Force, Motion and Energy

Overview

Force, Motion and Energy form the backbone of classical mechanics and are essential topics for the JKTET Paper II Science section. These concepts explain how objects move, why they move, and how energy transforms during motion. Understanding Newton's laws is crucial—they appear directly in questions and underpin virtually every mechanics problem.

For the JKTET, expect questions testing conceptual clarity on force types, Newton's three laws, work-energy relationships, and simple numerical problems. The examiner often checks whether candidates can distinguish between related concepts (force vs pressure, work vs energy) and apply formulas to everyday situations. Mastering this topic also helps in teaching middle-school students, as these ideas connect to their daily experiences—pushing carts, riding bicycles, and throwing balls.

Focus on definitions, SI units, Newton's laws with examples, and the work-energy-power triangle. Numerical ability at the Class 8-10 level is expected.

Key Concepts

• **Force** is a push or pull that can change an object's state of rest or motion, its shape, or its direction. It is a vector quantity with both magnitude and direction.

• **Balanced forces** produce no change in motion (net force = 0), while **unbalanced forces** cause acceleration.

• **Inertia** is the tendency of an object to resist changes 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 force produces acceleration.

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

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

• **Energy** is the capacity to do work. It exists in various forms—kinetic, potential, heat, light, sound—and can transform from one form to another but cannot be created or destroyed (Law of Conservation of Energy).

• **Power** is the rate of doing work. A machine doing the same work in less time has greater power.

Formulas / Key Facts

| Quantity | Formula | SI Unit | |----------|---------|---------| | Force | F = m × a | Newton (N) = kg·m/s² | | Weight | W = m × g (g ≈ 10 m/s²) | Newton (N) | | Work | W = F × d × cos θ | Joule (J) = N·m | | Kinetic Energy | KE = ½ × m × v² | Joule (J) | | Potential Energy | PE = m × g × h | Joule (J) | | Power | P = W / t = F × v | Watt (W) = J/s | | Momentum | p = m × v | kg·m/s |

**Key Facts:**

• 1 kW = 1000 W; 1 HP (horsepower) ≈ 746 W
• When θ = 90° (force perpendicular to displacement), work done = 0
• Mechanical energy = KE + PE (conserved in absence of friction)
• Friction always opposes relative motion; it converts kinetic energy to heat
• Free fall: all objects fall at the same rate (g) in vacuum regardless of mass

Worked Examples

**Example 1: Newton's Second Law**

*A 5 kg object is pushed with a force of 20 N. Find its acceleration.*

Solution:

• Given: m = 5 kg, F = 20 N
• Using F = ma
• 20 = 5 × a
• a = 20/5 = **4 m/s²**

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**Example 2: Work Done**

*A porter carries a 20 kg load on his head and walks 50 m on a horizontal platform. How much work is done against gravity?*

Solution:

• Force due to gravity acts vertically downward
• Displacement is horizontal
• Angle between force and displacement = 90°
• Work = F × d × cos 90° = F × d × 0 = **0 Joules**

(Note: Work is done against gravity only when there is vertical displacement.)

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**Example 3: Kinetic Energy**

*A car of mass 1000 kg is moving at 20 m/s. Calculate its kinetic energy.*

Solution:

• KE = ½ × m × v²
• KE = ½ × 1000 × (20)²
• KE = ½ × 1000 × 400
• KE = **200,000 J or 200 kJ**

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**Example 4: Power**

*A machine does 5000 J of work in 10 seconds. Find its power.*

Solution:

• P = W / t
• P = 5000 / 10
• P = **500 W**

Common Mistakes

• **Confusing mass and weight** → Mass is the amount of matter (kg), weight is the gravitational force on that mass (N). Weight = mg, and it varies with location; mass does not.

• **Thinking force is needed for uniform motion** → Once moving at constant velocity, an object needs no net force (Newton's First Law). Force is needed only to change velocity.

• **Believing heavier objects fall faster** → In the absence of air resistance, all objects fall at the same acceleration (g). A feather falls slower only due to air resistance.

• **Calculating work when carrying a load horizontally** → Students often multiply weight by horizontal distance. Work against gravity requires vertical displacement. Carrying a bag while walking on flat ground does zero work against gravity.

• **Confusing action-reaction pairs** → Action and reaction act on different bodies, not the same body. A book on a table: weight of book (on table) and normal force (on book) are not action-reaction pairs—both act on the book.

• **Mixing up energy and power** → Energy is total work capacity; power is how fast that work is done. Two machines can do equal work but have different powers if their times differ.

Quick Reference

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

• **F = ma** — double the mass, half the acceleration for same force.

• **Newton's Third Law**: Action-reaction pairs are equal, opposite, and act on different bodies.

• **Work = Force × Displacement × cos θ**; zero work if force ⊥ displacement.

• **Energy is conserved**: KE + PE remains constant in ideal systems.

• **Power = Work / Time**; measured in Watts.