Energy | ICSE Class 7 Physics Notes

This note covers energy and work, units of energy, different forms of energy, energy transformations, the conservation of energy, and applications involving a pendulum, a roller coaster and hydroelectricity.

What is energy, and how is it related to work?

Definition: Energy is the capacity to do work. A force is a push or pull. In the simple case of a force moving an object along its own direction, the force does work on that object.

The word capacity is important. An object can possess energy before it starts doing work. A flowerpot raised above the ground can do work if it falls and strikes something below. The energy it has while raised need not be accompanied by movement.

How can work transfer energy?

A fielder does work while throwing a cricket ball. The ball gains energy. When the moving ball strikes the wickets, it can make them fall. Energy passes from the ball to the wickets as the ball does work on them.

Similarly, work done in raising a flowerpot gives it energy. The work and the energy are connected: doing work can transfer energy to an object, and that object can then use its energy to do work on something else.

Energy transfer means energy passing from one object or place to another. Following the transfer helps explain a sequence of events. In the cricket example, first consider the fielder and ball, and then consider the ball and wickets.

Does every effort move an object?

Pushing a rigid wall that does not move does no work on the wall. The person can still feel tired because the muscles use energy. Feeling tired and doing work on the particular object are therefore different observations.

Note: When explaining work, identify both the force doing the work and the object receiving it. In the wall example, saying that no work is done on the wall does not mean that the person's body uses no energy.

How do we calculate work done by a constant force?

For a constant force acting along the displacement, $W = F s$, where $W$ is work, $F$ is force and $s$ is displacement. Work is positive when force and displacement have the same direction and negative when they have opposite directions.

Worked example 1. A goalkeeper stops a ball by applying a force of 200 N while her hand moves backwards by 15 cm. Calculate the work done by the goalkeeper on the ball.

Formula: $W = -F d$, where $d$ is the distance moved opposite to the force. Convert centimetres to metres: $d = 15/100 = 0.15\,\mathrm{m}$.

Substitute: $W = -(200\,\mathrm{N})(0.15\,\mathrm{m}) = -30\,\mathrm{J}$.

Answer: −30 J. The work is negative because the stopping force opposes the ball's displacement.

How do we measure energy in joules and calories?

A unit is an agreed standard used to express a measurement. The SI unit of energy is the joule. SI means the International System of Units. The symbol for joule is J. The SI unit of work is also the joule (J).

What does one joule mean?

The SI unit of force is the newton, symbol N. The SI unit of displacement is the metre, symbol m. One joule of work is done when a constant force of one newton moves an object one metre in the direction of that force.

$1\,\mathrm{J} = 1\,\mathrm{N} \times 1\,\mathrm{m}$

Here, × means multiplication. The direction condition belongs to the definition: the distance moved is along the force. The joule can describe energy associated with movement, a raised object or heating. Changing the form of energy does not require changing its unit.

What is a calorie?

Heat is energy transferred because of a temperature difference, from a hotter object to a colder one. Temperature tells us how hot or cold an object is. A calorie, symbol cal, is another unit used for energy, particularly heat.

The gram, symbol g, is a unit of mass, or the quantity of matter in an object. Degrees Celsius use the symbol °C. One calorie is the heat required to raise the temperature of one gram of water from 14.5 °C to 15.5 °C.

$1\,\mathrm{cal} = 4.186\,\mathrm{J}$

Joule and calorie name units, not different forms of energy. The conversion expresses the same energy in two ways. The specified temperature interval makes the calorie definition precise; it should not be replaced by an unspecified rise in temperature.

What is kinetic energy?

Definition: Kinetic energy is the energy an object possesses because of its motion. Motion means a change in the position of an object with time.

A moving bicycle and a rolling ball possess kinetic energy. The important feature is movement. A ball does not acquire this form of energy simply because it is a ball; it possesses kinetic energy while it is moving.

How does motion give an object the capacity to do work?

The cricket ball moving towards the wickets can apply a force to them and make them move. This connects the definition of kinetic energy to the definition of energy. Motion allows the ball to do work on another object.

When an object starts from rest and gains speed, it gains kinetic energy. Rest means that its position is not changing relative to the surroundings being considered. Speed describes how fast an object moves.

For the same object, an increase in speed means an increase in kinetic energy. As it slows down, its kinetic energy decreases. When it is at rest relative to the ground, its kinetic energy for that description is zero.

How should we explain a moving object's energy?

1. Identify the moving object, such as the cricket ball.
2. State that it has kinetic energy because it is moving.
3. Identify the object on which it can apply a force, such as the wickets.
4. Explain the resulting movement and the transfer of energy.

Do not confuse zero kinetic energy with no energy of any kind. A raised flowerpot at rest still has the capacity to do work when it falls. Naming the form of energy avoids this mistake.

Derivation: Kinetic energy of a moving object

Consider an object of mass $m$ whose velocity changes from $u$ to $v$ under a constant resultant force $F$. Its acceleration $a$ is constant, and its displacement $s$ is along the force.

1. The equation of motion gives $v^2 = u^2 + 2as$, so $s = \frac{v^2-u^2}{2a}$.
2. Newton's second law gives $F = ma$. The work done is therefore $W = Fs = mas$.
3. Substituting the displacement gives $W = ma\frac{v^2-u^2}{2a} = \frac{1}{2}m(v^2-u^2)$.
4. Work done equals the change in kinetic energy. If the object starts from rest, $u = 0$, so its initial kinetic energy is zero and the work done gives its final kinetic energy.

Result: $K = \frac{1}{2}mv^2$. The SI unit of kinetic energy is the joule (J). Use mass in kilograms and speed in metres per second.

How can we calculate kinetic energy and a stopping speed?

Worked example 2. A cricket ball of mass 0.2 kg is bowled at approximately 154.8 km/h. Calculate its kinetic energy at delivery.

Formula: $K = \frac{1}{2}mv^2$. Convert the speed: $v = 154.8 \times \frac{1000}{3600} = 43\,\mathrm{m\,s^{-1}}$.

Substitute: $K = \frac{1}{2}\times 0.2\times 43^2 = 184.9\,\mathrm{J}$.

Answer: 184.9 J. The speed must be converted before it is squared.

Worked example 3. A jet aircraft of mass 15000 kg is stopped within 100 m by a wire exerting an approximately constant backward force of 367500 N. Find its speed immediately before the wire catches it.

Formula: $W = -Fd$ and $W = K_f-K_i$, where $d$ is stopping distance and the subscripts mean final and initial. Since $K_f = 0$, the initial kinetic energy equals the magnitude of the stopping work.

Substitute: $W = -(367500\,\mathrm{N})(100\,\mathrm{m}) = -36750000\,\mathrm{J}$.

Thus $\frac{1}{2}mv^2 = 36750000\,\mathrm{J}$, giving $v^2 = \frac{2\times36750000}{15000} = 4900\,\mathrm{m^2\,s^{-2}}$.

Taking the square root gives $v = \sqrt{4900} = 70\,\mathrm{m\,s^{-1}}$. Converting to kilometres per hour gives $70\times 3.6 = 252\,\mathrm{km\,h^{-1}}$.

Answer: 70 m/s, or 252 km/h, towards the aircraft carrier.

What is potential energy, and how does it differ from kinetic energy?

Definition: Potential energy is stored energy associated with an object's changed shape or with the relative positions of objects that interact through forces.

A stretched rubber band and a compressed spring can store energy. Compression means squeezing an object so that it becomes shorter or smaller in the relevant direction. Work done while stretching or compressing can be stored and used when the object is released.

How can changing a shape store energy?

A spring that is compressed and held has the capacity to move an object when released. As the spring returns towards its original shape, it transfers stored energy to that object's motion. Stored energy can therefore become kinetic energy.

Three drawings show a spring attached to a support, a ball pressed against the compressed spring, and the spring returning towards its original shape as the ball moves to the right.

See Fig. 7.14 in your NCERT textbook

How can raising an object store energy?

Gravity is the attractive force between objects such as the Earth and a ball. Raising a ball involves doing work against the Earth's pull. Energy is stored because the positions of the ball and Earth have changed relative to one another.

This stored energy is often simply described as the gravitational potential energy of the ball. For the same ball near the Earth's surface, raising it higher gives it more potential energy. On release, its stored energy can become energy of motion.

The distinction is between why the energy is present. Movement explains kinetic energy. A changed shape or position explains potential energy. An object can have both forms during a single motion, as a falling ball does before reaching the ground.

Derivation: Gravitational potential energy near the Earth's surface

Raise an object of mass $m$ gradually from the ground to a height $h$. Take its potential energy at ground level as zero and treat gravitational acceleration $g$ as constant near the Earth's surface.

1. The upward force needed to balance the object's weight is $F = mg$.
2. The displacement along this force is the height gained, so the lifting work is $W = Fh$.
3. Substituting the force gives $W = mgh$.
4. With no change in kinetic energy during gradual lifting, this work is stored as gravitational potential energy relative to the ground.

Result: $U = mgh$, where $U$ denotes gravitational potential energy. Use mass in kilograms, gravitational acceleration in metres per second squared and height in metres to obtain energy in joules.

Worked example 4. A fielder throws a cricket ball of mass 200 g to a maximum height of about 10 m above the ground. Find its potential energy at that height, taking $g = 10\,\mathrm{m\,s^{-2}}$.

Formula: $U = mgh$. Convert the mass: $m = 200/1000 = 0.2\,\mathrm{kg}$.

Substitute: $U = (0.2\,\mathrm{kg})(10\,\mathrm{m\,s^{-2}})(10\,\mathrm{m}) = 20\,\mathrm{J}$.

Answer: 20 J, taking the potential energy at ground level as zero.

What other forms of energy do we encounter?

Mechanical energy is the sum of kinetic and potential energy. It describes energy associated with motion and position or shape. Other forms help us explain warming, lighting, sound and the operation of electrical devices.

How do the forms differ?

Thermal energy and heat are closely connected, but heat emphasises the transfer between objects at different temperatures. When hotter and colder objects are in contact, energy flows from the hotter one to the colder one.

The term heat energy is commonly used when discussing energy involved in heating. In an electric water heater, electrical energy is converted into thermal energy of the water. The energy is not newly created when the water warms.

Why should we identify the form?

Naming the form explains what the energy is doing or how it is stored. A fan's rotating blades involve mechanical energy. A bell's sound involves vibrating matter. Food contains stored chemical energy that can supply the muscles during movement.

A single event can involve more than one form. In explaining it, begin with the form supplied and follow the changes. Saying that a device “uses energy” is less informative than identifying the energy it receives and the forms produced.

The forms are different descriptions of energy, rather than separate substances that must remain unchanged. Electrical energy can become thermal energy, and chemical energy can become mechanical energy. All can be expressed in joules.

How does energy change from one form to another?

Definition: Energy transformation, also called energy conversion, is the change of energy from one form into another. Interconversion describes changes between forms, such as potential energy becoming kinetic energy and later changing back.

How do we write an energy conversion?

An energy conversion diagram uses arrows to connect the names of energy forms. The arrow symbol → means “is converted into”. Write the starting form on the left and the resulting form on the right.

These diagrams identify the particular change being discussed. They do not claim that every device has just one output form. A complete energy account must include other forms and transfers wherever these occur.

How can we distinguish transfer and transformation?

In the cricket example, energy transfers from the moving ball to the wickets. In the water heater, energy transforms from electrical to thermal. Asking where energy goes identifies a transfer; asking what form it takes identifies a transformation.

Both ideas may be needed to explain one event. A compressed spring gives energy to an object in contact with it. At the same time, the explanation follows stored potential energy becoming the kinetic energy of the moving object.

1. Name the object or device being considered.
2. Identify the energy available at the start.
3. Describe the event, such as release, heating or movement.
4. Name the resulting energy form and explain where the energy goes.

This method keeps the energy pathway, meaning the sequence of transfers and transformations, clear. An arrow by itself is not an explanation: link each change to what happens in the actual situation.

What does the law of conservation of energy mean?

Definition: The law of conservation of energy states that energy can neither be created nor destroyed. It can change from one form to another, but the total energy is conserved.

Conserved means that the total amount is maintained when all relevant energy transfers and forms are included. It does not mean that the energy of each individual object, or the amount in each form, must stay unchanged.

What must be included in an energy account?

A system is the object or group of objects selected for study. Its surroundings are everything outside that selection. If energy leaves the selected object, include the energy received by its surroundings when checking the total.

For a system that exchanges no energy with its surroundings, its total energy remains the same. If energy enters or leaves, the energy within the system can change. This change is consistent with conservation because the transfer is part of the full account.

Is mechanical energy always conserved?

Friction is a force that opposes relative motion between surfaces in contact. Air resistance is the opposing force experienced by an object moving through air. These effects can reduce the mechanical energy available for continued movement.

For example, a moving body can lose mechanical energy through friction while the body and floor gain thermal energy. The decrease in mechanical energy does not imply destruction of energy. A change into a different form explains it.

Note: Mechanical energy remains constant in the ideal falling-object example when gravity acts and other effects, such as air resistance, are neglected. Total energy conservation is the broader principle and still applies when friction is present.

While a ball falls under these ideal conditions, its potential energy decreases and its kinetic energy increases by the same amount. Their sum stays constant. Saying that energy is conserved describes this balance, not an absence of change.

How does a simple pendulum demonstrate energy changes?

A simple pendulum consists of a small suspended mass, called a bob, hanging from a fixed support by a string. When moved to one side and released, the bob swings to and fro. This repeated motion is called oscillation.

What happens at different positions?

An extreme position is an end position of the swing, where the bob changes direction. The mean position is the central, lowest position. For describing stored energy here, take the bob's potential energy at the lowest point as zero.

1. At the raised starting position, the bob is momentarily at rest and has potential energy.
2. As it descends, potential energy decreases and kinetic energy increases.
3. At the lowest position, its speed and kinetic energy are greatest during that swing.
4. As it rises on the other side, kinetic energy changes back into potential energy.
5. At the opposite extreme, it is momentarily at rest before returning.

A bob is shown at two raised end positions, labelled P and R, and a lower central position Q. The end positions are labelled with potential energy and no kinetic energy; Q has kinetic energy and no potential energy.

See Fig. 7.20 in your NCERT textbook

In this diagram, P and R are labels for the ends, and Q labels the lowest point. The zero potential energy at Q is the chosen reference, or comparison level. It is not a claim that the bob has no energy there.

What does a real pendulum show?

Release the bob from one side and compare the heights reached during the first couple of swings. It reaches almost the same height on the other side. A horizontal line behind the pendulum helps make this comparison.

In real life, the pendulum slows down and eventually stops because of friction at the support and air resistance. Its mechanical energy decreases as energy is transferred to the surroundings. The total energy is not destroyed.

An ideal model is a simplified description that leaves out specified effects. If friction and air resistance are neglected, mechanical energy remains constant and the bob returns to the same height. Keep this condition separate from the observation of a real pendulum.

How does a roller coaster illustrate conservation of energy?

A roller coaster provides another way to follow energy associated with height and movement. The same reasoning applies to a ball roller coaster in a science park: a ball released from a high point moves down and then climbs along the track.

How do the energy forms change along the track?

At the high starting point, the ball has potential energy because of its height. As it descends, potential energy changes into kinetic energy. Its speed increases. On a later upward part of the track, kinetic energy changes back into potential energy and the ball slows.

At a low point, more of the available mechanical energy is in the kinetic form than at a higher point. This comparison assumes that the ball has received no additional energy and that frictional effects are neglected while comparing the positions.

Photograph: Ball roller coaster in a science park (NCERT Class 9 Figure 7.22). The photograph shows a model track supported above a base, with a tall starting structure on the right, a downward arrow, and smaller rises and dips towards the left. Positions along the track are lettered.

Why can later rises be lower?

Later high points on such a track usually have lower heights. Friction provides an explanation: some mechanical energy becomes thermal energy. Less mechanical energy remains available for the ball to climb, even though the total energy is conserved.

The ideal description neglects friction and follows an unchanged total of kinetic and potential energy. The real description includes transfers into other forms. Both use conservation; they differ in the effects included in the account.

When explaining the roller coaster, connect height, motion and energy in that order. Describe the loss or gain of height, identify the corresponding energy transformation, and then explain why friction changes the amount available for further motion.

How is energy transformed when hydroelectricity is produced?

Hydroelectricity is electricity produced using the energy of moving or falling water. Water stored at a height has potential energy. When it moves down to a lower level, this energy can change into kinetic energy.

What happens between stored water and electricity?

In a hydroelectric installation, water can be held in a reservoir, a place where water is stored. Water flowing down from a height turns a turbine, a machine with blades that rotate when moving water acts on them.

The turbine drives a generator, a device that converts mechanical energy into electrical energy. The moving water supplies energy to the turbine, and the turning machinery supplies energy to the generator.

1. Water at a height stores potential energy.
2. As water flows down, potential energy becomes kinetic energy.
3. The moving water turns the turbine, transferring energy to its rotation.
4. The generator converts the mechanical energy of rotation into electrical energy.

Draw a labelled sequence: water stored at a height → water moving down → rotating turbine → generator supplying electrical energy. Beneath the sequence, identify potential energy, kinetic energy, mechanical energy and electrical energy in the corresponding stages.

Does a generator create energy?

The word “generation” describes the production of electricity from another energy form. It does not mean creating energy from nothing. The electrical output has an energy source in the moving water and, earlier in the sequence, the water's raised position.

This is a longer conversion chain than the simple change in a falling ball. The stages must remain in order: stored energy in raised water supplies motion, motion drives machinery, and the generator converts mechanical energy into electrical energy.

Conservation requires accounting for the energy supplied and its subsequent forms. Describing electrical output as transformed energy connects the practical installation to the same principle used for a pendulum and a roller coaster.

How does power describe the rate of doing work?

Power describes how quickly work is done. Carrying the same bag up the same stairs slowly or quickly involves the same work against gravity, but completing the task in less time requires greater average power.

The average power is $P = \frac{W}{t}$, where $W$ is work done and $t$ is time taken. The SI unit of power is the watt, symbol W. One watt means one joule of work done per second: $1\,\mathrm{W} = 1\,\mathrm{J\,s^{-1}}$.

How do we calculate power when lifting a load?

Worked example 5. A weightlifter raises a 75 kg mass through 2 m in 5 seconds. Calculate the average power required, using $g = 10\,\mathrm{m\,s^{-2}}$.

Formula: $W = mgh$ and $P = \frac{W}{t}$. First find the work done against gravity, then divide by the lifting time.

Substitute: $W = (75\,\mathrm{kg})(10\,\mathrm{m\,s^{-2}})(2\,\mathrm{m}) = 1500\,\mathrm{J}$.

Then $P = \frac{1500\,\mathrm{J}}{5\,\mathrm{s}} = 300\,\mathrm{W}$.

Answer: 300 W. The lifting work is 1500 J, performed over 5 s.

How do we calculate power when a car gains speed?

Worked example 6. A car of mass 1000 kg starts from rest and reaches 72 km/h in 10 seconds. Calculate the average engine power required for this increase in kinetic energy.

Formula: $W = \frac{1}{2}m(v^2-u^2)$ and $P = \frac{W}{t}$, where $u$ and $v$ are initial and final speeds.

Convert the final speed: $v = 72\times\frac{1000}{3600} = 20\,\mathrm{m\,s^{-1}}$. The initial speed is $u = 0$.

Substitute: $W = \frac{1}{2}\times1000\times(20^2-0^2) = 200000\,\mathrm{J}$.

Then $P = \frac{200000\,\mathrm{J}}{10\,\mathrm{s}} = 20000\,\mathrm{W}$.

Answer: 20000 W for the gain in kinetic energy over 10 s.

Glossary

• Energy — The capacity to do work, which can be transferred between objects or transformed between forms.
• Work — Energy transferred by a force when, in the simple case considered, it moves an object along its direction.
• Joule — The SI unit used to express work and energy, represented by the symbol J.
• Calorie — A unit of energy equal to the heat needed to warm one gram of water from 14.5 °C to 15.5 °C.
• Kinetic energy — Energy possessed by an object because it is moving, rather than because of its position.
• Potential energy — Stored energy associated with changed shape or the relative positions of objects interacting through forces.
• Mechanical energy — The sum of the kinetic energy and potential energy associated with an object or system.
• Thermal energy — Energy associated with the warmth or hotness of matter, which can increase during heating.
• Heat — Energy transferred from a hotter object to a colder object because of their temperature difference.
• Energy transformation — A change of energy from one form into another, such as electrical energy becoming thermal energy.
• Conservation of energy — The principle that energy is neither created nor destroyed, although transfers and changes of form occur.
• Simple pendulum — A bob suspended from a fixed support by a string, able to swing to and fro.
• Hydroelectricity — Electricity obtained by using the energy of moving or falling water to drive generating machinery.
• Generator — A device that converts mechanical energy supplied to it into electrical energy.

Common errors and misconceptions

• Misconception: An object at rest cannot have energy. Correct: A raised object or a compressed spring can store potential energy while at rest.
• Misconception: Energy and work have different SI units. Correct: Both are expressed in joules; doing work is one way of transferring energy.
• Misconception: Joule and calorie are forms of energy. Correct: They are units used to measure energy, whereas kinetic and potential describe energy forms.
• Misconception: Conservation means that each energy form stays unchanged. Correct: One form can decrease as another increases; the full energy account must balance.
• Misconception: The pendulum has no energy at its lowest point. Correct: Its kinetic energy is greatest during that swing, even when potential energy is taken as zero there.
• Misconception: A real pendulum must swing forever because energy is conserved. Correct: Friction and air resistance reduce its mechanical energy through transfers to the surroundings.
• Misconception: A generator creates energy from nothing. Correct: A generator converts supplied mechanical energy into electrical energy.

Exam-style questions with model answers

Q1. Define energy and name its SI unit, including the unit symbol. [2 marks]

1. Energy is the capacity to do work; an object possessing energy can use it to do work.
2. The SI unit of energy is the joule, represented by the symbol J.

Q2. A rolling ball is moving, while a compressed spring is held still. Identify the energy form associated with each stated condition and explain the distinction. [2 marks]

1. The rolling ball has kinetic energy because it is moving.
2. The held, compressed spring has potential energy because of its changed shape. Unlike kinetic energy, this stored energy can be present while the spring is still.

Q3. One calorie warms 1 g of water from 14.5 °C to 15.5 °C, and 1 cal = 4.186 J. Use these data to define one calorie, express it in joules, and explain whether calorie and joule name energy forms or units. [3 marks]

1. One calorie is the heat required to raise the temperature of one gram of water from 14.5 °C to 15.5 °C.
2. Using the stated relationship, one calorie equals 4.186 joules. The symbols cal and J represent calorie and joule respectively.
3. Both calorie and joule are units for measuring energy. They do not name separate energy forms such as kinetic energy or potential energy.

Q4. Identify and explain the energy transformation in each situation: an electric bulb gives light; an electric water heater warms water; a bell rings after being set vibrating. [3 marks]

1. In the electric bulb, electrical energy is converted into light energy. The light produced is the output form specified in the question.
2. In the electric water heater, electrical energy becomes thermal energy of the water, so the water becomes warmer.
3. In the ringing bell, mechanical energy becomes sound energy. The bell's vibrations produce sound; the supplied energy is transformed rather than newly created.

Q5. A ball is released from rest above the ground. Neglect air resistance and consider its motion before impact. Describe its energy at release, the changes during descent, and the conserved quantity. [4 marks]

1. At release, the raised ball has gravitational potential energy. Its kinetic energy is zero because it starts from rest.
2. As the ball falls, its height decreases and its potential energy decreases. The raised position is the source of this stored energy.
3. Its speed and kinetic energy increase during descent. The increase in kinetic energy equals the decrease in potential energy under the stated conditions.
4. The sum of kinetic and potential energy, called mechanical energy, remains constant because air resistance is neglected in this falling-ball model.

Q6. A pendulum bob is released from rest at a raised position P. It passes through the lowest point Q and rises to the opposite extreme R. Neglect friction and air resistance, and take potential energy at Q as zero. Explain the energy changes from P to R in five points. [5 marks]

1. At P, the bob has potential energy because it is above Q. It is released from rest, so its kinetic energy is zero at that instant.
2. As it moves from P towards Q, its height decreases. Potential energy changes into kinetic energy, and the bob gains speed.
3. At Q, the bob has its greatest speed and kinetic energy. Its potential energy is zero relative to the reference level given in the question.
4. As it rises from Q towards R, it slows down. Kinetic energy changes back into potential energy as the bob gains height.
5. At R, the bob is momentarily at rest and has regained its starting potential energy. With friction and air resistance neglected, it reaches the same height and mechanical energy is conserved.

Q7. In a hydroelectric installation, water stored at a height flows down to turn a turbine connected to a generator. Explain the energy sequence and why producing electricity does not violate conservation of energy. [5 marks]

1. The water initially has potential energy because it is stored at a height. This is the energy available at the beginning of the stated sequence.
2. As the water flows down to a lower level, potential energy changes into kinetic energy, the energy associated with the water's motion.
3. The moving water acts on the turbine's blades and turns them. Energy is transferred from the moving water to the rotating machinery.
4. The turbine drives the connected generator. The generator converts the supplied mechanical energy into electrical energy, which is the required output.
5. No energy is created from nothing. The electrical energy comes from the earlier energy forms, and conservation requires all transfers and resulting forms to be included in the full account.

Q8. A real pendulum gradually slows down because of friction at its support and air resistance. State the conservation law and use it to explain why stopping does not mean that energy has been destroyed. [3 marks]

1. The law of conservation of energy states that energy can neither be created nor destroyed, although it can change form and transfer between objects.
2. Friction and air resistance reduce the pendulum's mechanical energy. Energy passes to its surroundings rather than remaining available for continued swinging.
3. The complete account includes the pendulum and the surroundings receiving energy. Its stopping therefore shows a decrease in mechanical energy, not destruction of total energy.

Key takeaways

• Energy is the capacity to do work, and doing work can transfer energy from one object to another.
• The joule is the SI unit of energy; the calorie is another energy unit, with 1 cal equal to 4.186 J.
• Kinetic energy is associated with motion, while potential energy is stored through changed shape or relative position.
• Energy transformations connect everyday events such as electrical heating, lighting, ringing bells and movement powered by food.
• Conservation of energy concerns the total account, including energy transferred to surroundings and energy changing into other forms.
• A pendulum repeatedly exchanges potential and kinetic energy; a real pendulum gradually loses mechanical energy through friction and air resistance.
• A roller coaster illustrates conversion between height-related potential energy and kinetic energy as it descends and rises.
• Hydroelectricity uses energy from water to turn machinery, with a generator converting mechanical energy into electrical energy.

Test yourself

What is the connection between energy and work?

Energy is the capacity to do work. Doing work can transfer energy to an object, giving it the capacity to do further work.

What does the symbol J represent?

J represents the joule, the SI unit of both work and energy.

Can a compressed spring held at rest store energy?

Yes. It can store potential energy because of its changed shape, even while it is held at rest.

What energy transformation warms water in an electric water heater?

Electrical energy is converted into thermal energy of the water, making the water warmer.

Where does a pendulum have its greatest kinetic energy during a swing?

At its lowest position, where the bob has its greatest speed during that swing.

Why does a real pendulum eventually stop swinging?

Friction at the support and air resistance reduce its mechanical energy by transferring energy to the surroundings.

What happens to a descending roller coaster's potential energy in the ideal model?

It decreases as kinetic energy increases. With friction neglected and no additional energy supplied, total mechanical energy remains constant.

What does a generator convert in a hydroelectric installation?

It converts mechanical energy supplied by the rotating turbine into electrical energy.