Force, Motion and Energy

Overview

Force, Motion and Energy form the foundational pillars of classical mechanics and are essential for CG TET Paper II. This topic carries significant weightage in the science section and tests your understanding of how objects move, what causes them to move, and how energy transforms during motion.

For the exam, you must understand Newton's three laws of motion, distinguish between different types of forces, and apply work-energy concepts to solve numerical problems. Questions typically involve direct application of formulas, conceptual understanding of laws, and real-life examples connecting physics to everyday phenomena.

Mastering this topic also helps in understanding related concepts like machines, gravitation, and sound. Focus on memorizing formulas, understanding their physical meaning, and practising numericals involving work, power, and energy calculations.

Key Concepts

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

• **Balanced forces** produce no change in motion (object remains at rest or moves uniformly); **unbalanced forces** cause acceleration or change in direction.

• **Inertia** is the natural tendency of an object to resist change in its state of motion. Mass is the measure of inertia—greater mass means greater inertia.

• **Momentum** (p = mv) is the quantity of motion possessed by a body. It depends on both mass and velocity.

• **Work** is done only when a force causes displacement in its own direction. No displacement means no work done, regardless of force applied.

• **Energy** is the capacity to do work. It can neither be created nor destroyed, only transformed from one form to another (Law of Conservation of Energy).

• **Power** measures how fast work is done. A powerful machine does the same work in less time.

• **Friction** opposes relative motion between surfaces. It can be useful (walking, writing) or harmful (wear and tear, energy loss).

Formulas / Key Facts

| Concept | Formula | Unit | |---------|---------|------| | Force | F = ma (mass × acceleration) | Newton (N) = kg·m/s² | | Momentum | p = mv (mass × velocity) | kg·m/s | | Impulse | J = F × t = change in momentum | N·s or kg·m/s | | Work | W = F × d × cos θ (force × displacement × cos of angle) | Joule (J) | | Kinetic Energy | KE = ½mv² | Joule (J) | | Potential Energy | PE = mgh (mass × gravity × height) | Joule (J) | | Power | P = W/t (work ÷ time) | Watt (W) = J/s | | Weight | W = mg (mass × gravitational acceleration) | Newton (N) |

**Newton's Laws of Motion:** 1. **First Law (Law of Inertia):** A body continues in its state of rest or uniform motion unless acted upon by an external unbalanced force. 2. **Second Law:** Force equals rate of change of momentum; F = ma. 3. **Third Law:** For every action, there is an equal and opposite reaction.

**Key constants:** g = 9.8 m/s² (approximately 10 m/s² for calculations)

Worked Examples

**Example 1: Calculating Force**

A car of mass 1000 kg accelerates at 2 m/s². Find the force applied.

Solution:

• Given: m = 1000 kg, a = 2 m/s²
• Formula: F = ma
• F = 1000 × 2 = 2000 N

The force applied is **2000 N**.

---

**Example 2: Work Done Calculation**

A boy pushes a box with a force of 50 N through a distance of 10 m in the direction of force. Calculate work done.

Solution:

• Given: F = 50 N, d = 10 m, θ = 0° (force and displacement in same direction)
• Formula: W = F × d × cos θ
• W = 50 × 10 × cos 0° = 50 × 10 × 1 = 500 J

Work done is **500 J**.

---

**Example 3: Kinetic Energy**

Calculate the kinetic energy of a ball of mass 0.5 kg moving with velocity 20 m/s.

Solution:

• Given: m = 0.5 kg, v = 20 m/s
• Formula: KE = ½mv²
• KE = ½ × 0.5 × (20)² = ½ × 0.5 × 400 = 100 J

Kinetic energy is **100 J**.

---

**Example 4: Power Calculation**

A machine does 5000 J of work in 25 seconds. Find its power.

Solution:

• Given: W = 5000 J, t = 25 s
• Formula: P = W/t
• P = 5000/25 = 200 W

Power of machine is **200 W**.

Common Mistakes

• **Confusing mass and weight** → Mass is amount of matter (kg), weight is gravitational force on mass (N). Weight = mg, mass remains constant everywhere.

• **Thinking force is needed to maintain motion** → Newton's First Law states that uniform motion continues without force. Force is needed only to change motion (accelerate, decelerate, or change direction).

• **Forgetting the angle factor in work** → When force and displacement are perpendicular (θ = 90°), cos 90° = 0, so work done is zero. A coolie carrying load on head and walking horizontally does no work against gravity.

• **Confusing KE formula** → Students write KE = mv² instead of ½mv². Always remember the factor of ½.

• **Mixing up Newton's Third Law pairs** → Action and reaction act on different bodies, not on the same body. They cannot cancel each other because they act on different objects.

• **Assuming friction is always harmful** → Friction enables walking, writing, braking vehicles. Without friction, we couldn't even stand still.

Quick Reference

• **1 Newton** = Force needed to accelerate 1 kg mass by 1 m/s²

• **Work = 0** when force is perpendicular to displacement or displacement is zero

• **KE doubles** when velocity increases by √2 times; KE quadruples when velocity doubles

• **Conservation of Energy:** Total mechanical energy (KE + PE) remains constant in absence of friction

• **Action-reaction pairs** act on different bodies simultaneously

• **1 kW = 1000 W; 1 HP (horsepower) = 746 W**