The document discusses work, energy, and their units in physics. It defines work as force applied over a displacement. Positive work is done when force and displacement are in the same direction, negative when opposite. Kinetic energy is energy from an object's motion and depends on its mass and velocity. Potential energy depends on an object's position and mass. The law of conservation of energy states that energy cannot be created or destroyed, only transformed between forms.

1. WORK AND ENERGY
PHYSICS

2. WORK IS SAID TO BE DONE WHEN A FORCE IS APPLIED
ON AN OBJECT AND THE OBJECT IS DISPLACED FROM ITS
POSITION IN THE DIRECTION OF THE FORCE..
POSITIVE WORK
DONE
NEGATIVE WORK DONE ZERO WORK DONE
𝜭= 0° 𝜭=180° 𝜭=0°
D OF FORCE = D
OF DISPLACEMENT
D OF FORCE IS OPPOSITE
TO THE D OF DISPLACEMENT
NO DISPLACEMENT TAKES PLACE
● θ [THETA]IS THE ANGLE BETWEEN DIRECTION OF
DISPLACEMENT AND DIRECTION OF FORCE.

3. 1. W = F*S * COS THETA
[ THETA = 0]
W= F*S*1
W = + FS
2. W= F *S *COS THETA
[ THETA = 180]
W= F*S*-1
W= - FS
3. W = F*S *COS THETA
[ THETA = 90]
W=F*S*0
W= 0
POSITIVE WORK DONE
NEGATIVE WORK DONE
ZERO WORK DONE

4. SI UNIT OF WORK = JOULES
CGS UNIT OF WORK = ERG
SI UNIT OF FORCE = NEWTON
CGS UNIT OF FORCE = DYN
SI UNIT OF ENERGY = JOULES
SI UNITS AND CGS UNITS

5. SI UNIT OF ENERGY = JOULE
COMMERCIAL UNIT OF ENERGY = KILOWATT-HOUR
WATT-SECOND [ FROM THE DERIVATION OF RELATION OF kWh & J.]
N-m [ FROM ‘W=F*S’]
dB [SOUND IS A FORM OF ENERGY]
UNITS OF ENERGY

6. SI UNIT OF WORK = JOULES
SI UNIT OF ENERGY = JOULES
W=F*S 1 JOULE IS THE AMOUNT OF WORK DONE WHEN
1 NEWTON OF FORCE IS APPLIED AND RESULTS IN A DISPLACEMENT
OF 1 METRE.
JOULES

7. 1. ENERGY IS THE ABILITY TO DO WORK .
2. ALL THE MECHANICAL WORK IS DONE BECAUSE OF ENERGY.
3. THE OBJECT WHICH DOES THE WORK LOSES ENERGY.
4. THE OBJECT ON WHICH THE WORK IS DONE GAINS ENERGY.
5. SI UNIT OF ENERGY IS JOULE
1 KILOJOULE[ KJ ] = 1000 JOULES
ENERGY = POWER * TIME
ENERGY

8. KINETIC ENERGY -
➔ ENERGY POSSESSED BY A BODY IN MOTION.
➔ THE FASTER AN OBJECT MOVES , THE MORE ITS KINETIC ENERGY.
➔ K-e = ½ mv^2 [ K ∝ m ] [ K ∝ v^2 ]
➔ DUE TO VERY HIGH KINETIC ENERGY , A BULLET FIRED FROM A GUN CAN PIERCE A
TARGET .
POTENTIAL ENERGY -
➔ THIS ENERGY IS POSSESSED BY ANY OBJECT THAT IS KEPT AT A CERTAIN HEIGHT .
➔ IT DEPENDS ON ITS POSITION AND SHAPE.
➔ P-e = mgh [ P ∝ m ] [ P ∝ G ] [ P ∝ H ]
● TYPES OF ENERGY = ∞
● TYPES OF MECHANICAL ENERGY = 2
TYPES OF MECHANICAL ENERGY

9. THE ENERGY POSSESSED BY THE MOTION OF A MOVING OBJECT IS CALLED AS KINETIC
ENERGY .
Ke = ½ M*V^2
THE FACTORS ON WHICH KINETIC ENERGY DEPENDS ARE ;
- MASS OF AN OBJECT
- VELOCITY OF THE MOVING OBJECT
ABOUT KINETIC ENERGY

10. THE ENERGY POSSESSED BECAUSE OF THE POSITION OF THE OBJECT IS CALLED POTENTIAL
ENERGY.
Pe = m*g*h
IT IS ALSO CALLED ‘ WORK DONE AGAINST GRAVITY’
ABOUT POTENTIAL ENERGY

11. -
EXPRESSION OF POTENTIAL ENERGY
B.
A.
H.
MASS OF AN OBJECT= m
Work = F * S
Work = W * S
= (m*g)*(h)
This work done is stored in the form of
potential energy .
● POTENTIAL ENERGY IS ALSO CALLED
‘ WORK DONE AGAINST GRAVITY

12. LAW OF CONSERVATION OF ENERGY STATES THAT
ENERGY CAN NEITHER BE CREATED NOR DESTROYED ,
IT CAN ONLY BE TRANSFORMED FROM ONE FORM TO
ANOTHER. THE TOTAL ENERGY BEFORE AND AFTER
CONSERVATION ALWAYS REMAINS CONSTANT.
LAW OF CONSERVATION OF ENERGY

13. ONE FORM OF ENERGY CAN BE TRANSFORMED TO ANOTHER FORM AND
THIS PHENOMENON IS CALLED TRANSFORMATION OF ENERGY.
TRANSFORMATION OF ENERGY
1. ELECTRIC MOTOR - ELECTRICAL ENERGY TO MECHANICAL ENERGY
2. ELECTRIC GENERATOR - MECHANICAL ENERGY TO ELECTRICAL ENERGY
3. STEAM ENGINE - HEAT ENERGY TO KINETIC ENERGY
4. ELECTRIC BULB - ELECTRICAL ENERGY TO HEAT AND LIGHT ENERGY
5. DRY CELL - CHEMICAL ENERGY TO HEAT ENERGY AND LIGHT ENERGY
6. SOLAR CELL - LIGHT ENERGY TO ELECTRICAL ENERGY

14. Where ,
P = momentum
K= kinetic energy
m = mass
RELATIONSHIP BETWEEN KINETIC ENERGY AND
MOMENTUM
P = √2 K m

15. SI UNIT OF ENERGY - JOULE
COMMERCIAL UNIT OF ENERGY - KILOWATT-HOUR
● DERIVATION-
1 kWh
= 1 kilowatt * 1 hour
= 1000 watts * 3600 seconds [ watt*second = joule]
= 3600000 joules / 3.6 * 10^6 joules
RELATIONSHIP BETWEEN SI UNIT AND COMMERCIAL
UNIT OF ENERGY.

16. THE FORCE EXERTED ON AN OBJECT MOVING IN CIRCULAR
PATH IS CALLED CENTRIPETAL FORCE WHICH IS
GENERATED FROM THE CENTRE OF THE PATH .
THE ANGLE BETWEEN THE DIRECTION OF FORCE AND
THE DIRECTION OF DISPLACEMENT OF AN OBJECT MOVING
IN CIRCULAR MOTION IS 90 DEGREE .
ENERGY OF AN OBJECT IN CIRCULAR MOTION
F
S

17. 1. v=u + at ……………………. v= u + gt
2. s= ut + ½ at^2………………………………..s=ut + ½ gt^2
3. v^2 = u^2 + 2as
EQUATIONS OF MOTION UNDER THE EFFECT OF
GRAVITY DURING FREE-FALL

18. 1. ELASTICITY IS TYPE OF POTENTIAL ENERGY.
2. KINETIC ENERGY AND POTENTIAL ENERGY ARE COLLECTIVELY KNOWN AS MECHANICAL
ENERGY.
3. DURING WORK AGAINST GRAVITY , KINETIC ENERGY SIMULTANEOUSLY CONVERTS INTO
POTENTIAL ENERGY.
4. DURING FREEFALL , POTENTIAL ENERGY CONTINUOUSLY CHANGES INTO KINETIC ENERGY.
5. POTENTIAL ENERGY DEPENDS ON THE MASS AND ON THE HEIGHT OF THE OBJECT FROM THE
GROUND .
6. IN CIRCULAR MOTION , THE WORK DONE IS ALWAYS ZERO BECAUSE THE ANGLE BETWEEN THE
FORCE AND DISPLACEMENT IS ALWAYS 90 DEGREE.
7. SI UNIT OF ALL TYPES OF ENERGY IS JOULE.
8. KINETIC ENERGY DEPENDS ;
INVERSELY ON VELOCITY SQUARED / DIRECTLY ON MASS OF THE OBJECT .
SOME IMPORTANT POINTS TO REMEMBER

19. DERIVATION 1: OF RELATION BETWEEN MOMENTUM AND KINETIC ENERGY .
WE KNOW THAT
Ke = ½ m* v^2 Ke = p^2 / 2m
= ½ * m*v^2/1 * m /m 2mK = p^2
=½ * m^2*v^2 /m √2Km = p
= ½ (mv)^2 /m
= (mv)^2 / 2m
= ½ * p^2/ m
DERIVATIONS ;

20. DERIVATION 2: FOR THE EXPRESSION OF KINETIC ENERGY .
VELOCITY = U VELOCITY = V
WORK DONE : F*S = m*a*s………………..1 putting value of ‘s’ in eq.1
FOR ‘S’ v^2 = u^2 - 2as W = m*a *[ v^2 - u^2 / 2a ]
v^2 - u^2 = 2as THE OBJECT STARTS FROM
REST
v^2 - u^2 / 2a = s …………...2 W = ½ M * V^2
When the body starts from rest and then attains some velocity, the work done in this
process is known as the kinetic energy of the object.
DERIVATIONS ;
S
F

21. DERIVATIONS ;
H
DERIVATION 3: FOR THE EXPRESSION OF POTENTIAL ENERGY .
REST ; (u = 0 ) , MASS = m
Work = f *S = m*a*s
[ due to acceleration due to gravity (a=g) ]
Work = mgh
$ When an object is at rest on the ground and then attains
Some height then the work done is equal to the potential energy of the object .

22. WORK ENERGY THEOREM ;
WE KNOW BY THE THIRD EQUATION OF MOTION THAT : v^2 - u^2 = 2as
MULTIPLYING BOTH SIDES BY m[ MASS]
m(v^2 - u^2 ) = (2as)*m
mv^2 - mu^2 = 2asm
mv^2 - mu^2 / 2 = m*a*s
[mv^2 / 2 ]- [ mu^2 /2 ] = F * S
½ mv^2 - ½ mu^2 = W
Ke (final) - Ke (initial) = Work
When a moving body is acted upon
by an external force then the
change in the kinetic energy is equal
to the work done in this process.

23. LAW OF CONSERVATION OF ENERGY [ DERIVATION ] ;
FOR A FREELY FALLING OBJECT - let an object of mass ‘m’ be ‘h’ metre above the ground .
AT POINT ‘A’
u= 0 m/s
Ke = ½ *m*0^2
= 0 joule
Pe = m*g*h
# Ke + Pe = 0 + mgh
= mgh
AT POINT ‘B’
Ke = ½ * m*2gx
= mgx
Pe = mgh
= mg(h-x)
= mgh - mgx
# Ke + Pe = mgx+[mgh-mgx]
= mgh
AT POINT ‘C’
Ke= ½ *m*2gh
= mgh
Pe = mgh
= m*g*0
= 0
# Ke + Pe = mgh + 0
= mgh
h
A
C
B
v^2 = u^2 + 2as
= 0^2 + 2gs
= 2gs = 2gx
v^2 = 0^2 +
2gh
v^2 = 2gh