Energy | ICSE Class 8 Physics Notes

This note covers work, energy, joules, kinetic energy, potential energy, gravitational potential energy, energy transformations, conservation of energy, the simple pendulum, power, and calculations involving force, displacement, mass, speed, height and time.

What does work mean in physics?

Work is done by a force when an object undergoes displacement in the direction of that force. A force is a push or pull. Displacement describes the change from an object's initial position to its final position, including direction.

The scientific meaning of work is more precise than its everyday meaning. Feeling tired does not, by itself, show that work has been done on an object. Identify the object, the force acting on it and the displacement before deciding whether that force does work.

How are force and displacement connected?

For a constant force acting along the displacement, work is the product of the force and displacement. Constant means that the force does not change in magnitude or direction during the displacement. Magnitude means the size of a quantity.

Definition: Work done by a constant force equals the force multiplied by the displacement in the direction of that force.

Let W represent work done, F the force and s the displacement in the direction of the force. Their relationship is:

W = F × s

Lifting a bag gives a direct example. The lifting force acts upwards and the bag moves upwards. The force therefore does work on the bag. The same relationship applies when force and displacement both point horizontally.

The drawing shows blocks displaced horizontally in one part and vertically in the other. Arrows labelled F and s point along the same direction within each part.

See Fig. 7.3 in your NCERT textbook

At the same displacement, a larger force does more work. With the same force, a larger displacement in its direction also means more work. Both factors matter, so knowing the force alone is insufficient to calculate the work done.

How is work measured, and when is it zero?

The SI, or International System of Units, provides standard units for physical quantities. The SI unit of work is the joule, represented by J. The SI unit of force is the newton, represented by N. The SI unit of displacement is the metre, represented by m.

One joule is the work done when a constant force of one newton displaces an object one metre in the force's direction. The unit symbol m means metre; later, the letter m in a formula represents mass. Its meaning depends on its position.

1 J = 1 N × 1 m

Why can effort produce no work on an object?

When a person pushes a rigid wall that does not move, the displacement of the wall is zero. The work done on the wall is therefore zero. The person's muscles still use internal energy, which explains why the person may feel tired.

A force perpendicular to displacement also does no work on the object. Perpendicular means at a right angle. A girl supporting a box while walking horizontally applies an upward force, while the box's displacement is horizontal. That upward supporting force does no work on the box.

Note: State which force does work on which object. Saying that a supporting force does no work on a horizontally carried box does not mean that the carrier uses no energy.

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

Energy is the capacity to do work. An object with energy can apply a force to another object and cause it to move. The SI unit of energy is the joule, the same unit used for work.

A moving cricket ball can strike wickets and make them fall. A flowerpot raised to a height can damage something below if it falls. The ball and the raised pot possess energy, although one example involves motion and the other involves a raised position.

How does an object acquire energy?

The cricket ball gains energy from the work done by the fielder in throwing it. The flowerpot gains energy from the work done in raising it. These examples connect an object's capacity to do work with work previously done on it.

When the moving ball strikes the wickets, it transfers energy to them. The wickets move because the ball exerts a force during their displacement. Energy can therefore pass from one object to another through work.

Energy transfer means energy passing between objects or systems. A system is the object or group of objects being considered together. Identifying the system helps explain where energy comes from and where it goes during a process.

Doing mechanical work is one way of transferring energy. Energy can also pass from a hotter object to a colder object as heat. The energy that makes objects warm or hot is called thermal energy.

Work and energy are closely related, but the words describe different ideas. Work describes a transfer associated with force and displacement; energy describes the capacity to bring about such changes. Sharing the unit joule does not make the two definitions identical.

What is kinetic energy, and how is it calculated?

Kinetic energy is the energy an object possesses because of its motion. A moving bicycle and a rolling ball have kinetic energy. An object at rest has zero kinetic energy for the motion being considered.

Mass is the quantity measured in kilograms, symbol kg, and measures an object's resistance to changes in motion. Speed tells how much distance an object travels per unit time. Here speed is expressed in metres per second, written m/s.

Which factors determine kinetic energy?

Let K represent kinetic energy in joules, m mass in kilograms and v speed in metres per second. The square v² means v multiplied by itself. Kinetic energy is given by:

K = ½mv²

At the same speed, a greater mass means greater kinetic energy. For an object of unchanged mass, increasing speed increases kinetic energy. Because speed is squared, the increase in kinetic energy is not simply proportional to speed.

If a vehicle's speed doubles while its mass remains the same, its kinetic energy becomes four times its earlier value. Squaring twice the original speed produces four times the original squared speed. Retain the factor one-half when substituting into the formula.

Worked example 1. A cricket ball has an approximate mass of 0.2 kg and a speed of about 154.8 kilometres per hour, equivalent to 43 m/s. Find its kinetic energy.

Formula: K = ½mv². Substitute: K = ½ × 0.2 × 43². Answer: K = 184.9 J, approximately.

The numerical result depends on the stated mass and speed. Since those measurements are approximate, the calculated energy is approximate too. Use kilograms and metres per second together before applying this formula to obtain an answer in joules.

What is potential energy, and how does a spring store it?

Potential energy is energy stored because of an object's deformation or the relative positions of objects in a system. Deformation means a change in shape. An object need not be moving to possess potential energy.

Stretching a rubber band or bending a bow requires work. Energy is stored as the shape changes. When released, the band or bow can do work on another object, setting it in motion. This connects stored energy with the later appearance of kinetic energy.

What happens when a compressed spring is released?

A spring can store energy when it is stretched or compressed. Compression means squeezing it into a shorter shape. The stored energy associated with this deformation is called elastic potential energy.

1. A force acts on the spring and changes its shape.
2. Work is done during the deformation of the spring.
3. The spring stores energy while held in its deformed shape.
4. When released, the spring returns towards its original shape and can transfer energy to an object in contact with it.

Three drawings show a spring against a fixed support with a red ball beside it. The spring is shown in its original shape, compressed, and returning towards its original shape as the ball moves to the right.

See Fig. 7.14 in your NCERT textbook

The spring's stored energy and the ball's motion describe successive stages of a transfer. The ball did not gain energy without a source: work was previously done on the spring. Holding the compressed spring still does not remove its stored energy.

Potential energy also occurs without changing an object's shape. Raising an object changes its position relative to the Earth. This gives a different kind of potential energy, associated with gravitational attraction rather than with deformation.

How is gravitational potential energy calculated?

Gravity is the attractive interaction between masses. An object's weight is the gravitational force acting on it. Gravitational potential energy is stored energy associated with position in a gravitational interaction, such as that between an object and the Earth.

Strictly, this stored energy belongs to the Earth-object system. It is often simply called the gravitational potential energy of the object. Raising the object requires work against gravity, and that work increases the system's potential energy.

Which symbols and reference level are used?

Let g be acceleration due to gravity, measured in metres per second squared, written m/s². Acceleration is the rate of change of velocity; velocity describes speed together with direction. Let h be height above the chosen zero level, in metres.

Let U represent gravitational potential energy in joules. Near the Earth's surface, take g as constant. In the simple calculations here, g = 10 m/s². Choose the ground as the level where gravitational potential energy is zero.

Derivation: Gravitational potential energy

1. Raise an object of mass m gradually, so the upward lifting force F balances its weight. Thus, F = mg.
2. The upward displacement is the height h. Work done equals lifting force multiplied by this height.
3. Substituting the weight for the lifting force gives W = mgh. This work becomes the gain in gravitational potential energy.

U = mgh

The drawing shows a block at ground level and at a higher position. An upward arrow beside the lower block is labelled F = mg, and the vertical height between the positions is labelled h.

See Fig. 7.18 in your NCERT textbook

Worked example 2. A fielder throws a cricket ball of mass 200 grams, or 0.2 kg, to about 10 m above the ground. Take g = 10 m/s² and zero potential energy at ground level. Find the gravitational potential energy at that height.

Formula: U = mgh. Substitute: U = 0.2 × 10 × 10. Answer: U = 20 J, approximately.

The expression applies near the Earth's surface. For the same mass and g, greater height means greater potential energy. At the same height and g, greater mass means greater potential energy. The chosen zero level must stay the same during a comparison.

How can work and potential energy be compared in lifting tasks?

In a gradual lift, the work done against gravity depends on the mass, gravitational acceleration and vertical height gained. Time does not enter the expression mgh. A slower lift and a faster lift through the same height can involve the same work against gravity.

How does changing height affect the work?

Consider lifting a wheat bag. Raising the same bag three times as high requires three times the work against gravity, with g unchanged. Raising three identical bags to the original height also requires three times the work needed for one bag.

Worked example 3. A 5 kg wheat bag is lifted gradually through 1 m. Take g = 10 m/s². Find the lifting force and the work done against gravity.

Formula: F = mg; W = F × s. Substitute: F = 5 × 10 = 50 N; W = 50 × 1. Answer: The force is 50 N and the work is 50 J.

The force calculation comes first because the mass is given, whereas the work formula uses force. Do not substitute a mass directly as if it were a weight. Kilograms measure mass, while newtons measure force.

Does the path change the gain in potential energy?

For the same object, starting level and finishing level, the gain in gravitational potential energy is the same whether the object rises straight upwards or follows stairs. The height in mgh is the vertical rise, rather than the length of the route travelled.

Worked example 4. A student of mass 50 kg reaches a floor 72.5 m above ground, first by an elevator and later by stairs. Take g = 10 m/s². Find the gain in gravitational potential energy for each ascent.

Formula: U = mgh, with ground as the zero level. Substitute: U = 50 × 10 × 72.5. Answer: The gain is 36,250 J for each ascent.

This compares the change in gravitational potential energy. It does not calculate every energy transfer within the student's body or within the elevator. State clearly which energy change the calculation represents.

How does energy change form while remaining conserved?

An energy transformation is a change from one form of energy to another. The law of conservation of energy states that energy can neither be created nor destroyed; it changes form. A useful energy account identifies the initial form and the forms appearing later.

Chemical energy is energy stored in food and fuels. Electrical energy is associated with electric charges, the property of matter responsible for electrical interactions. Light energy enables sight, while sound energy is associated with vibrations travelling through matter.

Mechanical energy is energy associated with an object's motion or position. Its two forms here are kinetic and potential energy.

What is mechanical energy?

Total mechanical energy is the sum of kinetic and potential energy. Let E represent total mechanical energy, while K and U retain their earlier meanings. Then:

E = K + U

Consider an object released from rest at a height. Initially it has gravitational potential energy and zero kinetic energy. As it falls, its height decreases and its speed increases. Potential energy decreases while kinetic energy increases.

When gravity causes the motion and energy losses are neglected, the decrease in potential energy equals the increase in kinetic energy. The total mechanical energy remains constant. The condition matters: conservation of mechanical energy is not a claim that kinetic energy alone stays unchanged.

Water stored at height in a dam provides another application. As it moves down, gravitational potential energy becomes kinetic energy. This moving water can be used to generate electricity. The process converts energy already present; it does not create energy.

Note: A decrease in mechanical energy need not mean energy has been destroyed. Track other forms and transfers when friction or air resistance affects the motion.

How does a simple pendulum demonstrate energy changes?

A simple pendulum consists of a small suspended mass called a bob attached to a fixed support by a string. Its repeated back-and-forth movement is an oscillation. Its extreme positions are the turning points, and its mean position is the lowest position.

Choose the lowest position as the zero level for gravitational potential energy. At an extreme position, the bob is raised above this level and momentarily stops. Its kinetic energy is zero there, while its gravitational potential energy is high.

What happens during a swing?

1. Release the bob from a raised extreme position without pushing it.
2. As it moves down, its height decreases and gravitational potential energy changes into kinetic energy.
3. At the lowest position, speed and kinetic energy are greatest, while gravitational potential energy is zero relative to that level.
4. As the bob rises on the other side, kinetic energy changes back into gravitational potential energy, until the bob momentarily stops again.

Three bob positions are drawn beneath a common support. P and R mark the raised ends, and Q marks the lowest position. The end positions are labelled with potential energy only, and Q with kinetic energy only. A vertical height h is marked.

See Fig. 7.20 in your NCERT textbook

Why does a real pendulum eventually stop?

In the first few oscillations, a real bob reaches almost the same height from which it started. Friction at the support and air resistance cause it to slow down and eventually stop. Friction is resistance associated with surfaces interacting; air resistance opposes motion through air.

For an ideal comparison that neglects these effects, mechanical energy remains constant and the bob regains the starting height. For a real observation, keep the qualification “almost”. A gradual reduction in swing height is evidence of energy leaving the bob's mechanical motion.

How does power differ from work and energy?

Power is the rate of doing work. Two people can do the same work in different times. The person who completes that work in less time has the greater average power for that task.

Let P represent average power, W work done and t the time taken. Time is measured in seconds, symbol s. Here s after a numerical value is a unit; the earlier s in the work formula represented displacement.

P = W/t

The SI unit of power is the watt, represented by W. One watt means one joule of work done per second: 1 W = 1 J/s. The unit W means watt, while W in the formula represents work.

Derivation: Average power for a gradual lift

1. For a gradual lift near the Earth's surface, the work done against gravity is W = mgh.
2. Average power is the work done divided by the duration t of the lift.
3. Substitute mgh for W in the power expression, keeping the same mass, height and value of g.

P = mgh/t

Worked example 5. A weightlifter raises a 75 kg mass through 2 m in 5 s. Take g = 10 m/s². Calculate the work done against gravity and the average power for this work.

Formula: W = mgh; P = W/t. Substitute: W = 75 × 10 × 2 = 1500 J; P = 1500/5. Answer: Work is 1500 J and average power is 300 W.

Worked example 6. A 1000 kg car starts from rest and reaches 72 kilometres per hour, equivalent to 20 m/s, in 10 s. Calculate the average power transferred into its kinetic energy, neglecting other energy transfers.

Formula: K = ½mv²; P = W/t. The work W equals the kinetic energy gained from rest. Substitute: K = ½ × 1000 × 20² = 200,000 J; P = 200,000/10. Answer: Average power is 20,000 W.

For the same work, a shorter time means greater power. For the same time, more work also means greater power. Always distinguish the amount of work or energy from the rate at which work is done.

Glossary

• Work — Energy transfer by a force acting through displacement in its direction.
• Displacement — Change from an object's initial position to its final position, including direction.
• Joule — Work done by one newton displacing an object one metre along the force.
• Energy — Capacity to do work, measured in the same unit as work.
• Kinetic energy — Energy possessed by an object because it is in motion.
• Potential energy — Energy stored through deformation or the relative positions of interacting objects.
• Elastic potential energy — Energy stored in a deformed object, such as a compressed spring.
• Gravitational potential energy — Stored energy associated with relative position in a gravitational interaction.
• Mechanical energy — Sum of the kinetic energy and potential energy being considered.
• Energy transformation — Change of energy from one form into another during a process.
• Conservation of energy — Principle that energy cannot be created or destroyed, although its form changes.
• Pendulum bob — Suspended mass that swings to and fro below a fixed support.
• Power — Rate of doing work, found by dividing work by time.
• Watt — Unit of power equal to one joule of work per second.

Common errors and misconceptions

• Misconception: Feeling tired proves that work was done on a wall. Correct: If the wall does not move, no work is done on it, even though the person's muscles use energy.
• Misconception: Every force on a moving object does work. Correct: A force perpendicular to displacement does no work, as with the upward supporting force on a horizontally carried box.
• Misconception: An object at rest cannot possess energy. Correct: A raised object can have gravitational potential energy, and a compressed spring can store elastic potential energy while stationary.
• Misconception: Doubling speed doubles kinetic energy. Correct: At unchanged mass, doubling speed makes kinetic energy four times its original value because speed is squared in the formula.
• Misconception: Height in mgh means the length of the route travelled. Correct: It is vertical height above the chosen zero level; the potential energy gain is independent of the route.
• Misconception: A real pendulum returns to exactly the same height indefinitely. Correct: It initially returns to almost the same height, but friction and air resistance eventually stop it.
• Misconception: Power and energy have the same meaning and unit. Correct: Energy is measured in joules; power is the rate of doing work and is measured in watts.

Exam-style questions with model answers

Q1. Define one joule of work and state the condition concerning the direction of displacement. [2 marks]

1. One joule is the work done when a constant force of one newton displaces an object by one metre.
2. The displacement must be in the direction of the force for this definition to apply directly.

Q2. A person pushes a rigid wall, but it does not move. Explain why the work done on the wall is zero, although the person may feel tired. [3 marks]

1. Work done by a constant force depends on both the force and the displacement in the direction of that force.
2. The wall does not move, so its displacement is zero. Multiplying the applied force by zero gives zero work on the wall.
3. The person's muscles still use internal energy while applying the force. This can cause tiredness without work being done on the stationary wall.

Q3. A ball of mass 200 grams, equal to 0.2 kg, reaches about 10 m above the ground. Take acceleration due to gravity as 10 m/s² and zero potential energy at ground level. Calculate its gravitational potential energy. [3 marks]

1. Use gravitational potential energy U = mgh, where m is mass in kilograms, g is acceleration due to gravity and h is height above the chosen zero level.
2. Substitute the supplied values: U = 0.2 × 10 × 10. The height is measured vertically above the ground, where the potential energy is defined as zero.
3. The gravitational potential energy is approximately 20 J. The answer is approximate because the stated height is about 10 m.

Q4. A vehicle's speed doubles while its mass stays unchanged. Explain how its kinetic energy changes, using the kinetic energy formula. [3 marks]

1. Kinetic energy K = ½mv², where m is the vehicle's mass and v its speed. This shows that kinetic energy depends on the square of speed.
2. At double the speed, replace v by 2v. Squaring this gives (2v)² = 4v², while the mass and the factor one-half remain unchanged.
3. The new kinetic energy is four times the original kinetic energy. It therefore increases fourfold rather than merely doubling with speed.

Q5. A weightlifter raises a 75 kg mass through a vertical height of 2 m in 5 s. Take acceleration due to gravity as 10 m/s². Find the work against gravity and average power, and distinguish their units. [5 marks]

1. The work done against gravity is W = mgh, where W is work, m is mass, g is acceleration due to gravity and h is vertical height gained.
2. Substitute the given values: W = 75 × 10 × 2 = 1500 J. This is the work against gravity during the lift.
3. Average power is P = W/t, where P is average power and t is the time taken to perform the work.
4. Using the given duration, P = 1500/5 = 300 W. This is the average rate of doing the calculated work during the lift.
5. Work is measured in joules, while power is measured in watts. One watt represents one joule of work done per second.

Q6. A pendulum bob is released without a push from an extreme position. Take the lowest point as zero gravitational potential energy. Describe the energy changes over a swing, first neglecting friction and air resistance, then explaining the behaviour of a real pendulum. [5 marks]

1. At the release position, the raised bob has gravitational potential energy. Its speed and kinetic energy are zero because it is released from rest.
2. During the downward part of the swing, gravitational potential energy decreases and kinetic energy increases as the bob's speed increases towards the lowest point.
3. At the lowest point, kinetic energy and speed are greatest. Gravitational potential energy is zero relative to the zero level specified in the question.
4. On the upward part, kinetic energy changes back into potential energy. With losses neglected, the bob reaches the original height and momentarily stops at the other extreme.
5. A real pendulum initially reaches almost the same height. Friction at the support and air resistance reduce its mechanical energy, so it eventually stops swinging.

Q7. A 50 kg student reaches a floor 72.5 m above ground by elevator and later climbs stairs to the same floor. Take acceleration due to gravity as 10 m/s². Compare the gains in gravitational potential energy and explain the role of the path. [4 marks]

1. The gain in gravitational potential energy is mass multiplied by acceleration due to gravity multiplied by vertical height gained.
2. For the elevator ascent, the gain is 50 × 10 × 72.5 = 36,250 J, taking the ground as the zero level.
3. For the staircase ascent, the mass, gravitational acceleration and vertical height gained are unchanged. The gain is therefore also 36,250 J.
4. The change in gravitational potential energy depends on the vertical height difference, rather than the route taken between the two levels.

Key takeaways

• Work by a constant force depends on the force and displacement in its direction, not simply on effort or tiredness.
• Work and energy are measured in joules, but energy means capacity to do work rather than the rate of working.
• Kinetic energy depends on mass and the square of speed, so doubling speed quadruples it when mass remains unchanged.
• Potential energy can be stored through deformation or relative position, even when an object is stationary.
• Near the Earth's surface, gravitational potential energy is mgh, measured relative to a clearly chosen zero level.
• In a pendulum, kinetic and gravitational potential energy change into each other; real swings decrease because of resistance.
• Mechanical energy remains constant when the relevant energy losses are neglected; total energy accounting must include other forms when losses occur.
• Average power is work divided by time; greater power can mean doing the same work in less time.

Test yourself

What two quantities determine work done by a constant force along displacement?

The magnitude of the force and the displacement in its direction determine the work done.

Why can a stationary compressed spring possess energy?

Work done in compressing it is stored as elastic potential energy because its shape has changed.

Which unit is shared by work, kinetic energy and potential energy?

All three quantities are measured in joules in the International System of Units.

What does the height in gravitational potential energy calculations mean?

It is vertical height above the chosen level where gravitational potential energy is defined as zero.

Where is a swinging pendulum bob's speed greatest?

Its speed is greatest at the lowest, or mean, position, where kinetic energy is greatest.

Why must “almost” be retained when describing a real pendulum's return height?

Friction at the support and air resistance reduce its mechanical energy, so it does not return to exactly the same height.

What happens to average power if the same work is completed in less time?

Average power increases because the same amount of work is divided by a shorter time.

What is the main energy conversion when water descends from a dam?

The water's gravitational potential energy changes into kinetic energy as it moves down from its raised position.