Force, Motion and Energy

Overview

Force, Motion and Energy form the backbone of classical mechanics and are among the most frequently tested physics concepts in JTET Paper II. This topic connects everyday observations—pushing a cart, a ball rolling downhill, a swinging pendulum—to fundamental scientific principles. Understanding these concepts helps teachers explain physical phenomena to upper-primary students through relatable examples.

For JTET, you must master Newton's three laws, definitions of work and energy, and their mathematical relationships. Expect questions that test conceptual clarity (identifying balanced vs unbalanced forces), numerical problem-solving (calculating work done or kinetic energy), and real-life applications (friction in daily life, energy transformations). This topic also links to later concepts like simple machines and electricity.

The key to scoring well is building a clear mental model: force causes change in motion, work transfers energy, and energy is conserved but transforms between forms. Once this framework is solid, both conceptual and numerical questions become straightforward.

---

Key Concepts

• **Force** is a push or pull that can change an object's state of rest or uniform motion. It is a vector quantity with both magnitude and direction. SI unit: Newton (N).

• **Balanced forces** produce no change in motion (object at rest stays at rest, moving object continues at same speed). **Unbalanced forces** cause acceleration—change in speed or direction.

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

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

• **Newton's Second Law**: Force equals mass times acceleration (F = ma). This quantifies how much force is needed to produce a given acceleration.

• **Newton's Third Law**: For every action, there is an equal and opposite reaction. The two forces act on different bodies.

• **Work** is done when a force causes displacement in its direction. Work = Force × Displacement × cos θ. SI unit: Joule (J). No displacement means no work done.

• **Energy** is the capacity to do work. It exists in many forms—kinetic, potential, heat, light, sound, chemical, electrical. Energy can be transformed but neither created nor destroyed (Law of Conservation of Energy).

---

Formulas / Key Facts

| Concept | Formula | Notes | |---------|---------|-------| | Force | F = m × a | m in kg, a in m/s², F in Newton | | Weight | W = m × g | g ≈ 10 m/s² (or 9.8 m/s²) | | Work | W = F × s × cos θ | θ = angle between force and displacement | | Work (simple) | W = F × s | When force and displacement are in same direction | | Kinetic Energy | KE = ½ × m × v² | Energy of a moving body | | Potential Energy | PE = m × g × h | Energy due to height above ground | | Power | P = W / t | Rate of doing work; SI unit: Watt (W) | | Momentum | p = m × v | Product of mass and velocity |

**Must-Remember Facts:**

• 1 Newton = Force needed to accelerate 1 kg mass by 1 m/s²
• 1 Joule = Work done when 1 N force moves an object 1 m
• 1 Watt = 1 Joule per second
• Friction always opposes relative motion between surfaces
• Static friction > Sliding friction > Rolling friction
• Free fall acceleration (g) is same for all objects regardless of mass (ignoring air resistance)

---

Worked Examples

**Example 1: Calculating Force (Newton's Second Law)**

*A cart of mass 20 kg is pushed and accelerates at 3 m/s². Find the force applied.*

Solution:

• Given: m = 20 kg, a = 3 m/s²
• Formula: F = m × a
• F = 20 × 3 = 60 N

**Answer: 60 Newton**

---

**Example 2: Calculating Work Done**

*A boy pulls a box with a force of 50 N through a distance of 8 m in the direction of force. Calculate work done.*

Solution:

• Given: F = 50 N, s = 8 m, θ = 0° (same direction)
• Formula: W = F × s × cos θ = F × s (since cos 0° = 1)
• W = 50 × 8 = 400 J

**Answer: 400 Joules**

---

**Example 3: Kinetic Energy Calculation**

*A ball of mass 2 kg is moving with velocity 5 m/s. Find its kinetic energy.*

Solution:

• Given: m = 2 kg, v = 5 m/s
• Formula: KE = ½ × m × v²
• KE = ½ × 2 × 5² = ½ × 2 × 25 = 25 J

**Answer: 25 Joules**

---

**Example 4: Potential Energy and Energy Conservation**

*A stone of mass 0.5 kg is dropped from height 20 m. Find its potential energy at the top and velocity just before hitting ground. (Take g = 10 m/s²)*

Solution:

• PE at top = m × g × h = 0.5 × 10 × 20 = 100 J
• At bottom, all PE converts to KE (conservation of energy)
• KE = 100 J
• ½ × m × v² = 100
• ½ × 0.5 × v² = 100
• v² = 400
• v = 20 m/s

**Answer: PE = 100 J; Velocity = 20 m/s**

---

Common Mistakes

• **Confusing mass and weight** → Mass is amount of matter (kg), weight is gravitational force (N). Weight = m × g, not just m.

• **Thinking force is needed to maintain motion** → Newton's First Law says constant velocity needs no force. Force is needed only to change motion (accelerate/decelerate).

• **Forgetting that action-reaction forces act on different bodies** → When you push a wall, wall pushes you back. These forces don't cancel because they act on different objects.

• **Calculating work when force is perpendicular to displacement** → If a porter carries load on head and walks horizontally, work done against gravity is zero (force vertical, displacement horizontal, cos 90° = 0).

• **Doubling velocity doubles kinetic energy** → Wrong! KE depends on v². If velocity doubles, KE becomes 4 times (not 2 times).

• **Ignoring units in calculations** → Always convert to SI units before applying formulas. Mass in kg, distance in m, time in s.

---

Quick Reference

• **Newton's Laws**: 1st = Inertia, 2nd = F = ma, 3rd = Action-Reaction

• **Work done = Force × Displacement** (only when in same direction)

• **KE = ½mv²** — depends on square of velocity

• **PE = mgh** — depends on height above reference point

• **Energy cannot be created or destroyed**, only transformed

• **1 N = 1 kg·m/s²; 1 J = 1 N·m; 1 W = 1 J/s**

• **No displacement = No work done** (holding a heavy bag while standing still = zero work)