Work, Energy and Power — Full Explanation + 50 Practice
Questions
These topics are closely related in Physics:
Force can do work.
When work is done, energy is transferred.
Power tells us how fast the work is done or energy is transferred.
1. WORK
What is Work?
In everyday language, you may say you have done work when you are tired. In Physics, however, work
is done only when a force causes an object to move through a distance.
Formula
W = Fd
Where:
W = Work done in joules (J)
F = Force in newtons (N)
d = Distance moved in metres (m)
SI Unit of Work
The SI unit is the joule (J).
1 joule = 1 newton × 1 metre
Therefore:
1J = 1N m
Example 1
A force of 20N moves a box through 5m.
Calculate the work done.
Solution
W = Fd
W = 20 × 5
W = 100J
​
Example 2
A boy pushes a cart with a force of 50N through 10m.
W = Fd
W = 50 × 10
W = 500J
​
2. WORK DONE AT AN ANGLE
Sometimes the force does not act in exactly the same direction as the movement.
The formula becomes:
W = F d cos θ
Where:
θ is the angle between the force and the direction of motion.
Example
A force of 100N pulls an object through 5m at an angle of 60∘ .
W = F d cos θ
W = 100 × 5 × cos 60∘
Since:
cos 60∘ = 0.5
W = 100 × 5 × 0.5
W = 250J
3. WHEN IS NO WORK DONE?
​
No work is done when:
1. There is no movement
For example, if you push a wall and it does not move:
d=0
Therefore:
W = F × 0 = 0J
2. There is no force
If no force acts, no mechanical work is done.
3. The force is perpendicular to the movement
For example, in uniform circular motion, the centripetal force is perpendicular to the direction of
motion.
Therefore:
W = F d cos 90∘
Since:
cos 90∘ = 0
W =0
​
4. ENERGY
What is Energy?
Energy is the capacity or ability to do work.
The SI unit of energy is also the:
Joule (J)
There are different forms of energy.
Examples include:
Mechanical energy
Kinetic energy
Potential energy
​
Heat energy
Electrical energy
Chemical energy
Light energy
Sound energy
Nuclear energy
In this topic, we will concentrate mainly on:
1. Kinetic Energy
2. Potential Energy
5. KINETIC ENERGY
What is Kinetic Energy?
Kinetic energy is the energy possessed by an object because of its motion.
A moving car has kinetic energy.
A flying football has kinetic energy.
A running student has kinetic energy.
Formula
1 2
mv
2
KE =
​
Where:
KE = Kinetic Energy in joules
m = Mass in kilograms
v = Velocity in metres per second
Example 1
Calculate the kinetic energy of a 4kg object moving at 5m/s.
1 2
mv
2
KE =
​
Substitute:
KE =
1
× 4 × 52
2
​
First:
52 = 25
Therefore:
KE =
1
× 4 × 25
2
​
KE = 2 × 25
KE = 50J
​
Important Point
Velocity is squared.
KE =
1 2
mv
2
​
This means that if velocity doubles:
v → 2v
Then:
1
m(2v)2
2
1
KE = m(4v 2 )
2
KE =
Therefore, kinetic energy becomes:
4 times
​
If velocity triples, kinetic energy becomes:
9 times
​
6. POTENTIAL ENERGY
What is Potential Energy?
Potential energy is energy stored in an object because of:
Its position
Its condition
Its height
The most common type studied here is gravitational potential energy.
7. GRAVITATIONAL POTENTIAL ENERGY
The formula is:
PE = mgh
Where:
PE = Potential energy in joules
m = Mass in kilograms
g = Acceleration due to gravity
h = Height in metres
For many school calculations:
g = 10m/s2
unless another value is given.
Example
A 5kg object is lifted to a height of 8m.
Take:
g = 10m/s2
Calculate the potential energy.
PE = mgh
PE = 5 × 10 × 8
PE = 400J
8. MECHANICAL ENERGY
Mechanical energy is the combination of:
Kinetic Energy
​
Potential Energy
Therefore:
ME = KE + PE
Example
A 2kg object is moving at 4m/s at a height of 10m.
Take:
g = 10m/s2
Step 1: Calculate KE
1 2
mv
2
KE =
KE =
​
1
× 2 × 42
2
​
KE = 16J
Step 2: Calculate PE
PE = mgh
PE = 2 × 10 × 10
PE = 200J
Step 3: Calculate Mechanical Energy
ME = KE + PE
ME = 16 + 200
ME = 216J
​
9. LAW OF CONSERVATION OF ENERGY
Energy cannot be:
Created
Destroyed
Energy can only be transformed from one form to another.
For example:
Falling object
At the top:
PE = M aximum
KE = M inimum
As the object falls:
PE ↓
KE ↑
Just before reaching the ground:
PE ≈ M inimum
KE = M aximum
If air resistance is ignored:
Total Mechanical Energy remains constant
10. POWER
What is Power?
Power is the rate at which work is done.
It can also be defined as the:
Rate at which energy is transferred.
Formula
P =
Where:
P = Power in watts
W = Work done in joules
W
t
​
​
t = Time in seconds
SI Unit of Power
The SI unit is:
Watt (W)
​
One watt means:
1W = 1J/s
Therefore:
A machine with a power of 1 watt does 1 joule of work every second.
Example
A machine does 500J of work in 10s.
Calculate the power.
W
t
500
P =
10
P =
​
​
P = 50W
11. OTHER FORMULA FOR POWER
Since:
W = Fd
and:
P =
Then:
W
t
​
​
P =
Fd
t
​
But:
d
=v
t
​
Therefore:
P = Fv
​
Where:
F = Force
v = Velocity
12. EFFICIENCY
Not all energy supplied to a machine becomes useful energy.
Some energy may be lost as:
Heat
Sound
Friction
Formula
Efficiency =
Useful Output Energy
× 100%
Input Energy
Efficiency =
Useful Power Output
× 100%
Power Input
​
Or:
​
Example
A machine receives 1000J of energy and produces 800J of useful energy.
Eff iciency =
800
× 100
1000
​
Eff iciency = 80%
​
SUMMARY OF IMPORTANT FORMULAS
Quantity
Formula
Unit
Work
W = Fd
Joule (J)
Work at angle
W = F d cos θ
Joule (J)
Kinetic Energy
KE = 12 mv 2
Joule (J)
Potential Energy
PE = mgh
Joule (J)
Mechanical Energy
ME = KE + PE
Joule (J)
Power
P = Wt
Watt (W)
Power
P = Fv
Watt (W)
Efficiency
U sef ul
× 100%
Input
Percentage
​
​
​
50 PRACTICE QUESTIONS
SECTION A: WORK — Questions 1–10
1.
A force of 10N moves an object through 5m. Calculate the work done.
2.
A force of 25N pushes a box through 8m. Calculate the work done.
3.
A worker applies a force of 50N over a distance of 12m. Find the work done.
4.
A force of 200N moves a vehicle through 15m. Calculate the work done.
5.
A student pushes a table with a force of 100N , but the table does not move. Calculate the work done.
6.
A force of 80N moves an object through 20m. Find the work done.
7.
A force of 150N pulls a load through 4m. Calculate the work done.
8.
A force of 500N moves an object through 6m. Find the work done.
9.
A force of 40N acts at an angle of 60∘ to move an object through 10m. Calculate the work done.
10.
A force of 100N acts at 90∘ to the direction of motion. The object moves through 20m. Calculate the
work done.
SECTION B: KINETIC ENERGY — Questions 11–20
11.
Calculate the kinetic energy of a 2kg object moving at 4m/s.
12.
A 5kg object moves at 6m/s. Find its kinetic energy.
13.
Calculate the kinetic energy of a 10kg body moving at 3m/s.
14.
A car of mass 1000kg moves at 20m/s. Calculate its kinetic energy.
15.
A 0.5kg ball moves at 10m/s. Calculate its kinetic energy.
16.
A 4kg object has a kinetic energy of 200J . Calculate its velocity.
17.
A 2kg object moves at 8m/s. Calculate its kinetic energy.
18.
A body has a mass of 20kg and moves at 5m/s. Find its kinetic energy.
19.
Calculate the kinetic energy of a 50kg person running at 4m/s.
20.
A body has a kinetic energy of 450J and a mass of 10kg . Calculate its velocity.
SECTION C: POTENTIAL ENERGY — Questions 21–30
Take:
g = 10m/s2
unless otherwise stated.
21.
A 2kg object is lifted through 5m. Calculate its potential energy.
22.
Calculate the potential energy of a 10kg object at a height of 8m.
23.
A 5kg object is raised to a height of 20m. Calculate its potential energy.
24.
A 50kg student climbs to a height of 4m. Calculate the potential energy gained.
25.
A 100kg load is lifted through 3m. Calculate the potential energy gained.
26.
A body has a mass of 8kg and potential energy of 400J . Calculate its height.
27.
A 10kg object has potential energy of 500J . Calculate its height.
28.
A body is raised to a height of 15m and gains 3000J of potential energy. Calculate its mass.
29.
A 4kg object is lifted to a height of 25m. Calculate its potential energy.
30.
A 30kg object is lifted through 12m. Calculate the potential energy gained.
SECTION D: POWER — Questions 31–40
31.
A machine does 500J of work in 10s. Calculate its power.
32.
A motor does 2000J of work in 20s. Find its power.
33.
A student does 600J of work in 15s. Calculate the power.
34.
A machine has a power of 100W and operates for 30s. Calculate the work done.
35.
A motor does 5000J of work at a power of 250W . Calculate the time taken.
36.
A machine does 9000J of work in 30s. Calculate its power.
37.
A crane lifts a load and does 12000J of work in 40s. Find its power.
38.
A 500W machine works for 20s. Calculate the work done.
39.
A force of 100N moves an object at a velocity of 5m/s. Calculate the power.
40.
A force of 200N acts on an object moving at 10m/s. Find the power.
SECTION E: MIXED WORK, ENERGY AND POWER — Questions 41–
50
41.
A 10kg object is lifted through 5m.
Take:
g = 10m/s2
Calculate:
a. The work done
b. The potential energy gained
42.
A 20kg load is lifted through 10m in 5s.
Calculate:
a. The work done
b. The power developed
43.
A 5kg object falls freely from a height of 20m.
Calculate its potential energy at the top.
Take:
g = 10m/s2
44.
A 2kg stone falls from a height of 10m. Ignore air resistance.
Calculate:
a. Its potential energy at the top
b. Its kinetic energy just before hitting the ground
45.
A 1000kg car moves at 10m/s.
Calculate its kinetic energy.
If the speed doubles, calculate the new kinetic energy.
46.
A machine receives 2000J of energy and produces 1500J of useful work.
Calculate its efficiency.
47.
A motor has an input power of 500W and produces a useful output power of 400W .
Calculate its efficiency.
48.
A 50kg load is lifted through 8m in 4s.
Take:
g = 10m/s2
Calculate:
a. Work done
b. Power developed
49.
A 2kg object moves at 10m/s at a height of 5m.
Calculate:
a. Kinetic energy
b. Potential energy
c. Total mechanical energy
Take:
g = 10m/s2
50.
A 100kg machine lifts a load through a height of 15m in 30s.
Take:
g = 10m/s2
Calculate:
a. The work done
b. The potential energy gained
c. The power developed