Chapter 7: Work, Energy & Simple Machines
Explore how forces do work, how energy transforms between different forms, and how simple machines make our daily tasks easier.
W = F × s
Kinetic Energy (KE)
Potential Energy (PE)
Power (शक्ति)
Conservation of Energy
Pulley · Lever · Inclined Plane
Mechanical Advantage
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!
Where: W = Work done (J) | F = Force applied (N) | s = Displacement in direction of force (m)
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
Lifting 3 wheat bags (3F) to same height = 3× the work of lifting 1 bag (F).
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.
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
Force and displacement are in the SAME direction. Example: Pushing a wheelchair forward — you apply force in direction of motion. W = positive.
Force and displacement are in OPPOSITE directions. Example: Goalkeeper stopping a ball — applies force backward while ball moves forward. W = negative.
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
Work done = Area under Force-Displacement graph
The area under a Force-Displacement graph always gives the work done. This applies even when force varies (not constant)!
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 done on an object = Change in its energy
W = ΔE
Energy is the capacity to do work. An object that can do work possesses energy. The SI unit of energy is the joule (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)
The SI unit of work and energy — the joule (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!
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.
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
Electrical Energy → Light Energy + Thermal Energy
Mechanical Energy → Sound Energy
Chemical Energy → Mechanical Energy
Light Energy → Electrical Energy
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).
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.
K = ½mv²
Where: m = mass (kg) | v = velocity (m/s)
SI Unit: joule (J)
• KE is always positive (v² is always positive)
• KE has no direction (it’s a scalar quantity)
• If velocity doubles → KE becomes 4 times (since v² quadruples)
• An object at rest has KE = 0
K = ½mv² = ½ × 0.2 × (43)²
K = ½ × 0.2 × 1849
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).
A ball held at height h — it has stored energy due to its position above ground. When released, gravity converts it to KE.
A stretched rubber band (gulel), a compressed spring, a bent bow — they store energy due to deformation.
📐 Gravitational Potential Energy Formula
Where: m = mass (kg) | g = 9.8 m/s² | h = height above ground (m)
SI Unit: joule (J)
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.
U = mgh = 0.2 × 10 × 10
Free fall: PE converts to KE, but total mechanical energy stays the same
7.4.3 Conservation of Mechanical Energy
Mechanical Energy = Kinetic Energy + Potential Energy
(when no friction or external forces act)
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!
Simple Pendulum — Conservation of Mechanical Energy
🎿 Velocity at Bottom of a Slide
At top: PE = mgh, KE = 0 | At bottom: PE = 0, KE = ½mv²
Since ME is conserved: mgh = ½mv²
Solving: v = √(2gh)
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.
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!
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).
Power is the rate at which work is done.
More power = More work done in the same time, OR same work done in less time.
Where: P = Power (W) | W = Work done (J) | t = Time taken (s)
SI Unit: watt (W) | 1 W = 1 J/s
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 joule of work done per second. A small LED bulb uses about 5–10 W.
746 W. Used for car engines, water pumps. Your car engine may be 80–100 hp!
🧮 Solved Examples
Work done = mgh = 75 × 10 × 2 = 1500 J
Power = W/t = 1500 / 5
Work done = ΔKE = ½mv² − 0 = ½ × 1000 × (20)² = 200,000 J
Power = W/t = 200,000 / 10
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!
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!
The force WE apply to the machine.
The force that needs to be overcome (usually weight of object to be moved).
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.
Changes DIRECTION of force only (pull down to lift up). MA = 1. Used in flag hoisting, wells.
Can give MA > 1 — reduces effort needed to lift heavy loads. Used in cranes, elevators.
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.
Where: L = Length of inclined plane | h = Height
Since L > h → MA > 1 (always helps!)
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!
Length of ramp (Pythagoras): L = √(30² + 40²) = √(900+1600) = √2500 = 50 cm
MA = L/h = 50/30
🔩 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.
• 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
Effort × Effort Arm = Load × Load Arm
F₁ × d₁ = F₂ × d₂
MA = Effort Arm / 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) |
Using lever principle: 15 × 2 = 30 × L
30L = 30 → L = 1 m
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!
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!
Quick Revision Summary
Done when force displaces object in direction of force. Unit = joule (J). Can be +ve, −ve, or zero.
W = ΔE. Work done = change in energy. SI unit of energy = joule (J).
K = ½mv². Due to motion. If v doubles → KE × 4. Always positive.
U = mgh. Due to position/deformation. Gravitational PE stored when raised to height h.
KE + PE = constant (no friction). PE converts to KE in free fall. ME = mgh throughout.
Rate of doing work. SI unit = watt (W). 1 W = 1 J/s. 1 hp = 746 W.
Pulley: MA=1 (fixed). Inclined plane: MA=L/h. Lever: MA = effort arm / load arm.
Class I: fulcrum between (scissors). Class II: load between (wheelbarrow). Class III: effort between (tweezers).
W=Fs | K=½mv² | U=mgh | P=W/t | MA=L/h | F₁d₁=F₂d₂ | v=√(2gh) at bottom of slide
Important Exam Questions with Answers
This chapter has numericals every year! Master these: (1) W = F×s problems with sign, (2) KE = ½mv² — especially when velocity changes, (3) U = mgh — height problems, (4) Conservation: mgh = ½mv² to find velocity at bottom of slope, (5) Power = W/t, (6) MA = L/h for inclined plane and effort arm/load arm for lever. Always write the formula, substitute with units, and box your answer!
Leave a Reply