Non-uniform motion

General physics

Learning Objectives:

Qualitatively describe frictional and viscous resistive forces, including air resistance.
Explain motion of objects in a uniform gravitational field with air resistance.
Understand how objects reach a terminal (constant) velocity when moving against a resistive force.

Language Objectives:

Use key verbs: describe, explain, qualitatively understand.
Accurately define and spell terms: resistive force, terminal velocity, air resistance.
Write explanations using conditional clauses (e.g., “If drag equals weight…”).

Key Terms:

Term (ENG)	Russian	Kazakh
Frictional force	сила трения	жуылу күші
Viscous force	вязкая сила	гидродинамикалық кедергі
Air resistance	сопротивление воздуха	ауаның кедергісі
Terminal velocity	конечная скорость	шекті жылдамдық
Resistive force	сопротивляющая сила	кедергі күші

Flashcards:

Glossary:

Frictional force: force that opposes relative motion between surfaces in contact.
Translation
Kazakh: беттер арасындағы қозғалысқа қарсы тұратын күш.
Viscous force: resistive force experienced by an object moving through a fluid due to its viscosity.
Translation
Kazakh: сұйықтықтағы қозғалыс кезінде тұтқырлық салдарынан пайда болатын кедергі күші.
Terminal velocity: constant speed reached when resistive force equals weight.
Translation
Kazakh: кедергі күші салмаққа теңескенде жетілетін тұрақты жылдамдық.

Theory: Non-uniform Motion & Resistive Forces

When an object moves through a medium, it experiences a drag or frictional force that opposes its motion. In a uniform gravitational field with acceleration due to gravity g = 9.81 m/s², the weight is W = m g.

At low speeds, resistive (viscous) force F_d ∝ v; at higher speeds, F_d ∝ v². As speed increases, drag grows until F_d = m g, so net force is zero and the object falls at terminal velocity.

Check Your Understanding:

Easy: Give an example of an object reaching a constant speed in free fall.
Medium: A 0.5 kg ball falls at 5 m/s when drag ≈ 10 N. What is the drag coefficient k if F_d = k v²?
Medium: Explain why skydivers spread their limbs to slow their descent.
Hard: Two objects of equal mass fall through air. One has twice the cross-sectional area. Compare their terminal velocities and justify.

Illustrative Images:

Memorization Exercise:

Watch a Video:

Introduction to Friction & Drag:

https://www.youtube.com/watch?v=Z1NYCfOh2a4

Worked Examples:

Example 1: QualitativeSolution

Problem: Explain why a falling object stops accelerating after some time.

Answer

The drag force increases with speed until it equals weight, so net force → 0 and acceleration → 0.
Kazakh: Жылдамдық артқан сайын тарту күші массаның салмағына теңескенде таза күш 0-ге теңеседі, сондықтан үдеу 0-ге теңеседі.

Example 2: QuantitativeSolution

Problem: A 2 kg skydiver at 50 m/s experiences drag ≈ 600 N. Find k if F_d = k v².

Answer

k = F_d/v² = 600 N / (50 m/s)² = 0.24 N·s²/m².
Kazakh: k = 600 Н / (50 м/с)² = 0.24 Н·с²/м².

Investigation Task:

Explore resistive forces with PhET:

Answer

Observe how changing mass and drag coefficient sliders affects terminal velocity.
Kazakh: Массаны және тарту коэффициентін өзгерткенде шекті жылдамдық қалай өзгеретінін бақылаңыз.

Collaborative Activity:

Join this Quizizz game on drag forces:

https://quizizz.com/join/quiz/617e9b80e0f50c001bcbd8d6

Answer

1) Drag opposes motion;
2) Drag ∝ v at low speed, ∝ v² at high speed;
3) Terminal velocity when mg = F_d.
Kazakh: 1) Тарту қозғалысқа қарсы әсер етеді;
2) Тарту аз жылдамдықта v-ге, жоғары жылдамдықта v²-ге пропорционал;
3) mg = F_d болғанда шекті жылдамдық.

Individual Assignment:

Solve these structured questions (analysis & synthesis):

Derive qualitatively why drag ∝ v at low speeds but ∝ v² at high speeds.
Compare terminal velocities of two spheres of equal mass but different radii.
Design an experiment to measure terminal velocity using household materials.
Explain how air density affects terminal velocity with calculations.
Critique a real-world example (e.g., parachute deployment) in terms of non-uniform motion.

Answer

(Your detailed solutions here.)
Kazakh: (Мұнда талдауларыңыз бен шешімдеріңізді енгізіңіз.)

Further Resources:

Reflection:

In your journal, answer:

Which concept was most intuitive, and why?
What remains challenging?
Where have you observed resistive forces in daily life?