Infographics: Work, Energy and Power

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Work, Energy & Power
Work (W)
Force applied over a 
distance
W = F × d × cos »
Unit: Joule (J) or 
Newton-meter (N·m)
Energy (E)
Capacity to perform 
work
KE = ½mv²
PE = mgh
Unit: Joule (J)
Power (P)
Rate of doing work
P = W/t = F × v
Unit: Watt (W) or 
Joule/second (J/s)
Understanding Work
Work Formula
When force and displacement are in 
the same direction:
W = F × d
When force acts at an angle » to 
displacement:
W = F × d × cos »
Where F is the magnitude of force 
(N), d is displacement (m), and » is 
the angle between force and 
displacement vectors.
Key Conditions
Zero Work: When displacement 
is zero or force is perpendicular 
(» = 90°)
Positive Work: When angle 
between F and d is acute (0° f » 
< 90°)
Negative Work: When angle 
between F and d is obtuse (90° 
< » f 180°)
Maximum Work: When force 
and displacement are parallel (» 
= 0°)
0 1
Work Against Gravity
Work done in lifting an 
object vertically
W = m g h
Where m = mass (kg), g 
= 9.8 m/s² (acceleration 
due to gravity), h = 
vertical height (m)
0 2
Work by Variable 
Force
When force changes 
with position
W = F d s +
Equals the area under 
the force-displacement 
graph
0 3
Dimensional Analysis
Work has dimensions 
of:
[ M L T ]
2 22
Same as energy 
dimensions
Types of Energy
Kinetic Energy
Energy possessed 
by a body due to its 
motion
K E = m v
2
1
2
Always positive or 
zero, scalar quantity
Gravitational PE
Energy due to 
position above 
ground
P E = m g h
Depends on height 
and reference point
Elastic PE
Energy stored in 
compressed or 
stretched spring
P E = k x
2
1
2
k is spring constant 
(N/m), x is 
displacement
Work-Energy Theorem
The work done by all forces acting on a body equals the change in its 
kinetic energy
W = ? K E = K E 2
f
K E =
i
 m( v 2
2
1
f
2
v )
i
2
Power: The Rate of Work
Time-Based
P = 
t
W
Power equals work 
divided by time 
interval
Velocity-Based
P = F × v
Power equals force 
multiplied by velocity
Energy-Based
P = 
t
? E
Power equals rate of 
energy transfer
Spring Potential Energy
Hooke's Law & Energy Storage
When a spring is compressed or stretched from its equilibrium position, it 
stores elastic potential energy. The restoring force follows Hooke's Law:
F =
r
2 k x
The negative sign indicates the force opposes displacement. Work done 
against this restoring force is stored as potential energy:
P E =
s p r in g
 k x
2
1
2
Where k is the spring constant (N/m) and x is displacement from equilibrium 
(m).
Conservation of Energy
Law of Conservation of Mechanical Energy
In the absence of non-conservative forces (like friction), the total 
mechanical energy of a system remains constant:
E =
M
K E + P E = c ons t a nt
K E +
i
P E =
i
K E +
f
P E 
f
When non-conservative forces are present:
? E =
M
W 
n o n2 c o n s e r v a t i v e
Collisions: Types & Conservation Laws
Elastic Collision
Characteristics:
Kinetic energy is conserved
Momentum is conserved
Objects bounce off each other
No deformation or heat 
generated
Coefficient of Restitution: e = 1
Inelastic Collision
Characteristics:
Kinetic energy is NOT 
conserved
Momentum is conserved
Some KE converts to 
heat/sound
Objects may stick together
Coefficient of Restitution: 0 f e 
< 1
Elastic Collision in One Dimension
Before Collision
Two objects with masses m¡ and m¢ 
moving with velocities u¡ and u¢
After Collision
Objects separate with velocities v¡ 
and v¢
Conservation Equations:
Momentum Conservation
m u +
1 1
m u =
2 2
m v +
1 1
m v 
2 2
Kinetic Energy Conservation
 m u +
2
1
1
1
2
 m u =
2
1
2
2
2
 m v +
2
1
1
1
2
 m v 
2
1
2
2
2
Final Velocity Formulas:
v =
1
 
m + m 
1 2
( m 2 m ) u + 2 m u 
1 2 1 2 2
v =
2
 
m + m 
1 2
( m 2 m ) u + 2 m u 
2 1 2 1 1
Inelastic Collision (Objects Stick Together)
When object of mass m¡ moving with velocity u¡ collides with object of mass 
m¢ at rest, and they move together with common velocity v:
m u =
1 1
( m +
1
m ) v
2
v = 
m + m 
1 2
m u 
1 1
Loss in Kinetic Energy:
? K E = 
2( m + m )
1 2
m m u 
1 2
1
2
Elastic Collision in Two Dimensions
When particle m¡ moving along X-
axis with velocity u¡ collides with 
stationary particle m¢, the particles 
move at angles »¡ and »¢ after 
collision.
Conservation along X-axis:
m u =
1 1
m v cos » +
1 1 1
m v cos » 
2 2 2
Conservation along Y-axis:
0 = m v sin » 2
1 1 1
m v sin » 
2 2 2
Energy Conservation:
m u =
1
1
2
m v +
1
1
2
m v 
2
2
2
Coefficient of Restitution (e)
The coefficient of restitution is the ratio of relative velocity of separation 
after collision to relative velocity of approach before collision
e = =
u 2 u 
1 2
v 2 v 
2 1
 
Relative velocity of approach
Relative velocity of separation
100%
Perfectly Elastic
e = 1 (ideal bouncing)
50%
Partially Elastic
0 < e < 1 (real 
collisions)
0%
Perfectly Inelastic
e = 0 (objects stick)
Important Unit Conversions
Energy Units
1 Joule = 10w erg
1 cal = 4.184 J
1 J = 0.239 cal
1 kWh = 3.6 × 10v J
Power Units
1 HP = 746 W
1 kW = 1000 W
1 W = 1 J/s
Dimensional Formula
Work: [ML²T{²]
Energy: [ML²T{²]
Power: [ML²T{³]
Potential Energy
At maximum height
Conversion
PE converts to KE
Kinetic Energy
At lowest point
Conversion
KE converts to PE