the box slides and steady motion occurs with a constant friction force of 30 N.

Analysis:

1. Before motion: static friction balances your applied force up to F_max = 35 N.
2. Once moving: kinetic friction is 30 N (less than the limiting static friction).
3. Normal force N = mg = 10 × 9.81 = 98.1 N.
4. Coefficient of limiting friction μ_l = F_max / N = 35 / 98.1 ≈ 0.357.

Static friction prevented motion until 35 N. After motion, kinetic friction (30 N) opposes motion. Calculated μ_l ≈ 0.357 (dimensionless).

Practical note: In many real systems μ_k < μ_s. Lubrication or smoother surfaces reduce both values.

2. Coefficient of Limiting Friction — How to determine & Example

The coefficient of limiting friction μ_l is defined as:

μ_l = F_max / N

Where F_max is the maximum static frictional force measured just before motion starts, and N is the normal force (often equal to weight = mg on a horizontal surface).

Experimental setup (simple)

1. Place a block on a horizontal surface and attach a spring balance horizontally.
2. Gradually pull with the balance until the block just begins to move — record the balance reading F_max.
3. Measure the mass m of the block, compute N = mg, then μ = F_max/N.

Calculator — find μ

Mass (kg) Measured F_max (N) g (m/s²)

Worked calculation

Mass = 5.00 kg, F_max = 30.0 N, g = 9.81 m/s² → N = 49.05 N → μ = 30 / 49.05 = 0.611.

Compute N = mg = 5 × 9.81 = 49.05 N. μ = 30 / 49.05 ≈ 0.611.

3. Advantages and Disadvantages of Friction; Ways to Reduce It

Advantages

• Traction for walking, driving and braking — without friction we would slip.
• Enables simple machines like belts and pulleys to transmit force.
• Helps fasten bolts and screws (prevents loosening).
• Allows control — e.g., using brakes on vehicles.

Disadvantages

• Energy loss as heat in engines and machines (efficiency loss).
• Wear and tear of components — requires maintenance.
• Heat generation can lead to failure in sensitive parts.
• Requires additional power to overcome in moving systems.

Practical methods to reduce friction

1. Lubrication: Oils and greases form films separating surfaces and reduce direct contact.
2. Bearings: Use rollers or ball bearings to convert sliding into rolling friction (much lower).
3. Surface finish: Polishing and smoother surfaces reduce asperity contact.
4. Streamlining: For fluids, shape objects to reduce drag (aircraft, cars).
5. Material selection: Use materials with low μ for sliding applications (e.g., PTFE/Teflon).

4. Viscosity and Terminal Velocity — Explanation & Worked Example

Viscosity is a fluid property that measures internal resistance to flow. High-viscosity fluids (honey) flow slowly; low-viscosity fluids (water) flow easily. Viscosity depends on temperature (usually decreases as temperature increases for liquids) and molecular interactions.

Factors affecting viscosity: temperature, molecular size/shape, pressure (for gases), presence of solutes or suspended particles, and fluid composition.

Terminal velocity (qualitative)

A falling object reaches terminal velocity when the downward weight is balanced by upward drag (and buoyant) forces, so net acceleration becomes zero. For small spheres in viscous fluids, Stoke's law gives a good approximation for drag.

Interactive terminal velocity calculator (Stoke's-law regime)

Radius (m) Density of sphere (kg/m³) Density of fluid (kg/m³) Viscosity η (Pa·s) g (m/s²)

Worked example (Stoke's-law approximation)

Consider a small steel sphere r = 1.0 mm (0.001 m), ρ_s = 7800 kg/m³, in water (ρ_f = 1000 kg/m³), η = 0.001 Pa·s, g = 9.81 m/s².

Calculation: v = (2/9) (r² g (ρ_s - ρ_f) / η)

r² = 1e-6 m²; (ρ_s - ρ_f) = 6800 kg/m³; numerator = 1e-6 * 9.81 * 6800 ≈ 0.066708; divide by η = 0.001 → 66.708; multiply by 2/9 → v ≈ 14.8 m/s.

Note: Stoke's law applies when Reynolds number is very small (laminar flow around sphere). For a steel sphere in water at this size, the Reynolds number may be large and the formula overestimates v. Use Stoke's law only for small particles in very viscous fluids or very small sizes.

5. Stoke's Law — Derivation sketch & Practical Applications

Stoke's law for drag on a sphere in a viscous fluid (low Reynolds number) states: F_d = 6 π η r v, where η is dynamic viscosity, r radius, v relative velocity.

At terminal velocity for a falling sphere: weight - buoyancy - drag = 0 ⇒ (4/3) π r³ ρ_s g - (4/3) π r³ ρ_f g - 6 π η r v = 0. Solve for v to get:

v_t = (2/9) (r² g (ρ_s - ρ_f) / η)

Applications

• Estimating settling speeds of small particles in fluids (sedimentation).
• Design of centrifuges and particle separators (when in the appropriate regime).
• Cloud physics (fall of water droplets — though corrections often needed).

Reminder: Stoke's law is valid only for laminar (very low Re) flows — check Reynolds number for your case.

Key Terms & Definitions

Static friction

The frictional force that prevents motion up to a maximum value.

Kinetic friction

The friction experienced by moving surfaces; usually lower than static friction.

Coefficient of limiting friction (μ_l)

Ratio F_max/N at the point motion starts.

Viscosity

Internal resistance of a fluid to flow (Pa·s).

Terminal velocity

When net force = 0 and acceleration = 0 for a falling object.

Stoke's law

F_d = 6 π η r v for a sphere in viscous fluid (low Re).

6. Worked Examples (More practice)

Example: Block on an incline — find μ

A block of mass 2.0 kg rests on an incline. The block just begins to slip when the incline angle is 25°. Find the coefficient of limiting friction.

Solution outline: At impending motion down the plane, component of weight down plane W_‖ = mg sin θ. Normal N = mg cos θ. For slipping, limiting friction = mg sin θ. μ = F_max/N = (mg sin θ)/(mg cos θ) = tan θ. Therefore μ = tan 25° ≈ 0.466.

Compute μ = tan 25° ≈ 0.466 (dimensionless).

Example: Settling particle in viscous oil (Stoke's law)

Find approximate terminal speed of a small glass bead r = 0.0005 m (0.5 mm), ρ_s=2500 kg/m³ in oil (ρ_f=900 kg/m³) with η = 0.1 Pa·s. Use v = (2/9)(r² g Δρ / η).

r² = 2.5e-7; Δρ = 1600; numerator = 2.5e-7 * 9.81 * 1600 ≈ 0.3924e-1? (calculate below)

Compute: r² = 2.5×10⁻⁷; r² g Δρ = 2.5e-7 * 9.81 * 1600 = 0.3924; divide by η = 0.1 gives 3.924; multiply by 2/9 ≈ 0.2222 gives v ≈ 0.873 m/s (approx). Note: check arithmetic carefully; units m/s.

7. JAMB-style 30-question CBT Quiz on Friction

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