Understanding work, energy, power, and their real-world applications
In physics, work is said to be done when a force applied on an object causes it to move in the direction of the force. Work is the product of force and displacement.
Work (W) = Force (F) × Displacement (s)
W = F × s
SI Unit: Joule (J)
1 Joule = 1 Newton × 1 meter
1 J = 1 N⋅m
For work to be done, TWO conditions must be satisfied:
1. Force must be applied on the object
2. Object must move (there must be
displacement)
If any one condition is not satisfied, NO work is done!
In everyday life, we say "I worked all day" even while sitting at
a desk. But in physics, if you push a wall for hours and it
doesn't move - you did ZERO work!
Examples where NO work is done:
• Pushing a wall (no displacement)
• Carrying a bag while walking (force is vertical, motion is
horizontal)
• Holding a heavy object still (no displacement)
• A coolie standing with luggage on head (no movement)
Physics cares only about: Did the force cause movement? If yes,
work is done!
A force of 10 N moves an object 5 m in the direction of the force.
Calculate the work done.
Solution:
Force (F) = 10 N
Displacement (s) = 5 m
Work = Force × Displacement
W = F × s
W = 10 × 5
W = 50 J
Answer: 50 Joules of work is done.
When force is applied at an angle θ to the direction of motion:
Work (W) = F × s × cos θ
Where:
F = Applied force
s = Displacement
θ = Angle between force and displacement
When you walk horizontally while carrying a bag:
• Force applied: Upward (to hold bag)
• Direction of motion: Horizontal (forward)
• Angle between force and motion: 90°
Work done = F × s × cos 90°
Since cos 90° = 0
Work = 0
That's why scientifically, you do NO work on the bag while walking
with it! (Even though you feel tired - that's your body's internal
work)
| Type of Work | Condition | Example | Effect |
|---|---|---|---|
| Positive Work | Force and motion in same direction (0° ≤ θ < 90°) | Pushing a moving car forward | Speed increases |
| Negative Work | Force opposes motion (90° < θ ≤ 180°) | Applying brakes to stop a car | Speed decreases |
| Zero Work | Force perpendicular to motion (θ = 90°) or no displacement | Carrying bag while walking, pushing a wall | No change in speed |
Imagine you're pushing a sled uphill, but it's sliding down. You
push up (your force), but it moves down (displacement). Your force
and motion are in opposite directions - you're doing NEGATIVE work
on the sled.
Negative work means you're trying to oppose the motion. When
friction slows down a moving object, friction does negative work.
When you catch a fast-moving ball, your hands do negative work to
stop it.
Energy is the capacity or ability to do work. An object that has energy can exert a force on another object and do work on it.
SI Unit: Joule (J)
1 Joule = Work done when 1 N force moves object 1 m
Larger units:
1 kilojoule (kJ) = 1000 J
1 megajoule (MJ) = 1,000,000 J
Commercial unit:
1 kilowatt-hour (kWh) = 3.6 × 10⁶ J
Just like money gives you the ability to buy things, energy gives
objects the ability to do work!
• A charged battery has energy = has "money" to spend
• Using the battery (doing work) = spending money
• Energy in different forms = money in different currencies
• Energy conservation = money never disappears, just changes
hands
You can't see money or energy directly, but you see their effects
when they're used!
Kinetic Energy is the energy possessed by an object due to its motion. Any object that is moving has kinetic energy.
Kinetic Energy (KE) = ½ × mass × (velocity)²
KE = ½mv²
Where:
m = Mass of object (kg)
v = Velocity of object (m/s)
SI Unit: Joule (J)
A car of mass 1000 kg is moving with velocity 20 m/s. Calculate
its kinetic energy.
Solution:
Mass (m) = 1000 kg
Velocity (v) = 20 m/s
Kinetic Energy = ½mv²
KE = ½ × 1000 × (20)²
KE = ½ × 1000 × 400
KE = 500 × 400
KE = 200,000 J
KE = 200 kJ
Answer: The car has kinetic energy of 200,000
Joules or 200 kJ.
Notice that kinetic energy depends on v² (velocity squared). This
means velocity has a HUGE effect!
Example: Compare two situations:
• Doubling the mass → KE becomes 2 times
• Doubling the velocity → KE becomes 4 times!
That's why speeding is so dangerous! If you drive at 100 km/h
instead of 50 km/h, your kinetic energy is 4 times greater. In a
crash, 4 times more energy needs to be absorbed, making it much
more destructive!
This is also why bullets (small mass but VERY high velocity) can
cause so much damage.
The work done by a force on an object is equal to the change in its kinetic energy. This is called the Work-Energy Theorem.
Work = Change in Kinetic Energy
W = KEfinal - KEinitial
W = ½m(v²) - ½m(u²)
W = ½m(v² - u²)
Where:
u = Initial velocity
v = Final velocity
m = Mass
A force accelerates a 5 kg object from rest to 10 m/s. Calculate
the work done.
Solution:
Mass (m) = 5 kg
Initial velocity (u) = 0 m/s (starts from rest)
Final velocity (v) = 10 m/s
Initial KE = ½mu² = ½ × 5 × 0² = 0 J
Final KE = ½mv² = ½ × 5 × (10)² = ½ × 5 × 100 = 250 J
Work = Final KE - Initial KE
W = 250 - 0
W = 250 J
Answer: 250 Joules of work was done to accelerate
the object.
Potential Energy is the energy possessed by an object due to its position or configuration. It is the stored energy that can be converted to kinetic energy.
The potential energy possessed by an object due to its height above the ground is called Gravitational Potential Energy.
Potential Energy (PE) = mass × g × height
PE = mgh
Where:
m = Mass of object (kg)
g = Acceleration due to gravity (9.8 m/s²)
h = Height above reference point (m)
SI Unit: Joule (J)
A 2 kg book is placed on a shelf 3 m above the floor. Calculate
its potential energy relative to the floor.
(Take g = 10 m/s²)
Solution:
Mass (m) = 2 kg
Height (h) = 3 m
g = 10 m/s²
Potential Energy = mgh
PE = 2 × 10 × 3
PE = 60 J
Answer: The book has 60 Joules of potential
energy relative to the floor.
When you lift an object to a height, you're doing work against
gravity - like putting money in a savings account. This work gets
"saved" as potential energy.
Later, when the object falls:
• The "saved" potential energy is "withdrawn"
• It converts to kinetic energy (motion)
• The object gains speed as it falls
Example: Water stored in a dam has huge potential energy. When it
falls, this converts to kinetic energy, which turns turbines to
generate electricity. The height of the dam is like the "account
balance" - more height means more stored energy!
1. Hydroelectric Dams: Water stored at height has
PE, which converts to KE when it falls, turning turbines.
2. Roller Coasters: Pulled up to great height
(high PE), then falls converting PE to KE for thrilling ride.
3. Pendulum Clock: Raised weight has PE, which
gradually converts to KE to run the clock mechanism.
4. Bow and Arrow: Stretched bow stores PE
(elastic potential), which converts to KE of arrow when
released.
5. Pile Driver: Heavy weight lifted high has PE,
which converts to KE when dropped to drive piles into ground.
Energy can neither be created nor destroyed. It can only be transformed from one form to another. The total energy of an isolated system remains constant.
This is one of the most fundamental laws in physics! It tells
us:
• Energy never appears out of nowhere
• Energy never disappears into nothing
• Energy only changes form (light → heat, PE → KE, etc.)
• Total energy before = Total energy after (in any process)
This law has NEVER been violated in any experiment ever conducted!
Mechanical Energy is the sum of kinetic energy and potential energy of an object.
Total Mechanical Energy = KE + PE
E = ½mv² + mgh
For a freely falling body (no air resistance):
Total Mechanical Energy = Constant
KE + PE = Constant
½mv² + mgh = Constant
A 1 kg ball is dropped from height of 10 m. Calculate its PE, KE,
and total energy at:
(a) Initial position (h = 10 m)
(b) Middle position (h = 5 m)
(c) Just before hitting ground (h = 0 m)
(Take g = 10 m/s²)
Solution:
Mass = 1 kg, Initial height = 10 m, g = 10 m/s²
(a) At h = 10 m (starting point):
v = 0 (starts from rest)
PE = mgh = 1 × 10 × 10 = 100 J
KE = ½mv² = 0 J
Total Energy = 100 + 0 = 100 J
(b) At h = 5 m (middle):
Using v² = u² + 2gs: v² = 0 + 2 × 10 × 5 = 100, so v = 10 m/s
PE = mgh = 1 × 10 × 5 = 50 J
KE = ½mv² = ½ × 1 × 100 = 50 J
Total Energy = 50 + 50 = 100 J
(c) At h = 0 m (ground):
Using v² = u² + 2gs: v² = 0 + 2 × 10 × 10 = 200, so v = 14.14
m/s
PE = mgh = 1 × 10 × 0 = 0 J
KE = ½mv² = ½ × 1 × 200 = 100 J
Total Energy = 0 + 100 = 100 J
Notice: Total energy remains 100 J at all
heights! As PE decreases, KE increases by the same amount.
Imagine energy as water in a container that can be split into two
connected vessels:
Left vessel = Potential Energy (height)
Right vessel = Kinetic Energy (motion)
When object is at maximum height:
Left vessel is FULL (high PE), Right vessel is EMPTY (no KE)
As object falls:
Water flows from left to right vessel
(PE converts to KE)
When object hits ground:
Left vessel is EMPTY (no PE), Right vessel is FULL (maximum KE)
But total water (total energy) remains the same throughout!
Power is the rate at which work is done or energy is transferred. It tells us how quickly work is being done.
Power = Work done / Time taken
P = W / t
Or
Power = Energy transferred / Time taken
P = E / t
SI Unit: Watt (W)
1 Watt = 1 Joule / 1 second
1 W = 1 J/s
Larger units:
1 kilowatt (kW) = 1000 W
1 megawatt (MW) = 1,000,000 W
1 horsepower (hp) = 746 W
A motor does 5000 J of work in 10 seconds. Calculate its power.
Solution:
Work done (W) = 5000 J
Time taken (t) = 10 s
Power = Work / Time
P = 5000 / 10
P = 500 W
P = 0.5 kW
Answer: The motor has power of 500 Watts or 0.5
kilowatts.
Think of work as a distance you need to travel, and power as your
speed:
Situation 1: You walk 10 km in 2 hours (slow)
Situation 2: You drive 10 km in 10 minutes
(fast)
Same distance (same work), but driving is faster (more power)!
Similarly:
• A 100W bulb and 40W bulb both convert electrical to light
energy
• But 100W bulb does it FASTER, so it's brighter
• A powerful engine lifts a car faster than a weak engine
• Both do the same work eventually, but powerful one is quicker!
Person A lifts 50 kg to height of 2 m in 5 seconds.
Person B lifts same 50 kg to same height of 2 m in 10 seconds.
Who is more powerful? (g = 10 m/s²)
Solution:
Person A:
Work = Force × distance = (mg) × h = (50 × 10) × 2 = 1000 J
Time = 5 s
Power = 1000 / 5 = 200 W
Person B:
Work = Same = 1000 J
Time = 10 s
Power = 1000 / 10 = 100 W
Answer: Person A is more powerful (200 W vs 100
W) because they do the same work in less time!
The commercial unit of electrical energy is kilowatt-hour (kWh), also known as a "unit" of electricity. This is what your electricity meter measures.
1 kilowatt-hour is the energy consumed when a device of power 1
kilowatt operates for 1 hour.
1 kWh = 1 kW × 1 h
1 kWh = 1000 W × 3600 s
1 kWh = 3,600,000 J
1 kWh = 3.6 × 10⁶ J
1 kWh = 3.6 MJ
Why use kWh instead of Joules?
Because Joule is too small for everyday electricity consumption. 1
kWh = 3.6 million Joules!
A 100 W bulb is used for 5 hours daily for 30 days. Calculate:
(a) Energy consumed in kWh
(b) Cost of electricity if rate is ₹5 per kWh
Solution:
Power = 100 W = 0.1 kW
Time per day = 5 hours
Number of days = 30
Total time = 5 × 30 = 150 hours
(a) Energy consumed:
Energy = Power × Time
E = 0.1 kW × 150 h
E = 15 kWh (or 15 "units")
(b) Cost:
Cost = Energy × Rate
Cost = 15 × ₹5
Cost = ₹75
Answer: (a) 15 kWh, (b) ₹75
Understanding power can help save electricity:
• Replace 100W bulbs with 20W LED bulbs (same brightness, 80% less
energy)
• Turn off appliances when not in use
• Use natural light during daytime
• Higher power rating = more electricity consumption
• Energy consumed = Power (kW) × Time (hours)
• Small savings daily add up to big savings yearly!
A force of 50 N acts on an object and moves it 4 m in the
direction of force. Calculate the work done.
Solution:
Force (F) = 50 N
Displacement (s) = 4 m
Work = Force × Displacement
W = 50 × 4
W = 200 J
Answer: 200 Joules
A bullet of mass 20 g is fired with velocity 500 m/s. Calculate
its kinetic energy.
Solution:
Mass (m) = 20 g = 0.02 kg
Velocity (v) = 500 m/s
Kinetic Energy = ½mv²
KE = ½ × 0.02 × (500)²
KE = 0.01 × 250000
KE = 2500 J
KE = 2.5 kJ
Answer: 2500 J or 2.5 kJ (despite small mass,
high velocity gives large KE!)
A 5 kg object is raised to height of 10 m. Calculate the work done
against gravity and potential energy gained.
(g = 10 m/s²)
Solution:
Mass (m) = 5 kg
Height (h) = 10 m
g = 10 m/s²
Work done against gravity = Force × distance = (mg) × h
W = (5 × 10) × 10 = 50 × 10 = 500 J
Potential Energy gained = mgh = 5 × 10 × 10 = 500 J
Answer: Work done = PE gained = 500 J (Work done
is stored as PE!)
A 2 kg stone is dropped from height of 20 m. Find its kinetic
energy when it is 5 m above the ground.
(g = 10 m/s²)
Solution:
Mass = 2 kg, Initial height = 20 m, g = 10 m/s²
At starting point (h = 20 m):
Total Energy = PE = mgh = 2 × 10 × 20 = 400 J
KE = 0 (at rest)
At h = 5 m:
PE = mgh = 2 × 10 × 5 = 100 J
Total Energy = 400 J (constant)
KE = Total Energy - PE = 400 - 100 = 300 J
Or, distance fallen = 20 - 5 = 15 m
Work done by gravity = mgh = 2 × 10 × 15 = 300 J = KE
Answer: 300 J
A pump lifts 200 kg of water to height of 5 m in 10 seconds.
Calculate:
(a) Work done by pump
(b) Power of pump
(g = 10 m/s²)
Solution:
Mass (m) = 200 kg
Height (h) = 5 m
Time (t) = 10 s
g = 10 m/s²
(a) Work done:
Work = Force × distance = (mg) × h
W = (200 × 10) × 5
W = 2000 × 5
W = 10,000 J = 10 kJ
(b) Power:
Power = Work / Time
P = 10,000 / 10
P = 1000 W = 1 kW
Answer: (a) 10,000 J or 10 kJ, (b) 1000 W or 1 kW
An electric heater of 2 kW is used for 3 hours daily for 20 days.
Calculate:
(a) Energy consumed in kWh
(b) Energy consumed in Joules
(c) Cost if rate is ₹6 per kWh
Solution:
Power = 2 kW
Time per day = 3 hours
Number of days = 20
Total time = 3 × 20 = 60 hours
(a) Energy in kWh:
Energy = Power × Time
E = 2 × 60 = 120 kWh
(b) Energy in Joules:
E = 120 × 3.6 × 10⁶
E = 432 × 10⁶ J
E = 4.32 × 10⁸ J
(c) Cost:
Cost = 120 × ₹6 = ₹720
Answer: (a) 120 kWh, (b) 4.32 × 10⁸ J, (c) ₹720
For Work Problems:
• Identify force and displacement
• Check if they're in same direction
• If at angle, use W = F × s × cos θ
• Check sign: same direction (+), opposite (-), perpendicular
(0)
For Kinetic Energy:
• Use KE = ½mv²
• Remember: v² means velocity has large effect
• Convert mass to kg, velocity to m/s
• For change in KE, use Work-Energy theorem
For Potential Energy:
• Use PE = mgh
• Height should be from reference point
• Work done to lift = PE gained
• g = 10 m/s² (approximation) or 9.8 m/s² (accurate)
For Conservation of Energy:
• Total energy at start = Total energy at end
• (KE + PE)initial = (KE + PE)final
• As object falls: PE → KE
• As object rises: KE → PE
For Power:
• Use P = W/t or P = E/t
• Convert units: kW to W, hours to seconds (if needed)
• For electricity: Energy (kWh) = Power (kW) × Time (hours)
• Cost = Energy × Rate per unit
Common Mistakes to Avoid:
• Forgetting to convert g to kg or cm to m
• Using wrong formula (KE vs PE)
• Not squaring velocity in KE = ½mv²
• Mixing up power with energy or work
• Forgetting that 1 kWh = 3.6 × 10⁶ J
• Not including units in final answer