Force, Motion and Energy

Overview

Force, Motion and Energy form the backbone of classical mechanics and are heavily tested in Assam TET Paper II Science. This topic connects everyday phenomena—pushing a cart, falling mangoes, flowing rivers—to fundamental physical laws. Students must understand not just definitions but also the mathematical relationships and real-world applications.

For Assam TET, expect questions on Newton's three laws, types of forces (friction, gravitational, muscular), work-energy calculations, and conservation principles. The syllabus emphasises conceptual clarity alongside numerical problem-solving at the upper primary level (Classes VI–VIII). Mastering this topic also helps in understanding later concepts like machines, electricity and planetary motion.

Focus areas include: distinguishing between contact and non-contact forces, applying Newton's laws to practical situations, calculating work and energy, and understanding energy transformations in daily life contexts relevant to Assam (river transport, agricultural work, tea factory machinery).

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Key Concepts

• **Force** is a push or pull that can change an object's state of rest or motion, its speed, direction, or shape. SI unit: Newton (N).

• **Contact forces** require physical touch (friction, muscular, normal force), while **non-contact forces** act at a distance (gravitational, magnetic, electrostatic).

• **Inertia** is the tendency of an object to resist change in its state of motion; mass is the measure of inertia.

• **Newton's First Law (Law of Inertia)**: An object remains at rest or in uniform motion unless acted upon by an external unbalanced force.

• **Newton's Second Law**: Force equals mass times acceleration (F = ma). This quantifies how force affects motion.

• **Newton's Third Law**: For every action, there is an equal and opposite reaction. Forces always occur in pairs acting on different bodies.

• **Work** is done when a force causes displacement in its direction. Work = Force × Displacement × cos θ. SI unit: Joule (J).

• **Energy** is the capacity to do work. It exists in various forms—kinetic, potential, heat, light, chemical, electrical—and can be transformed but not created or destroyed (Law of Conservation of Energy).

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Formulas / Key Facts

| Quantity | Formula | Unit | Notes | |----------|---------|------|-------| | Force | F = m × a | Newton (N) | 1 N = 1 kg·m/s² | | Weight | W = m × g | Newton (N) | g ≈ 10 m/s² (approx.) | | Work | W = F × d × cos θ | Joule (J) | θ = angle between force and displacement | | Kinetic Energy | KE = ½ × m × v² | Joule (J) | Energy of moving objects | | Potential Energy | PE = m × g × h | Joule (J) | Energy due to height | | Power | P = W / t | Watt (W) | Rate of doing work; 1 W = 1 J/s |

**Key Facts:**

• 1 kJ = 1000 J; 1 kWh = 3.6 × 10⁶ J
• Friction opposes relative motion; it can be static (object at rest) or kinetic (object moving)
• Gravitational force on Earth: g = 9.8 m/s² (use 10 m/s² for quick calculations)
• Momentum (p) = mass × velocity; conserved in collisions
• Free fall: all objects fall at same rate in vacuum regardless of mass

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Worked Examples

### Example 1: Applying Newton's Second Law

**Problem:** A boat of mass 500 kg is pushed with a force of 2000 N. Calculate the acceleration.

**Solution:**

• Given: m = 500 kg, F = 2000 N
• Using F = m × a
• 2000 = 500 × a
• a = 2000 ÷ 500 = **4 m/s²**

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### Example 2: Calculating Work Done

**Problem:** A farmer pulls a plough with a force of 150 N over a distance of 20 m in the direction of the force. Calculate work done.

**Solution:**

• Given: F = 150 N, d = 20 m, θ = 0° (force along displacement)
• W = F × d × cos 0° = 150 × 20 × 1
• W = **3000 J or 3 kJ**

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### Example 3: Kinetic and Potential Energy

**Problem:** A stone of mass 2 kg is dropped from a height of 10 m. Find (a) its potential energy at the top, (b) its kinetic energy just before hitting the ground. (Take g = 10 m/s²)

**Solution:** (a) PE at top = m × g × h = 2 × 10 × 10 = **200 J**

(b) By conservation of energy, all PE converts to KE at bottom. KE at bottom = **200 J**

(Verification: v² = 2gh = 2 × 10 × 10 = 200; v = √200 ≈ 14.14 m/s KE = ½ × 2 × 200 = 200 J ✓)

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Common Mistakes

| Wrong Thinking | Correct Understanding | |----------------|----------------------| | "Heavy objects fall faster than light ones" | In absence of air resistance, all objects fall at the same rate. A feather falls slowly due to air resistance, not lesser gravity. | | "If an object is at rest, no forces act on it" | Forces may be acting but they are balanced (net force = zero). A book on a table has gravity and normal force balancing each other. | | "Action and reaction cancel out" | Action and reaction act on **different bodies**, so they don't cancel. When you push a wall, wall pushes you back—these forces are on different objects. | | "Work is done whenever force is applied" | Work requires displacement in the direction of force. Pushing a wall without moving it does zero work (d = 0). | | "Energy is consumed/destroyed when used" | Energy is transformed from one form to another, never destroyed. A bulb transforms electrical energy to light and heat. |

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Quick Reference

• **Force changes motion**; no net force means no change in velocity.

• **F = ma** — doubling force doubles acceleration; doubling mass halves acceleration.

• **Work = Force × Displacement** — no displacement means no work done.

• **KE depends on v²** — doubling speed quadruples kinetic energy.

• **Conservation of Energy** — total energy in an isolated system remains constant.

• **Newton's Third Law** — forces always come in equal and opposite pairs on different objects.