Work, Energy, and Power ⚡

students, in this lesson you will learn how motion, force, and energy are connected in everyday situations like lifting a backpack, braking a bike, or charging a phone. The ideas of work, energy, and power help physicists describe how forces change motion and how quickly energy is transferred. By the end of this lesson, you should be able to explain the main terms, use IB Physics SL methods to solve problems, and connect these ideas to the larger topic of Space, Time and Motion.

Learning objectives

• Explain the meanings of work, energy, and power.
• Apply the equations and reasoning used in IB Physics SL.
• Connect these ideas to motion, force, momentum, and energy transfer.
• Use examples and evidence to describe how work, energy, and power appear in real life.

What is work? 🔧

In physics, work has a precise meaning. Work is done when a force causes an object to move through a distance in the direction of the force. If a force does not move the object, then no mechanical work is done on that object.

The basic equation for work is

$$W = Fd\cos\theta$$

where $W$ is work, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and the displacement.

This equation shows an important idea: only the part of the force in the direction of motion does work. If the force is exactly in the same direction as the motion, then $\theta = 0$ and $\cos\theta = 1$, so

$$W = Fd$$

If the force is perpendicular to the motion, then $\theta = 90^\circ$ and $\cos\theta = 0$, so

$$W = 0$$

That is why carrying a heavy box horizontally at steady speed can feel tiring, but the upward force from your arms does no work on the box if the box moves horizontally. The force is upward while the motion is sideways.

Work is measured in joules, symbol $\text{J}$. One joule is one newton-meter:

$$1\,\text{J} = 1\,\text{N}\,\text{m}$$

A useful real-world example is pushing a shopping cart. If you push with a force of $50\,\text{N}$ over a distance of $4\,\text{m}$ in the same direction, the work done is

$$W = 50 \times 4 = 200\,\text{J}$$

This means $200\,\text{J}$ of energy has been transferred by the force.

Energy: the ability to do work 🌟

Energy is the ability to do work. In physics, energy is not “used up” in a simple way. Instead, energy is transferred from one store to another. For example, when you lift a book, chemical energy in your muscles is transferred into gravitational potential energy of the book.

Two of the most important energy stores in IB Physics SL are:

• Gravitational potential energy, $E_p$
• Kinetic energy, $E_k$

Gravitational potential energy near Earth’s surface is given by

$$E_p = mgh$$

where $m$ is mass, $g$ is gravitational field strength, and $h$ is height.

Kinetic energy is the energy of motion:

$$E_k = \frac{1}{2}mv^2$$

where $m$ is mass and $v$ is speed.

These formulas are very useful because they link directly to motion. If an object moves faster, its kinetic energy increases as the square of speed. That means doubling the speed makes the kinetic energy four times larger.

Example: a moving bicycle 🚲

Suppose a bicycle of mass $20\,\text{kg}$ moves at $6\,\text{m s}^{-1}$. Its kinetic energy is

$$E_k = \frac{1}{2}(20)(6^2) = 360\,\text{J}$$

If the speed increases to $12\,\text{m s}^{-1}$, then

$$E_k = \frac{1}{2}(20)(12^2) = 1440\,\text{J}$$

The speed has doubled, but the kinetic energy has become four times larger. This is one reason braking from a high speed needs a lot more energy transfer than braking from a low speed.

The work-energy principle 📘

A key IB Physics idea is that the total work done on an object equals the change in its kinetic energy:

$$W_{\text{net}} = \Delta E_k$$

where $W_{\text{net}}$ is the net work done by all forces, and $\Delta E_k$ is the change in kinetic energy.

This is called the work-energy principle. It is very useful because it connects forces with motion without always needing to analyze every detail of acceleration.

For example, if a net force does positive work on an object, the object speeds up and its kinetic energy increases. If a net force does negative work, the object slows down and its kinetic energy decreases.

Example: braking a car 🚗

When a car brakes, friction in the brakes and tires does negative work on the car. The car’s kinetic energy is transferred mainly into thermal energy in the brakes and surroundings.

If a car of mass $1000\,\text{kg}$ slows from $20\,\text{m s}^{-1}$ to rest, the change in kinetic energy is

$$\Delta E_k = 0 - \frac{1}{2}(1000)(20^2) = -200000\,\text{J}$$

The negative sign means the car lost kinetic energy. That energy was transferred away from the car, mostly as heat.

This is an important scientific idea: energy is conserved, but it changes form and location.

Power: how fast work is done ⏱️

Power tells us the rate at which work is done or energy is transferred. The equation for power is

$$P = \frac{W}{t}$$

where $P$ is power, $W$ is work, and $t$ is time.

Power is measured in watts, symbol $\text{W}$, and

$$1\,\text{W} = 1\,\text{J s}^{-1}$$

A device with high power transfers energy quickly. A low-power device transfers energy more slowly.

Example: climbing stairs 🪜

Two students climb the same stairs to the same height. They do the same amount of work against gravity if their masses are the same. But if students climbs faster, students’s power output is larger because the same work is done in less time.

If a person does $600\,\text{J}$ of work in $5\,\text{s}$, then

$$P = \frac{600}{5} = 120\,\text{W}$$

If the same work is done in $10\,\text{s}$, then

$$P = \frac{600}{10} = 60\,\text{W}$$

So power is about speed of energy transfer, not how much total energy is transferred.

There is also a useful relation when an object moves at constant speed under a force in the same direction as the motion:

$$P = Fv$$

This follows from $W = Fd$ and $v = \frac{d}{t}$. It is often used in transport questions.

Efficiency and energy transfer ✅

Not all energy transferred by a device becomes useful energy. Some is usually transferred to the surroundings as thermal energy or sound. Efficiency measures how much of the input energy becomes useful output energy.

The equation for efficiency is

$$\text{Efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}$$

Sometimes it is written as a percentage:

$$\text{Efficiency} = \frac{\text{useful output}}{\text{input}} \times 100\%$$

For example, an electric motor may transfer energy to lift a load, but some energy is wasted as heat in the wires and motor. A more efficient system wastes less energy.

This matters in everyday life. A bicycle is often more energy-efficient than a car for short trips because much less energy is transferred to unnecessary thermal energy. A household lamp that becomes hot is less efficient than one that transfers more of the input energy into light.

Connecting work, energy, and power to motion and forces 🧠

Work, energy, and power fit naturally into the wider topic of Space, Time and Motion because they describe how forces affect movement.

• Forces cause acceleration and change momentum.
• Work explains how forces transfer energy.
• Energy helps predict changes in speed and height.
• Power tells how quickly these changes happen.

For example, when a runner accelerates from rest, their muscles apply forces that do work on their body. Chemical energy is transferred into kinetic energy. If the runner climbs a hill, some kinetic energy may be transferred into gravitational potential energy. If friction is large, some energy is transferred into thermal energy.

In many problems, you can use conservation of energy to find unknown speeds or heights. A dropped object loses gravitational potential energy and gains kinetic energy. If air resistance is neglected, the total mechanical energy remains constant:

$$E_p + E_k = \text{constant}$$

This is a powerful way to analyze motion without tracking every force in detail.

Conclusion 🎯

students, work, energy, and power are core ideas that help explain motion in a clear and measurable way. Work is done when a force causes displacement in its direction. Energy is the ability to do work and is transferred between stores such as kinetic energy and gravitational potential energy. Power shows how quickly work is done or energy is transferred. These ideas are essential in IB Physics SL because they connect forces, motion, and conservation laws in everyday and scientific situations.

When you study moving objects, think about the force, the displacement, the energy changes, and the rate of transfer. Doing so will help you solve problems and understand how physics describes the world. 🌍

Study Notes

• Work is done when a force causes displacement in the direction of the force.
• The equation for work is $W = Fd\cos\theta$.
• Work is measured in joules, and $1\,\text{J} = 1\,\text{N}\,\text{m}$.
• Energy is the ability to do work, and it is transferred between stores.
• Gravitational potential energy is $E_p = mgh$.
• Kinetic energy is $E_k = \frac{1}{2}mv^2$.
• The work-energy principle is $W_{\text{net}} = \Delta E_k$.
• Positive net work increases kinetic energy; negative net work decreases it.
• Power is the rate of doing work: $P = \frac{W}{t}$.
• Power is measured in watts, and $1\,\text{W} = 1\,\text{J s}^{-1}$.
• Another useful power equation is $P = Fv$ when force and motion are in the same direction.
• Efficiency is $\frac{\text{useful output}}{\text{total input}}$.
• Work, energy, and power connect force and motion to the broader study of Space, Time and Motion.