FALGUNI MISS

PHYSICS X SUMMARY

02. WORK, ENERGY & POWER. 2023 – 24.

(A) WORK, ENERGY AND POWER, THEIR MEASUREMENTS
AND UNITS.

➢ Scope: Work, energy, power and their relation with force.

o Definition of work, W = FS cos 𝜃, Special cases of 𝜃 = 0°, 90°, W = mgh.
𝑊
o Definition of energy, Definition of power, P = 𝑡 .
o Various units of work, energy, power and their relation with S.I. units. [erg,
calorie, kWh and eV].
o Other units, kilowatt (kW), megawatt (MW) and gigawatt (GW), Horse power (1
HP = 746 W)
o Simple numerical problems on work, power and energy.
➢ Work:
o Definition: Work is said to be done only when the force applied on a body
produces displacement of the body.

o Factors affecting amount of work done:

▪ The magnitude of the applied force – Directly Proportional.
▪ The displacement produced by the applied force – Directly Proportional.
▪ The angle of inclination – Directly Proportional.

o Conditions for the work done by the force to be zero:

▪ It produces no displacement. (S = 0) OR
▪ It produces displacement of a body which is normal to the direction of
applied force. [𝜃 = 90o].

o Units of work:
▪ SI unit is joule. (J)
▪ 1 joule = 1 newton × 1 meter.
▪ Definition: 1 joule of work is said to be done when a force of 1 newton
displaces a body through a distance of 1 meter in the same direction.
▪ 1 kJ = 103 J, 1 MJ = 106 J and 1GJ = 109 J.
▪ M.K.S. unit:

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 1
 FALGUNI MISS
• Force = kg m s-2.
• Work = kg m2 s-2.
▪ C.G.S unit of work is erg.
▪ 1 erg = 1 dyne × 1 cm.
▪ Definition: 1 erg of work is said to be done when a force of 1 dyne
displaces a body through a distance of 1 cm in the same direction.
▪ 1 joule = 1 N × 1 m. [1 N = 105 dyne and 1 m = 102 cm]
▪ 1 joule = 105 dyne × 102 cm.
▪ 1 joule = 107 dyne × cm.
▪ 1 joule = 107 erg.
➢ Energy:
o Definition: The energy of a body is its capacity to do work.

o Units of energy: (Same as work.)

▪ SI unit of energy is joule.
▪ C.G.S unit of energy is erg.
▪ 1 J = 107 erg.

o Other units of energy:

▪ Watt hour: One watt hour is the energy spent / work done by a source of
power 1 W in 1 h.
▪ Kilowatt hour: One kilowatt hour is the energy spent / work done by a
source of power 1 kW in 1 h.
▪ Calorie: 1 calorie is the heat energy required in raising the temperature
of 1 g of water from 14.5℃ to 15.5℃.
▪ Electron volt: 1 eV is the energy gained by an electron when it
accelerates through a potential difference of 1 volt.

o Conversion all of units of energy/work:

▪ 1 watt hour (Wh) = 1 watt × 1 hour
= 1 J s–1 × 3600 s
= 3600 J
= 3.6 kJ
▪ 1 kilowatt hour (kWh) = 1 kilowatt × 1 hour
= 1000 J s–1 × 3600 s
= 3.6 × 106 J
= 3.6 MJ
▪ 1 eV = Charge on an electron × 1 volt
= 1.6 × 10–19 coulomb × 1 volt

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 2
 FALGUNI MISS
= 1.6 × 10–19 joule
o List of all conversions:
▪ 1 watt hour (Wh) = 3600 J = 3.6 kJ.
▪ 1 kilowatt hour (kWh) = 3.6 × 106 J = 3.6 MJ.
▪ 1 J = 0.24 calorie.
▪ 1 calorie = 4.18 J.
▪ 1 kilocalorie = 4180 J = 1000 calories.
▪ 1 eV = 1.6 × 10-19J.
➢ Power:
o Definition: The rate of doing work is called power.
𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑊
o Power = ; P=
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 𝑡
o Power = Force × Average speed
o P = Fv. (if displacement is in straight line)
o P = Fv cos θ. (if displacement is at an angle.)

o Factors affecting power spent by a source:

▪ The amount of work done by the source – Directly Proportional.
▪ The time taken by the source to do the said work – Inversely Proportional.

o Units of power:
▪ S.I. unit of power is watt.
▪ 1 watt = 1 J s-1.
▪ Definition: If 1 joule of work is done in 1 second, the power spent is said
to be 1 watt.
▪ Definition: Horse power is a unit of power, largely used in mechanical
engineering.

▪ M.K.S unit: kg m2 s-3.

▪ C.G.S unit: erg per second (erg s-1).
▪ 1 W = 1 Js-1 = 107 erg s-1.
▪ 1 H.P = 746 W = 0.746 kW.
▪ Other units of power:
• 1 kilowatt (1 kW) = 1000W = 103 W.
• 1 megawatt (1 MW) = 1000,000 W = 106 W.
• 1 gigawatt (1 GW) = 1000,000,000 W = 109 W.
• 1 milli watt (1 mW) = 10-3W.
• 1 micro watt (1 µW) = 10-6W

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 3
 FALGUNI MISS
(B) DIFFERENT FORMS OF ENERGY.

➢ Scope:
o Both types of Mechanical energy:
▪ Potential energy U = mgh (derivation included), gravitational potential
energy with examples.
1
▪ Kinetic energy K = 2 mv2 (derivation included);
o Different forms of kinetic energy – Translational, rotational and vibrational.
o Numerical problems on K and U – Translational motion only.
o Qualitative discussion and conversion of different forms of energies – Electrical,
chemical, heat, nuclear, light and sound energy.

➢ Mechanical energy and different forms of mechanical energy: The energy possessed by
a body due to its state of rest or motion is called the mechanical energy.

➢ Potential Energy (mgh): The energy possessed by a body at rest by virtue of its specific
position or changed configuration is called the potential energy.
o Gravitational potential energy: The potential energy possessed by a body due to
its position relative to the center of earth is called its gravitational potential
energy.
o Elastic potential energy: The potential energy possessed by a body in the
deformed state due to change in its configuration, is called the elastic potential
energy.

𝟏
➢ Kinetic Energy: (K = 𝟐 mv2) The energy possessed by a body by virtue of its state of
motion is called the kinetic energy.

➢ Conversion of one form of energy to the other form:

o Mechanical energy to electrical energy - dynamo.
o Electrical energy to mechanical energy-electric motor; which is used in devices
such as: electric fan, washing machine, mixer, grinder, industrial machine.
o Electrical energy to heat energy-electric iron, heater, oven, toaster, geyser etc.
o Heat energy to electrical energy-thermo couple.
o Electrical energy to sound energy- loudspeaker, electric bell.
o Sound energy to electrical energy- microphone.
o Electrical energy to chemical energy- charging a battery.

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 4
 FALGUNI MISS
o
Chemical energy to electrical energy- electric cell.
o
Chemical energy to light energy- lighted candle, kerosene lamp.
o
Light energy to chemical energy- photosynthesis.
o
Electrical energy to light energy- electric bulb.
o
Light energy to electrical energy- photoelectric cell, solar cells.
o
Heat energy to mechanical energy-steam engine (chemical to heat to mechanical).
o
Chemical energy to heat energy- Burning of fuel such as wood, coal, biogas etc.
Burning of firecrackers, lighting a matchstick.
o Chemical energy to mechanical energy-in automobiles when in motion.
o Electrical energy to magnetic energy- electromagnet.
o Mechanical energy to heat energy- The potential energy stored in water at a height
changes to kinetic energy in falling waters. On reaching the ground, this kinetic energy
changes to heat energy due to which the temperature of water rises. Similarly, the moving
parts of a machine get heated due to friction, thus changing mechanical into heat energy.
➢ Note:
o When mechanical energy changes to any form of energy, the potential energy first
changes to kinetic energy and then the kinetic energy changes to the other forms.
o Energy converted to undesirable form or is lost to the environment during the desired
transformation from one form to the other is called the degraded energy.
o The conversion of energy to the undesirable/non-useful form is called the dissipation
of energy.

(C) CONSERVATION OF ENERGY.

➢ Scope:
o Statement of the principle of conservation of energy.
o Theoretical verification that U + K = Constant for a freely falling body.
o Qualitative application of this law to simple pendulum.
o Simple numerical problems.

➢ Principle of conservation of energy:

o Statement: Energy can neither be created nor destroyed, it only changes from one
form to another.

➢ Conservation of mechanical energy (Fundamental Principle of nature):

o Statement: According to the law of conservation of mechanical energy, whenever
there is an interchange between the potential energy and the kinetic energy, the
total mechanical energy remains constant.
o K + U = constant, when there are no frictional forces.

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 5
 FALGUNI MISS
o Table showing the U and K of a body:
Motion. Height above the Kinetic Potential energy Total energy
ground. energy K. U. E = K + U.
Downward h (highest point A). 0 mgh. mgh
motion. 1 1 1 mgh
2
ℎ (middle point B). 2
mgh. 2
mgh.
(i.e., free fall) 0 (ground C). mgh. 0 mgh
Upward 0 (ground C) Mgh 0 mgh
motion. 1 1 1 mgh
2
ℎ(middle pt B). 2
mgh 2
mgh
h (highest pt A) 0 Mgh mgh
o Note: The conservation of mechanical energy is strictly valid in vacuum, where
friction due to air is absent, although the law of conservation of total energy of
all kinds is always true.

➢ Application of principle of conservation of energy to a simple pendulum:

o A swinging the bob has:
▪ Maximum Potential energy at extreme position B or C.
▪ Kinetic energy at resting position A is maximum.
▪ At an intermediate position (between A and B or between A and C), the bob has
both the kinetic energy and potential energy, and the sum of both the energies
(i.e., total mechanical energy) remains constant throughout the swing.
▪ This is strictly true in vacuum where there is no friction due to air.
➢ Differences:
o Work and power:
Work Power
Work is said to be done only when the Power of a source is the rate of doing
force applied on a body makes the work by it.
body move. (i.e., there is a
displacement of the body).
Work done does not depend on time. Power spent depends on the time in
which work is done.
SI unit of work is joule (J). SI unit of power is watt (W).
o Energy and power:
Energy Power
Energy of a body is its capacity to do Power of a source is the energy spent
the work. by it in 1 s.
Energy spent does not depend on time Power spent depends on the time in
which energy is spent.
S.I. unit of energy – joule (J). S.I. unit of power – watt (W).
o Watt and watt hour:
Watt Watt hour
It is the unit of power. It is the unit of energy.

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 6
 FALGUNI MISS
o Kinetic energy and potential energy:
Kinetic Energy Potential Energy
The energy possessed by a body by virtue The energy possessed by a body by virtue
of its state of motion is called the kinetic of its specific position (or changed
energy. configuration) is called the potential
energy.
𝟏 U = mgh
K = 𝟐 mv2

FORMULAE:

1. W = F × S (horizontal motion)
2. W = F × S cos 𝜽 (angular motion)
3. F = Weight = mg
4. F = ma
5. W = FS (Horizontal) = mgh (Vertical)
6. Energy = Work
𝑾
7. P = 𝒕
8. P = Fv
9. P = Fv (cos 𝜽)
10. V = u ± at
𝟏 𝟏
11. S = 𝟐 (u + v)t = ut ± 𝟐 at2
12. v2 = u2 ± 2aS
13. F = ma
14. U = mgh
15. p =mv
16. W =U=K
17. W = FS
𝟏
18. K = 𝟐 mv2
𝐩𝟐
19. K = 𝟐𝒎
20. p = √𝟐𝒎𝑲
21. Gain in U = mg (h2 – h1)
22. Loss in U = mg (h1 – h2)
𝟏
23. ∆ K = 𝟐 m (v2 – u2)
24. W = mgh
25. U = mgh
26. Δ in P.E. = mg (h2–h1)
𝟏
27. K.E. = 𝟐 mv2
1
28. ∆ In K.E. = 𝟐 (mv2 – mu2)

Falguni Thakker, 03, Sapna bldg. S.V Road, Vile Parle (w), Mumbai 56. Tel 9820428493 Page 7