Class 9: Work, Energy & Power - Notes

Work, Energy & Power

Class 9 Science, NCERT - Notes

Work

In science, work is said to be done only when a force is applied on an object and the object is displaced in the direction of the force. [Positive Work]

Factors affecting the work:

• Magnitude of applied force: The greater the force, the greater the work done.
• Magnitude of displacement: The greater the displacement, the greater the work done.
• Cosine of angle between the force and the displacement: The smaller the angle, the greater the work done.

Conditions for No Work or Work = 0:

• If there is force but no displacement, work is zero. Example: pushing a wall.
• When displacement is perpendicular to the force (i.e. angle ϴ between force and displacement is 90°). e.g. a man carrying a load on his head: Here the force acting on the load is F=mg (gravitational force) in downward direction and the displacement is forward. Thus the angle between the force and displacement is 90°. Cos 90° is zero. So that, the work done by the gravitational force is also zero.

The work done by the man (muscle force holding the load up) is also effectively zero in terms of displacement since his force is vertical and displacement is horizontal, so muscle force does no work in the horizontal displacement direction in this context.

Work done by centripetal force is always zero because centripetal force acts perpendicular to the displacement of the body moving in a circle. Since work depends on the component of force in the direction of displacement, and here that component is zero (cos 90° = 0), no work is done by centripetal force. It only changes direction, not the speed, of the body.

Negative Work

If there is displacement in the direction opposite to the applied force, the work done by that force is said to be negative. Example: when we lift an object through some height, then work done by the gravitational force is negative.

👉 When we are lifting an object through some height the work done by us is positive because both force by our muscle and displacement is in upward direction.
👉 While, the work done by gravitational force is negative because displacement is upward and gravitational force is downward.
👉 Negative work reduces energy of system.

Work can be positive (if force and displacement are in same direction) or negative (if force acts opposite to displacement). Example: friction does negative work.

Mathematical Expression

Work is mathematically given as:

W = F × s

where F = force, s = displacement in direction of force.

Actual formula: W = F s cosϴ

Work has only magnitude, no direction (scalar quantity).

Units for measurement of work done:

• SI unit: joule
• CGS unit: erg [1 joule = 10⁷ erg]

1 joule = 1 N × 1 m = 10⁵ dyne × 100 cm = 10⁷ dyne-cm = 10⁷ erg

1 joule (J) = work done when a force of 1 N displaces an object by 1 m in the direction of force.

Work done against gravity is path-independent; it depends only on vertical height gained.

Just because you feel tired does not mean work is done in scientific sense. Example: holding a suitcase does zero work.

Why you feel tired then?
Your muscles are still active, contracting continuously to hold the weight.
This uses energy inside your body, producing heat.
But this energy is not transferred to the suitcase, so scientifically, no work is done on the object.

Energy

Energy is capacity to do work.

When work is done, energy is transferred. The body doing work loses energy, the body on which work is done gains energy.

SI Unit of energy: joule (J).

Other units of Energy: 1 kJ = 1000 J.

Major forms: mechanical energy (kinetic + potential), heat energy, chemical, electrical, light.

Energy is sometimes referred to as stored work.

Kinetic Energy (KE)

Energy possessed by a body due to motion.

A faster moving body has more KE.

Work-energy theorem → Net work done on a body by all the forces acting on it is equal to the change in its kinetic energy.

KE = ½ mv²

KE depends only on mass and square of velocity. So doubling velocity makes KE four times, tripling makes KE nine times.

KE increases rapidly with velocity because of square relation.

Examples: moving bullet, flowing water, speeding car.

Potential Energy (PE)

Energy possessed by an object due to its position or configuration.

Work done against gravity in raising a body gets stored as gravitational potential energy.

PE = mgh

Examples: water stored in a dam, stretched rubber band, bent bow.

PE depends on reference point chosen as zero height.

Interconversion of Energy

Energy can change from one form to another.

Examples:

• Plants convert solar → chemical energy.
• Fan converts electrical → kinetic + sound.
• Solar cooker converts solar → heat.

Law of Conservation of Energy: Energy can neither be created nor destroyed; it only changes form. Total energy in an isolated system remains constant.

Total Energy Initial = Total Energy Final

Illustration (Falling Body)

• At top: only PE = mgh, KE = 0.
• During fall: PE decreases, KE increases.
• Just before reaching ground: PE = 0, KE = maximum = mgh.
• At all points: PE + KE = constant.

Mechanical Energy

Sum of kinetic energy and potential energy.

Conservation: In absence of friction and air resistance, total mechanical energy remains constant.

Power

Rate of doing work.

P = W/t = Energy used/time

Unit: watt (W).

1 watt = 1 joule of work done in 1 second.

Larger unit: kilowatt (kW), 1 kW = 1000 W.

Power may vary, so we define average power = total work / total time.

Power does not measure total work, it measures how fast the work is done.
A powerful machine does not always do more work, but it does the same work in less time.

Commercial Unit of Power (Electricity)

1. Definition

The commercial unit of electrical energy is the amount of energy consumed when 1 kilowatt (kW) of electrical power is used for 1 hour.

It is also called kilowatt-hour (kWh).

2. Formula

Energy (in kWh) = Power (in kW) × Time (in hours)

1 kWh = 1000 watt × 3600 seconds = 3.6 × 10⁶ Joules

3. Example

A 100 W bulb used for 10 hours:

Energy = 0.1 kW × 10 h = 1 kWh

4. Usage

Electricity bills are calculated in units = kWh.

Example: If your monthly consumption = 250 units → you are charged for 250 kWh.

5. Key Points

• 1 unit of electricity = 1 kWh.
• Higher power appliances (AC, heater, geyser) consume more units.
• Always convert watt → kW before calculating units.

Angle (θ)	sin(θ)	cos(θ)	tan(θ)
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	1/√2	1/√2	1
60°	√3/2	1/2	√3
90°	1	0	Undefined
180°	0	-1	0

Square Root	Approximate Value
√2	≈ 1.4142
√3	≈ 1.7321
√5	≈ 2.2361
√10	≈ 3.1623
1/√2	≈ 0.707
1/√3	≈ 0.577