Work and Energy — Class 9 (CBSE)

Lift a book. Push a wall. Run up a flight of stairs. In daily speech, all three feel like "work." In physics, only one of them is actually work. This chapter teaches the scientific definition of work, the related idea of energy, and the rule that energy can never be created or destroyed — only changed from one form to another.

1. The story — the redefinition of work

In ordinary life, "work" means effort: studying for an exam, pushing a heavy box, even thinking hard. In physics, the definition is much more precise — and counterintuitive.

Work, in physics, is done when a force produces a displacement in the direction of the force.

So pushing a wall (with no displacement) = ZERO work, even though you sweat doing it. Lifting a book = work was done against gravity. Carrying a book horizontally = ZERO work on the book (no vertical displacement in the direction of the lifting force).

This redefinition allows physics to connect work directly to ENERGY — the capacity to do work. Energy can never be created or destroyed (conservation law), only transformed.

This chapter is short on equations and long on careful thinking. Let's begin.

2. Scientific definition of work

For a constant force $F$ acting on a body that moves a displacement $s$ in the direction of the force:

$W=F\times s$

SI unit: joule (J) = N·m = kg·m²/s².

Three conditions must be met for work to be done:

1. A force is applied.
2. The body moves (there's displacement).
3. The displacement has a component along the direction of the force.

If any of these is missing, work done = 0.

Three special cases

(a) Force and displacement in same direction $W=F\times s$ (positive). A horse pulls a cart forward; positive work on the cart.

(b) Force and displacement in opposite directions $W=-F\times s$ (negative). Friction on a moving box; brake on a car. The agent of force REMOVES energy from the body.

(c) Force perpendicular to displacement $W=0$. A boy carries a suitcase horizontally — his lifting force (vertical) is perpendicular to his horizontal motion. Zero work done on the suitcase.

Famous examples of zero work

• Pushing a wall that doesn't move: no displacement → zero work.
• A satellite orbiting the Earth at constant altitude: gravity (toward centre) is perpendicular to motion (along orbit) → zero work.
• Carrying a book at constant height while walking forward: lifting force is vertical, motion is horizontal → zero work on book.

In everyday speech, all three "feel like effort." In physics, none counts as work.

3. Energy — the capacity to do work

Energy is what a body needs to be able to do work. If a body can do work, it has energy. SI unit: same as work, joule (J).

Forms of energy (preview)

• Mechanical (kinetic + potential).
• Thermal (heat).
• Chemical (in food, fuel, batteries).
• Electrical (in moving charges, current).
• Light / radiant (in EM waves).
• Sound (in vibrating media).
• Nuclear (in atomic nuclei).

Class 9 focuses on mechanical energy in detail.

4. Kinetic energy — energy of motion

Energy possessed by a body due to its motion.

Derivation

A body of mass $m$ at rest is acted on by force $F$ to accelerate it to velocity $v$ over a distance $s$. The work done equals the kinetic energy gained.

From the equation of motion: $v^2=u^2+2as$, with $u=0$: $v^2=2as$, so $s=v^2/(2a)$.

Work done: $W=Fs=(ma)\times v^2/(2a)=\frac{1}{2}m{v}^2$.

$\boxed{KE=\frac{1}{2}m{v}^2}$

KE is a scalar. SI unit: joule.

Properties

• KE is always $\ge 0$ (because of the square).
• KE depends on mass and velocity. A doubled mass doubles KE. A doubled velocity QUADRUPLES KE (because of $v^2$).
• KE is the SAME regardless of direction of motion (scalar). Two cars moving north and south at the same speed have the same KE.

Example

A 1000 kg car moving at 20 m/s: $KE=\frac{1}{2}(1000)(20^2)=\frac{1}{2}(1000)(400)=200,000\text{J}=200\text{kJ}$

That's the energy stored in the car's motion. To bring it to rest, brakes must do 200 kJ of negative work (converting that KE to heat, sound, friction).

5. Work-energy theorem

The work done on a body equals the change in its kinetic energy.

$W=\Delta KE=K{E}_{\text{final}}-K{E}_{\text{initial}}=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

This is one of the most useful results in mechanics. Why?

Many problems give you mass, initial speed, final speed and ask about distance — without explicitly providing acceleration. Use $W=\Delta KE$ + the fact $W=F\times s$ to bypass acceleration entirely.

Example: a 5 kg block moving at 10 m/s is brought to rest by a 25 N braking force. Distance over which it stops?

By work-energy theorem: $W=\Delta KE\Rightarrow -F\times s=0-\frac{1}{2}(5)(10^2)$ $\Rightarrow -25s=-250\Rightarrow s=10\text{m}$.

6. Potential energy — energy of position/configuration

Energy stored in a body due to its position or shape.

Gravitational potential energy

A body of mass $m$ raised through height $h$ above the ground gains potential energy:

$\boxed{PE=mgh}$

This is the work done against gravity to lift the body. When the body falls, PE converts to KE.

Other forms of PE

• Elastic PE in a stretched/compressed spring: $PE=\frac{1}{2}k{x}^2$ (Class 11).
• Chemical PE in a stretched chemical bond.
• Electrostatic PE between two charges.

Reference level matters

PE is defined relative to a chosen ZERO reference (often the ground). The same body at the same height has different PE values measured from different references — but DIFFERENCES in PE (which is what matters physically) are the same.

7. Conservation of mechanical energy

For a body moving under gravity alone (no friction, no air resistance):

$KE+PE=\text{constant}$

This is the law of conservation of mechanical energy — a special case of the more general law of conservation of energy.

A falling object — energy snapshots

A 1 kg ball is dropped from a height of 20 m. Track its energy at three points (g = 10 m/s²).

At height 20 m (just released):

• $PE=mgh=1\times 10\times 20=200\text{J}$
• $KE=0$ (at rest)
• Total = 200 J

At height 10 m (halfway down):

• Velocity from $v^2=2g{h}_{\text{fallen}}=2\times 10\times 10=200\Rightarrow v=\sqrt{200}\approx 14.14\text{m/s}$
• $KE=\frac{1}{2}(1)(200)=100\text{J}$
• $PE=mgh=1\times 10\times 10=100\text{J}$
• Total = 200 J ✓

At the ground ($h=0$):

• $PE=0$
• $v^2=2\times 10\times 20=400\Rightarrow v=20\text{m/s}$
• $KE=\frac{1}{2}(1)(20^2)=200\text{J}$
• Total = 200 J ✓

Total mechanical energy is constant. As PE decreases, KE increases by exactly the same amount.

8. Law of conservation of energy

Energy can neither be created nor destroyed; it can only be transformed from one form to another. Total energy of an isolated system is constant.

When mechanical energy seems to disappear (e.g., a bouncing ball gradually stops), it doesn't actually vanish — it converts to heat (friction), sound (vibration), and deformation. Total energy is always conserved.

Energy transformations in real life

• Pendulum: alternates between KE (at bottom) and PE (at top). Friction at the pivot + air resistance slowly convert it to heat. Pendulum eventually stops.
• Falling object on a spring: KE → elastic PE → KE → ... (with damping due to friction).
• Hydroelectric dam: PE of water at top → KE of falling water → KE of turbine → electric energy → light/heat/motion.
• You eating food: chemical PE in food → ATP (chemical) → mechanical (muscle contraction) + heat (metabolism).

The Sun → photosynthesis (chemical) → food → eat → ATP → motion. The energy you spend doing pushups originally came from the Sun, fixed by plants billions of years ago for fossil fuels (or seconds ago for fresh food).

9. Power — rate of doing work

How FAST work is done.

$\boxed{P=\frac{W}{t}}$

SI unit: watt (W) = J/s.

• A 100-watt bulb consumes 100 J of electrical energy every second.
• A typical human at rest dissipates ~100 W as heat (like a light bulb).
• A microwave: ~1000 W. A car engine: ~75,000 W (100 horsepower).

Average vs instantaneous power

Average power $=\frac{\text{total work done}}{\text{total time taken}}$. Instantaneous power = $P=F\times v$ (force × instantaneous velocity, when $F$ is constant).

Commercial unit of energy — the kilowatt-hour

Electricity bills are charged in kilowatt-hours (kWh) because joules are too small.

$1\text{kWh}=1000\text{W}\times 3600\text{s}=3.6\times 10^6\text{J}$

One unit of electricity on your bill = 1 kWh = the energy used by a 1 kW heater running for 1 hour.

Example

A 60-watt bulb runs for 5 hours. How many units of electricity does it consume?

Power = 60 W = 0.06 kW. Time = 5 h. Energy = P × t = 0.06 × 5 = 0.3 kWh.

That's 0.3 units. At Rs. 5 per unit (typical residential rate), the cost is Rs. 1.50.

10. Worked example — pendulum complete cycle

A 1 kg pendulum bob is released from a height of 0.5 m above its lowest point. Find: (a) Its KE at the lowest point. (b) Its speed at the lowest point. (c) The height it would reach on the other side (ignoring friction).

(g = 10 m/s²)

Step 1 — PE at the highest point = $mgh=1\times 10\times 0.5=5\text{J}$.

Step 2 — At the lowest point, all PE has converted to KE. $KE=5\text{J}$.

Step 3 — Find velocity from KE. $\frac{1}{2}m{v}^2=5\Rightarrow v^2=10\Rightarrow v=\sqrt{10}\approx 3.16\text{m/s}$.

Step 4 — On the other side, all KE converts back to PE. $mg{h}^{\prime }=5\Rightarrow h^{\prime }=5/(1\times 10)=0.5\text{m}$.

So the pendulum rises to the SAME height on the other side. Energy is conserved.

(In reality, friction at the pivot + air resistance gradually reduce the swing.)

11. Closing thought

You started with a simple, almost philosophical definition of work as "displacement in the direction of force." Three chapters later, this work-energy framework explains:

• Why your car needs 4× the braking distance at twice the speed (KE ∝ v²).
• Why hydroelectric dams generate immense power (huge mass × big height drop).
• Why a small bullet can do massive damage (high KE despite low mass, because of $v^2$).
• Why electricity bills charge in kWh, not joules.
• Why total energy of the universe has been constant since the Big Bang.

Work and energy is the most CONCEPTUAL chapter of Class 9 physics — and the one that pays the most dividends in later studies. Master conservation of energy and most subsequent physics looks easy.