Notes Class 9 Science Exploration Chapter 7 Work, Energy and Simple Machines

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7.1 Introduction & Work Done by a Constant Force

In everyday life, we use the word “work” loosely — studying hard, lifting bags, or running. But in science, work (कार्य) has a very precise meaning!

🔬 Scientific Definition of Work

Work is done when a force applied on an object causes the object to move (displace) in the direction of the force. Both force AND displacement are needed!

W = F × s

Where: W = Work done (J) | F = Force applied (N) | s = Displacement in direction of force (m)

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Definition of 1 Joule

1 joule of work is done when a constant force of 1 newton displaces an object by 1 metre in the direction of the force.

1 J = 1 N × 1 m = 1 kg·m²·s⁻²

📊 Work ∝ Force AND Work ∝ Displacement

More Force → More Work

Lifting 3 wheat bags (3F) to same height = 3× the work of lifting 1 bag (F).

More Displacement → More Work

Lifting 1 bag 3 metres (3s) = 3× the work of lifting same bag 1 metre.

🚫 When is Work Done ZERO?

No force: F = 0 → W = 0 (trivially obvious)
No displacement: s = 0 → W = 0. Example: Pushing a rigid wall — no matter how hard you push, if the wall doesn’t move, W = 0!
Force ⊥ Displacement: When force and displacement are perpendicular (90°). Example: Carrying a bag while walking horizontally — the upward force you apply is perpendicular to horizontal motion → W = 0 by that force.

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Tricky Point!

You feel tired when pushing a wall even though W = 0 on the wall. That’s because your muscles internally contract/expand using up body energy. Scientific work on the wall = 0, but biological energy is used!

➕➖ Positive and Negative Work

Positive Work (+W)

Force and displacement are in the SAME direction. Example: Pushing a wheelchair forward — you apply force in direction of motion. W = positive.

Negative Work (−W)

Force and displacement are in OPPOSITE directions. Example: Goalkeeper stopping a ball — applies force backward while ball moves forward. W = negative.

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Solved Example

A goalkeeper’s hand moved back 15 cm while stopping a ball with 200 N force.

W = F × (−s) = 200 N × (−0.15 m) =−30 J(negative — force opposes displacement)

📈 Force-Displacement Graph

F(N)s(m)101Area = Work Done= 10 N × 1 m = 10 JWork = area under F-s graph

Work done = Area under Force-Displacement graph

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Exam Tip — Graph Questions

The area under a Force-Displacement graph always gives the work done. This applies even when force varies (not constant)!

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7.2 The Work-Energy Theorem

When you do work on an object, what happens? The object gains energy (ऊर्जा) — the capacity to do further work. A moving cricket ball hits the wickets. A flowerpot raised high can damage things below when dropped. Both gained energy from the work done on them.

Work-Energy Theorem:

Work done on an object = Change in its energy

W = ΔE

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Energy Definition

Energy is the capacity to do work. An object that can do work possesses energy. The SI unit of energy is thejoule (J)— same as work.

🎯 Energy Transfers in Action

Positive work done on object → it gains energy
Negative work done on object → it loses energy
Energy transferred from one object to another during collisions (e.g., carom striker → white coin → black coin)

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Meet the Scientist — James Prescott Joule

The SI unit of work and energy — thejoule (J)— is named after James Prescott Joule. He discovered the relationship between mechanical energy and thermal energy, showing they can convert from one to the other. This unified our understanding of energy!

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Energy Transfer Methods

Work is just ONE way to transfer energy. Energy can also transfer as: heat (conduction), radiation (sunlight reaching Earth), electric current, sound waves, and nuclear reactions.

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7.3 Forms of Energy

Energy doesn’t exist in just one form — it comes in many varieties and can convert from one to another!

Form of Energy	Definition	Example
Mechanical Energy	Due to motion or position of objects	Moving car, falling ball
Thermal (Heat) Energy	Makes things warm or hot	Boiling water, fire
Light Energy	Allows us to see	Sunlight, electric bulb
Sound Energy	Vibrations of air molecules	Bell ringing, music
Electrical Energy	Related to position/motion of charges	Electric current in wire
Chemical Energy	Stored in chemical bonds of fuels/food	Food, petrol, coal
Nuclear Energy	Stored in nuclei of atoms	Nuclear reactor, Sun

🔄 Energy Conversions

Electric Bulb

Electrical Energy → Light Energy + Thermal Energy

Ringing Bell

Mechanical Energy → Sound Energy

Food → Muscles

Chemical Energy → Mechanical Energy

Solar Panel

Light Energy → Electrical Energy

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Exam Tip — Energy Transformation Table

Questions on energy transformation are very common! Always name: input energy form → output energy form. For a truck moving uphill: Chemical (fuel) → Mechanical + Thermal (heat from engine).

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7.4 Mechanical Energy — Kinetic & Potential

🏃 7.4.1 Kinetic Energy (गतिज ऊर्जा)

The energy possessed by an object due to its motion is called kinetic energy (KE). Any moving object — a bicycle, a bullet, a flowing river — has kinetic energy.

Kinetic Energy Formula:

K = ½mv²

Where: m = mass (kg) | v = velocity (m/s)

SI Unit: joule (J)

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Key Facts About Kinetic Energy

• KE is always positive (v² is always positive)

• KE has no direction (it’s a scalar quantity)

• If velocity doubles → KE becomes4 times(since v² quadruples)

• An object at rest has KE = 0

Example: An Indian cricketer bowled at 154.8 km/h (≈ 43 m/s). Mass of ball = 0.2 kg. Find KE.

K = ½mv² = ½ × 0.2 × (43)²

K = ½ × 0.2 × 1849

✅ K = 184.9 J

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Important Relationship — Velocity Doubled!

If velocity doubles (v → 2v), new KE = ½m(2v)² = 4 × ½mv² =4 times original KE. Speed doubles → KE quadruples!

🏔️ 7.4.2 Potential Energy (स्थितिज ऊर्जा)

The energy stored in an object due to its position or deformation is called potential energy (PE).

Gravitational PE

A ball held at height h — it has stored energy due to its position above ground. When released, gravity converts it to KE.

Elastic PE

A stretched rubber band (gulel), a compressed spring, a bent bow — they store energy due to deformation.

📐 Gravitational Potential Energy Formula

U = mgh

Where: m = mass (kg) | g = 9.8 m/s² | h = height above ground (m)

SI Unit: joule (J)

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How is U = mgh derived?

To lift an object of mass m to height h slowly, we apply an upward force = mg (equal to weight). Work done = F × s = mg × h = mgh. By the work-energy theorem, this work appears as potential energy.

Example: A fielder threw a cricket ball (0.2 kg) 10 m high in the air (g = 10 m/s²). Find PE at the top.

U = mgh = 0.2 × 10 × 10

✅ U = 20 J

Ground (PE = 0)hBallPE = mghKE = 0PE decreasingKE increasingPE = 0KE = mgh (max)Total Mechanical Energy = mgh (CONSTANT throughout!)

Free fall: PE converts to KE, but total mechanical energy stays the same

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7.4.3 Conservation of Mechanical Energy

Mechanical Energy = Kinetic Energy + Potential Energy

E_mechanical = KE + PE = ½mv² + mgh = constant

(when no friction or external forces act)

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Law of Conservation of Mechanical Energy

The total mechanical energy of a system remains constant when only conservative forces (gravity) act on it. Energy is neither created nor destroyed — it only changes form!

🎢 Understanding Conservation — Free Fall

Position	Potential Energy	Kinetic Energy	Total (ME)
At top (height h)	mgh	0	mgh
Midway (height h/2)	mg(h/2)	mg(h/2)	mgh
At ground (height 0)	0	mgh	mgh

🎡 Pendulum — Conservation in Action

A simple pendulum is a perfect example! At the extreme positions (P and R), the bob has only PE and zero KE. At the bottom (Q), it has only KE and zero PE. The total energy remains the same throughout!

PQROnly PEKE = 0Only KEPE = 0Only PEKE = 0Total ME = constant at all points

Simple Pendulum — Conservation of Mechanical Energy

🎿 Velocity at Bottom of a Slide

Using Conservation of Energy: A child slides down a slide of height h.

At top: PE = mgh, KE = 0 | At bottom: PE = 0, KE = ½mv²

Since ME is conserved: mgh = ½mv²

Solving: v = √(2gh)

✅ v = √(2gh) — velocity depends ONLY on height, not mass or shape of slide!

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Real World — Friction Losses

In real life, friction converts some mechanical energy into heat. So the pendulum slows down and stops eventually. Conservation of mechanical energy is an ideal case — it holds perfectly only when there’s NO friction.

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Indian Heritage — Gharat / Panchakki (Water Mill)

In the Himalayan region, traditional water mills (gharats or panchakkis) use the potential energy of water flowing downhill. Water’s PE → KE → rotational energy of wheel → grinds grain. In modern times, this principle powers hydroelectric dams that generate electricity for millions of Indian homes!

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7.5 Power (शक्ति)

Running up a flight of stairs and walking up slowly — you do the same work in both cases. But they feel very different! That difference is described by power (शक्ति).

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Definition of Power

Power is therate at which work is done.

More power = More work done in the same time, OR same work done in less time.

P = W / t

Where: P = Power (W) | W = Work done (J) | t = Time taken (s)

SI Unit: watt (W) | 1 W = 1 J/s

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Meet the Scientist — James Watt

The unit of power —watt (W)— is named after James Watt, who invented an efficient steam engine that could generate rotational motion. In early days, engine powers were compared to actual horses — hence “horsepower” (hp).1 hp = 746 W.

1 Watt

1 joule of work done per second. A small LED bulb uses about 5–10 W.

1 Horsepower (hp)

746 W. Used for car engines, water pumps. Your car engine may be 80–100 hp!

🧮 Solved Examples

Example 1: A weightlifter lifts 75 kg by 2 m in 5 seconds. Find power (g = 10 m/s²).

Work done = mgh = 75 × 10 × 2 = 1500 J

Power = W/t = 1500 / 5

✅ Power = 300 W

Example 2: A 1000 kg car accelerates from rest to 72 km/h (= 20 m/s) in 10 s. Find engine power.

Work done = ΔKE = ½mv² − 0 = ½ × 1000 × (20)² = 200,000 J

Power = W/t = 200,000 / 10

✅ Power = 20,000 W = 20 kW

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Exam Tip — Power vs Work vs Time

Same work, double the time → HALF the power. Same work, half the time → DOUBLE the power. Power and time are inversely related for the same amount of work!

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7.6 Simple Machines — Pulley, Inclined Plane & Lever

Simple machines help us do work more easily — they can change the magnitude or direction of the force needed, but they do NOT reduce the total work done!

Effort (प्रयास)

The force WE apply to the machine.

Load (भार)

The force that needs to be overcome (usually weight of object to be moved).

Mechanical Advantage (MA) = Load / Effort

MA > 1 → Machine amplifies force (less effort needed)

MA = 1 → No force amplification (only direction change)

🎡 7.6.1 Pulley (घिरनी)

A pulley is a wheel with a groove that guides a rope. It changes the direction or magnitude of the applied force.

Fixed Pulley

Changes DIRECTION of force only (pull down to lift up). MA = 1. Used in flag hoisting, wells.

Movable Pulley / System

Can give MA > 1 — reduces effort needed to lift heavy loads. Used in cranes, elevators.

Fixed Pulley (MA=1)Load↓ EffortDirection changes only

Pulley System (MA>1) Load → Effort Smaller effort, larger load

Fixed pulley changes direction. Pulley system gives mechanical advantage > 1

📐 7.6.2 Inclined Plane (आनत तल)

An inclined plane is a ramp that lets you raise a heavy load to a height using LESS force — but over a LONGER distance.

MA of Inclined Plane = L / h

Where: L = Length of inclined plane | h = Height

Since L > h → MA > 1 (always helps!)

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Key Principle

Work done remains the same! If force decreases (less steep ramp), displacement increases (longer path). Force × Distance = constant = mgh. This is why winding roads on hills are easier than going straight up!

Example: An inclined ramp raises an object over a 30 cm step. Width of ramp = 40 cm. Find MA.

Length of ramp (Pythagoras): L = √(30² + 40²) = √(900+1600) = √2500 = 50 cm

MA = L/h = 50/30

✅ Mechanical Advantage = 1.67

🔩 7.6.3 Lever (उत्तोलक)

A lever is a rigid bar that can rotate about a fixed point called the fulcrum (आधार बिंदु). Levers let you lift heavy loads with a small effort by trading force for distance.

Parts of a Lever

• Fulcrum — fixed pivot point

• Load — force to be overcome

• Effort — force applied

• Effort arm — distance from effort to fulcrum

• Load arm — distance from load to fulcrum

Principle of Lever

Effort × Effort Arm = Load × Load Arm

F₁ × d₁ = F₂ × d₂

MA = Effort Arm / Load Arm

Lever Principle: effort × effort arm = load × load arm

MA of Lever = Load/Effort = Effort Arm / Load Arm

📋 Three Classes of Levers

Class	Arrangement	Examples	MA
Class I	Fulcrum BETWEEN load and effort	Scissors, crowbar, seesaw, pliers, balance scale	Can be >1, =1, or <1
Class II	Load BETWEEN fulcrum and effort	Lemon squeezer, wheelbarrow, bottle opener	Always > 1
Class III	Effort BETWEEN fulcrum and load	Tweezers, broom, hammer, oar, tongs	Always < 1 (speed/distance advantage)

Seesaw Example: AC = EC = 2 m, BC = DC = 1 m. Child of 15 kg sits at A. Where should 30 kg child sit?

Using lever principle: 15 × 2 = 30 × L

30L = 30 → L = 1 m

✅ The 30 kg child should sit at D (1 m from fulcrum C)

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Important — Machines Don’t Create Energy!

A machine reduces the force needed but increases the distance. Total work done = same. Machines cannot create energy — they only help us use it more conveniently. This is why perpetual motion machines are impossible!

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Fun Fact — Archimedes Said It Best!

The ancient Greek mathematician Archimedes reportedly said: “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” Using a very long effort arm, any load could theoretically be moved with a tiny effort — though you’d have to push for an unimaginably large distance!

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Quick Revision Summary

Work (W = F×s)

Done when force displaces object in direction of force. Unit = joule (J). Can be +ve, −ve, or zero.

Work-Energy Theorem

W = ΔE. Work done = change in energy. SI unit of energy = joule (J).

Kinetic Energy

K = ½mv². Due to motion. If v doubles → KE × 4. Always positive.

Potential Energy

U = mgh. Due to position/deformation. Gravitational PE stored when raised to height h.

Conservation of ME

KE + PE = constant (no friction). PE converts to KE in free fall. ME = mgh throughout.

Power (P = W/t)

Rate of doing work. SI unit = watt (W). 1 W = 1 J/s. 1 hp = 746 W.

MA = Load/Effort

Pulley: MA=1 (fixed). Inclined plane: MA=L/h. Lever: MA = effort arm / load arm.

3 Lever Classes

Class I: fulcrum between (scissors). Class II: load between (wheelbarrow). Class III: effort between (tweezers).

Key Formulas

W=Fs | K=½mv² | U=mgh | P=W/t | MA=L/h | F₁d₁=F₂d₂ | v=√(2gh) at bottom of slide

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Important Exam Questions with Answers

Q1. Define work. When is work done said to be zero? Give two examples. (CBSE / 3 Marks)

Work is done when a constant force applied on an object causes a displacement in the direction of the force. W = F × s. Work is zero when: (i) displacement is zero — e.g., pushing a rigid wall, (ii) force and displacement are perpendicular — e.g., carrying a box while walking (upward force, horizontal displacement).

Q2. Derive the expression for kinetic energy of an object of mass m moving with velocity v. (CBSE / 3 Marks)

Starting from kinematics: v² = u² + 2as → s = (v²−u²)/2a. Work done W = F×s = ma × (v²−u²)/2a = ½m(v²−u²). If initial velocity u=0, W = ½mv². By work-energy theorem, this work equals kinetic energy: K = ½mv².

Q3. State the law of conservation of mechanical energy and verify it for a freely falling body. (CBSE / 5 Marks)

The total mechanical energy (KE + PE) of a system remains constant if only conservative forces act on it. For a freely falling body of mass m dropped from height h: At top: PE = mgh, KE = 0, ME = mgh. At midpoint h/2: PE = mgh/2, v² = 2g(h/2) = gh → KE = ½mv² = mgh/2, ME = mgh. At ground: PE = 0, v² = 2gh → KE = mgh, ME = mgh. Total ME = mgh at all points. Hence verified.

Q4. A ball of mass 0.5 kg is thrown upward with velocity 20 m/s. Calculate its (i) KE at the point of throw, (ii) maximum height reached (g = 10 m/s²). (CBSE / 3 Marks)

(i) KE = ½mv² = ½ × 0.5 × (20)² = ½ × 0.5 × 400 = 100 J. (ii) At max height, all KE converts to PE: mgh = 100 J → h = 100/(0.5 × 10) = 20 m.

Q5. Explain with an example the three classes of levers. (CBSE / 3 Marks)

Class I Lever: Fulcrum between load and effort. Example: Scissors — the pivot (fulcrum) is at the center, hands apply effort, blades exert force on the load (paper). Class II Lever: Load between fulcrum and effort. Example: Wheelbarrow — the wheel is the fulcrum, the load sits in the middle, and hands at the handles apply effort. Class III Lever: Effort between fulcrum and load. Example: Tweezers — the closed end is the fulcrum, fingers apply effort at the middle, and the tip grips the load.

Notes Class 9 Science Exploration Chapter 7 Work, Energy and Simple Machines

Amresh Academy

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