Think about the last time you climbed a flight of stairs. You felt your legs working, your heart pumping, your breath quickening. You were doing work — in the physics sense of the word. Now think about a car engine turning fuel into motion, a wind turbine turning breeze into electricity, or a crane lifting a heavy load. All of these are stories about work, energy, power, and machines.
These four ideas are among the most practical in all of physics. They explain how much effort is needed to get a job done, how quickly it can be done, and how machines can help us do it more easily. They are the language of engineers, athletes, and anyone who has ever tried to move something heavy. In this chapter, we are going to explore them deeply. Let us begin.
I once asked a class, "If you hold a heavy suitcase and stand still, are you doing work?" Most students said yes. I asked, "Is the suitcase moving?" They said no. "Then," I said, "according to physics, you are not doing work. You are applying a force, but no work is being done." They were shocked. Physics has its own precise language — and in this chapter, we are going to learn it.By the end of this chapter, you should be able to:
In everyday language, work means anything that requires effort. But in physics, work has a precise meaning: work is done when a force moves an object in the direction of the force.
Work: W = F × d
W = work done (J), F = force applied (N), d = distance moved in the direction of the force (m)
The SI unit of work is the joule (J). One joule is the work done when a force of one newton moves an object one metre in the direction of the force.
Think of pushing a box across the floor. You apply a force, and the box moves. You have done work. Now think of holding the box still. You are applying a force, but the box is not moving. According to physics, no work is being done — even though your muscles are tired.
| Situation | Force Applied? | Object Moves? | Work Done? |
|---|---|---|---|
| Pushing a box across the floor | Yes | Yes | Yes |
| Holding a box still | Yes | No | No |
| Carrying a box horizontally | Yes (upward) | Yes (horizontal) | No (force and motion perpendicular) |
| Lifting a box upward | Yes (upward) | Yes (upward) | Yes |
Energy is the ability to do work. It is a scalar quantity, measured in joules (J). Energy is what allows things to happen — it is the currency of the universe.
Forms of energy:
| Form | Description | Example |
|---|---|---|
| Kinetic energy | Energy of motion | A moving car, a flying arrow |
| Potential energy | Stored energy due to position | A book on a shelf, water behind a dam |
| Thermal energy | Energy from heat | A hot cup of tea |
| Chemical energy | Energy stored in chemical bonds | Food, fuel, batteries |
| Electrical energy | Energy from electric charges | Electricity in wires |
| Light energy | Energy from electromagnetic waves | Sunlight, a lamp |
| Sound energy | Energy from vibrations | A ringing bell |
| Nuclear energy | Energy stored in atomic nuclei | The Sun, nuclear power plants |
Energy can be converted from one form to another, but it cannot be created or destroyed. This is the law of conservation of energy.
The law of conservation of energy is one of the most fundamental laws of the universe. It tells us that energy is never lost — it just changes form. When you burn fuel in a car, chemical energy becomes kinetic energy and thermal energy. The total amount of energy in the universe is constant. This is a profound truth.Kinetic energy is the energy of motion. Any object that is moving has kinetic energy.
Kinetic energy: KE = ½ × m × v²
KE = kinetic energy (J), m = mass (kg), v = velocity (m/s)
Notice that kinetic energy depends on the square of the velocity. This means that doubling the speed gives four times the kinetic energy. This is why speeding is so dangerous — a car travelling at 100 km/h has four times the kinetic energy of a car travelling at 50 km/h.
Think of a moving car. The faster it goes, the more kinetic energy it has. A heavier car also has more kinetic energy at the same speed. This is why large trucks need longer braking distances.
The squared relationship between kinetic energy and velocity is one of the most important safety lessons in physics. It is why speed limits exist, why crash tests are conducted at different speeds, and why a small increase in speed can dramatically increase the severity of an accident. Physics saves lives.Potential energy is stored energy due to an object's position or condition. There are several types, but the most common in mechanics is gravitational potential energy.
Gravitational potential energy: PE = m × g × h
PE = potential energy (J), m = mass (kg), g = gravitational field strength (N/kg), h = height above reference point (m)
The higher an object is, the more gravitational potential energy it has. The heavier it is, the more potential energy it has.
Think of a book on a shelf. If you lift it higher, it gains potential energy. If it falls, that potential energy converts to kinetic energy. This is the energy that allows a roller coaster to speed down a hill without an engine.
Other forms of potential energy:
The law of conservation of energy states: Energy cannot be created or destroyed; it can only be converted from one form to another.
In a closed system, the total energy remains constant. When a ball falls, its potential energy converts to kinetic energy. When it hits the ground, some energy converts to thermal and sound energy. But the total amount of energy never changes.
Example: A ball at the top of a hill has potential energy. As it rolls down, potential energy converts to kinetic energy. At the bottom, all the potential energy has become kinetic energy (ignoring friction).
| Position | Potential Energy | Kinetic Energy | Total Energy |
|---|---|---|---|
| Top of hill | Maximum | Zero | Constant |
| Middle of hill | Half | Half | Constant |
| Bottom of hill | Zero | Maximum | Constant |
Power is the rate of doing work or the rate of transferring energy. It tells you how quickly work is done.
Power: P = W / t
P = power (W), W = work done (J), t = time taken (s)
Alternative form: P = F × v (when force and velocity are in the same direction)
The SI unit of power is the watt (W). One watt is one joule per second (1 W = 1 J/s).
Think of two people lifting the same box to the same height. One does it quickly, the other slowly. They both do the same amount of work, but the faster one has more power. Power is about speed.
| Device | Power |
|---|---|
| LED bulb | 10 W |
| Laptop | 50 W |
| Electric kettle | 2 000 W |
| Car engine | 100 000 W |
| Jet engine | 100 000 000 W |
A machine is a device that makes work easier by changing the size or direction of a force. Machines do not create energy — they simply transfer or transform it.
Key terms:
Mechanical advantage: MA = Load / Effort
Velocity ratio: VR = distance moved by effort / distance moved by load
Efficiency: Efficiency = (MA / VR) × 100%
Types of machines:
| Machine | Type | Example |
|---|---|---|
| Lever | Simple | See-saw, crowbar |
| Pulley | Simple | Flagpole, crane |
| Inclined plane | Simple | Ramp |
| Wedge | Simple | Axe, knife |
| Screw | Simple | Bolt, jar lid |
| Wheel and axle | Simple | Bicycle, car |
| Gears | Compound | Bicycle gears, clock |
A pulley is a wheel with a groove for a rope or cable. Pulleys are used to lift heavy loads. There are three main types:
Think of lifting a flag. A fixed pulley at the top of the flagpole allows you to pull down on the rope to lift the flag up. You are not lifting the flag with less force — you are just changing the direction of your pull.
| Pulley System | Mechanical Advantage | Effort Needed |
|---|---|---|
| Fixed pulley | 1 | Equal to load |
| Movable pulley | 2 | Half the load |
| Block and tackle (4 ropes) | 4 | Quarter of the load |
An inclined plane is a flat surface set at an angle. It allows you to raise a load to a height using less force than lifting it directly.
How it works:
Inclined plane: VR = length of slope / height of slope
Think of pushing a wheelchair up a ramp. It is easier than lifting it straight up, but you have to push it a longer distance. The ramp trades force for distance.
The inclined plane is one of the oldest machines in human history. The pyramids of Egypt were built using ramps. The principle is simple: spread the work over a longer distance to reduce the force needed at any moment. It is a beautiful example of physics in action.No machine is 100% efficient. Some energy is always lost to friction, heat, or sound. Efficiency is a measure of how much of the input energy is converted to useful output energy.
Efficiency: Efficiency = (useful work output / total work input) × 100%
Alternative: Efficiency = (MA / VR) × 100%
A machine with high efficiency wastes less energy. A machine with low efficiency wastes more. For example, a car engine is only about 25% efficient — most of the energy in the fuel is lost as heat.
| Machine | Typical Efficiency |
|---|---|
| Electric motor | 85–95% |
| Car engine | 20–30% |
| Incandescent bulb | 5% |
| LED bulb | 40–50% |
| Human body (muscles) | 20–25% |
Work: W = F × d
W = work (J), F = force (N), d = distance (m)
Kinetic energy: KE = ½ × m × v²
Potential energy: PE = m × g × h
Power: P = W / t
Power (alternative): P = F × v
Mechanical advantage: MA = Load / Effort
Velocity ratio: VR = distance moved by effort / distance moved by load
Efficiency: Efficiency = (MA / VR) × 100%
Conservation of energy: Total energy before = Total energy after
Question: A force of 50 N moves an object 8 m in the direction of the force. Calculate the work done.
Answer:
Formula: W = F × d
Substitution: W = 50 N × 8 m
Answer: W = 400 J
Units check: N × m = J. The answer is in joules, correct for work. Does 400 J make sense? Yes, it is a moderate amount of work — about the energy needed to lift a 40 kg box 1 metre.Question: A 1 200 kg car is moving at 20 m/s. Calculate its kinetic energy.
Answer:
Formula: KE = ½ × m × v²
Substitution: KE = ½ × 1 200 kg × (20 m/s)²
KE = ½ × 1 200 × 400
Answer: KE = 240 000 J = 240 kJ
Units check: kg × (m/s)² = kg m²/s² = J. The answer is in joules. Does 240 kJ make sense? Yes — a moving car has a lot of kinetic energy, which is why car crashes can be so dangerous.Question: A 5 kg book is lifted to a shelf 2 m above the floor. Calculate its gravitational potential energy. Use g = 10 N/kg.
Answer:
Formula: PE = m × g × h
Substitution: PE = 5 kg × 10 N/kg × 2 m
Answer: PE = 100 J
Units check: kg × N/kg × m = N m = J. The answer is in joules. Notice that the potential energy is equal to the work done in lifting the book. This is a beautiful example of energy conservation.Question: A machine does 3 000 J of work in 15 seconds. Calculate its power.
Answer:
Formula: P = W / t
Substitution: P = 3 000 J / 15 s
Answer: P = 200 W
Units check: J / s = W. The answer is in watts, correct for power. Does 200 W make sense? Yes, it is about the power of a small electric motor or a bright light bulb.Question: A machine has a mechanical advantage of 5 and a velocity ratio of 8. Calculate its efficiency.
Answer:
Formula: Efficiency = (MA / VR) × 100%
Substitution: Efficiency = (5 / 8) × 100%
Answer: Efficiency = 62.5%
Units check: the answer is a percentage. Notice that the efficiency is less than 100%, as expected for a real machine. Some energy is always lost to friction and heat.Graphs help us understand the relationships between work, energy, and power.
Force vs distance: If you plot force on the vertical axis and distance on the horizontal axis, the area under the graph gives the work done. For a constant force, the graph is a horizontal line, and the area is a rectangle: W = F × d.
Kinetic energy vs velocity: If you plot kinetic energy on the vertical axis and velocity on the horizontal axis, you get a curve. Kinetic energy is proportional to the square of velocity, so the graph is a parabola.
Power vs time: If you plot power on the vertical axis and time on the horizontal axis, the area under the graph gives the energy transferred.
These graphs help us visualise the relationships in work, energy, and power. They turn equations into pictures.
Think of a graph as a map of a relationship. The shape tells you how one quantity changes with another.
Apparatus: A pulley system (block and tackle), weights, a spring balance, a metre rule, and a string.
Method:
Calculation: If the load is 20 N, the effort is 6 N, the distance moved by effort is 0.4 m, and the distance moved by load is 0.1 m, then MA = 20/6 = 3.33, VR = 0.4/0.1 = 4, and efficiency = (3.33/4) × 100% = 83.3%.
Precautions:
Likely source of error: Friction in the pulleys reduces efficiency. The weight of the moving parts also affects the results.
This experiment is a beautiful way to see the trade-off between force and distance. You will find that the effort is less than the load, but you have to pull a longer distance. And you will see that no machine is 100% efficient — some energy is always lost.Work is done when a force moves an object in the direction of the force. Its SI unit is the joule (J).
Energy is the ability to do work. It is measured in joules (J).
Energy cannot be created or destroyed; it can only be converted from one form to another.
KE = ½ × m × v²; PE = m × g × h.
Power is the rate of doing work. Its SI unit is the watt (W).
W = F × d = 30 × 5 = 150 J.
Mechanical advantage is the ratio of load to effort. MA = Load / Effort.
Because some energy is always lost to friction, heat, or sound. No machine is perfectly efficient.
(a) Define work and state its SI unit. [2]
(b) A force of 80 N moves an object 12 m in the direction of the force. Calculate the work done. [3]
(c) Explain why no work is done when you carry a box horizontally. [3]
(a) Work is done when a force moves an object in the direction of the force. SI unit: joule (J). (2 marks.)
(b) W = F × d = 80 × 12 = 960 J. (1 mark for formula, 1 mark for substitution, 1 mark for answer.)
(c) The force you apply is upward (to support the box), but the box moves horizontally. The force and motion are perpendicular, so no work is done in the physics sense. (3 marks.)
(a) Define kinetic energy and potential energy. [4]
(b) A 0.5 kg ball is moving at 10 m/s. Calculate its kinetic energy. [3]
(c) A 2 kg book is lifted 1.5 m. Calculate its potential energy. Use g = 10 N/kg. [3]
(a) Kinetic energy is the energy of motion (KE = ½mv²). Potential energy is stored energy due to position (PE = mgh). (4 marks.)
(b) KE = ½ × 0.5 × (10)² = ½ × 0.5 × 100 = 25 J. (3 marks.)
(c) PE = m × g × h = 2 × 10 × 1.5 = 30 J. (3 marks.)
(a) Define power and state its SI unit. [2]
(b) A machine does 5 000 J of work in 20 seconds. Calculate its power. [3]
(c) A machine has a mechanical advantage of 6 and a velocity ratio of 10. Calculate its efficiency. [4]
(a) Power is the rate of doing work. SI unit: watt (W). (2 marks.)
(b) P = W / t = 5 000 / 20 = 250 W. (1 mark for formula, 1 mark for substitution, 1 mark for answer.)
(c) Efficiency = (MA / VR) × 100% = (6 / 10) × 100% = 60%. (2 marks for formula, 2 marks for answer.)
A roller coaster car of mass 500 kg starts from rest at a height of 20 m. Calculate its speed at the bottom of the track, assuming no energy losses. Use g = 10 N/kg.
PE at top = mgh = 500 × 10 × 20 = 100 000 J. At the bottom, all PE has converted to KE: KE = ½mv² = 100 000 → ½ × 500 × v² = 100 000 → 250v² = 100 000 → v² = 400 → v = 20 m/s.
Explain why a machine cannot have an efficiency greater than 100%.
A machine cannot output more energy than it takes in, because energy cannot be created. Some energy is always lost to friction, heat, or sound. Therefore, the useful work output is always less than the total work input, so efficiency is always less than 100%.
A student says, "A machine reduces the force needed, so it reduces the work done." Is this correct? Explain.
No. A machine reduces the force needed, but it increases the distance over which the force is applied. The work done (force × distance) remains the same (ignoring friction). Machines trade force for distance — they do not reduce the total work.
Work, energy, and power are the currency of the universe — they explain how everything gets done, from lifting a feather to launching a rocket.
