Work, Energy and Power - Definition, Examples, Formula, Units, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 05:09 PM IST

In physics, power, work, and energy have almost the same meaning, which must not be confused with everyday meaning. Let us understand this concept of work, energy, and power with the help of an example: when we lift a box full of stuff, we get tired, and we need to eat food to get more energy. Thus, we can say that the work transfers energy. In this article we are going to learn the definition, SI unit, and dimensional formula of work, power, and energy and their characteristics.

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Work: Definition, SI unit, Dimension and Formula
Energy: Definition, Dimension, Unit and Formula
Power: Definition, Dimension, Unit and Formula

Work, Energy and Power - Definition, Examples, Formula, Units, FAQs

Work: Definition, SI unit, Dimension and Formula

Work Definition: Work is said to be done when the force acting on the body and the body moves through some distance in the direction of force.

This work is said to be done on a body if it satisfies the below two conditions:

1. A force must act on the body.

2. The object should move in the direction of force.

Work done Formula

Work formula Physics is given by

$W=F d \cos \theta$

Where F is the component of the force and d is the magnitude of displacement.

and $\cos \theta$ = angle between the force and displacement

SI unit of work or work done

Unit of work done = unit of force × unit of displacement

⇒ Unit of work done = Newton (N) × meter (m)

⇒ Unit of work done = N.m

The SI unit of work is the joule (J).

Dimensional formula of work done

Dimensional formula of work done = dimensional formula of force × dimensional formula of displacement

⇒ Dimensional formula of work done = $\left[M^1 L^1 T^{-2}\right]$ × $\left[M^0 L^1 T^0\right]$

⇒ Dimensional formula of work done = $\left[M^1 L^2 T^{-2}\right]$

Examples of work done

1. A man climbing the hills

2. A horse pulling the cart

3. A satellite orbiting the planet

4. Kicking the football

5. Pushing the table in the floor

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Nature of the work done

Work done is a scalar quantity, and its magnitude may be positive, negative, or zero.

Positive work

When force is applied along with displacement, which are in the same direction, then the work done on the object is said to be positive work. For example, when a horse pulls the cart, the cart is displaced in the direction of the force applied.

Negative work

When the applied force and the displacement are in opposite directions, the work done on the body is said to be negative work. For example, when we apply brakes to a moving bicycle, the work done by the brake is negative because the braking force and the displacement act in opposite directions.

Zero work

When the body gets displaced along a direction perpendicular to the direction of applied force, then the work done on an object is said to be zero work. For example, the work done in pushing an immovable wall is zero because displacement of the wall is zero. So, work done is zero.

Energy: Definition, Dimension, Unit and Formula

Energy Definition: Energy of a body is defined as its capacity or ability to do work.

Energy is a scalar quantity.

Dimensional formula of energy

The dimensional formula for energy is the same as that of work done.

Dimensional formula of energy = dimensional formula of work done

⇒ Dimensional formula of energy = dimensional formula force × dimensional formula of displacement

⇒ Dimensional formula of energy = $\left[M^1 L^1 T^{-2}\right]$ × $\left[M^0 L^1 T^0\right]$

⇒ Dimensional formula of energy = $\left[M^1 L^2 T^{-2}\right]$

Energy Equation

Change in K.E. = Final K.E. – Initial K.E.

Some characteristics of Energy

The entire mass/matter possesses energy.
Energy can neither be created nor be destroyed; it always remains conserved.
Energy can be stored and transferred from one form to another form.
Some energy transfers or energy transformations can be seen, heard, or felt.
The total quantity of the energy that exists in the universe is constant.

Several forms of energy

Mechanical energy
Sound energy
Heat energy
Thermal energy
Light energy
Nuclear energy
Chemical energy
Solar energy
Magnetic energy

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Mechanical Energy

The energy produced by mechanical means is called mechanical energy. Let discuss the two forms of mechanical energy:

Kinetic energy: The energy possessed by the body by virtue of its motion is called kinetic energy.

Kinetic energy formula physics:

$E_k=\frac{1}{2} m v^2$

Also, we can say that the kinetic energy of a body is equal to one-half the product of body mass along with the square of its velocity.

Example of kinetic energy: A bullet fired from a gun can hit the target on account of the kinetic energy of the bullet. Windmills work on the kinetic energy of the air. Ships sail using the kinetic energy of the wind. Watermills work on the kinetic energy of the water.

Potential Energy: The energy possessed by a body with principles of its position. Mathematically,

$\mathrm{PE}=\mathrm{mgh}$

For example, the potential energy of food is converted into electrochemical energy to operate our body system. Potential energy can be stored in an object by compressing it, stretching it, or bending it. When we stretch the bow and release it, the arrow goes forward with a large velocity on account of the potential energy of the stretched bow.

Work-energy and power Theorem for a constant force

Work-Energy Theorem Statement: According to this theorem, the work done on a body by the net force is equal to the change in kinetic energy of the body.

Proof of Work-Energy Theorem:

Suppose a constant force F acting on a body of mass m produces acceleration a in it. After covering distances, suppose the velocity of the body changes from u to v.

Use the equation of motion,

$v^2-u^2=2 \mathrm{as}$

Multiplying both side by 1/2m

$\frac{1}{2} m v^2-\frac{1}{2} m u^2=m a \mathrm{~S}$

By Newton’s second law,

F=ma

Therefore,

$\frac{1}{2} m v^2-\frac{1}{2} m u^2=\mathrm{Fs}=\mathrm{W}$

$\mathrm{K}_{\cdot} \mathrm{E}_{\cdot(f)}-\mathrm{K}_{\cdot} \mathrm{E}_{\cdot(i)}=\mathrm{W}$

Change in the kinetic energy of the body = work done on the body

Hence, the work-energy theorem proves for a constant force.

Also Read:

Power: Definition, Dimension, Unit and Formula

Power Definition: Power is outlined because of the rate of doing work.

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

Power is the scalar quantity.

SI unit of power

SI unit of power = SI unit of work/SI unit of time

⇒ SI unit of power = Joule / second

The Si unit of power is joule per second, i.e., $\mathrm{Js}^{-1}$

Dimensional formula of Power

$[P]=\frac{[\mathrm{W}]}{[\mathrm{t}]}$

$[P]=\frac{\left[\mathrm{L}^2 \mathrm{M}^1 \mathrm{~T}^{-2}\right]}{\left[\mathrm{L}^0 \mathrm{M}^0 \mathrm{~T}^1\right]}$

$[P]=\left[\mathrm{L}^2 \mathrm{M}^1 \mathrm{~T}^{-3}\right]$

The dimensinal formula for power is $[P]=\left[\mathrm{L}^2 \mathrm{M}^1 \mathrm{~T}^{-3}\right]$.

One watt: The ability of an agent is one watt if work done on the object is one joule per second.

One watt = (1 joule)/(1 second)

Instantaneous Power: The electric power at any instant of time is termed as instantaneous power.

Also check-

NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. If the force acts perpendicular to bodies motion direction. What is work done on body?

Since, the displacement of the body is zero within the direction of force applied. Hence, work done is zero.

2. What proportion of work and energy is powered by coolie walking with load above his head on horizontal platform?

Zero work as a result of coolie is additionally applying force within the upward direction to adequate its weight so as to keep up balance. His displacement is in the horizontal direction. Therefore angle between force as well as displacement is ninety degrees therefore work done = Fs cos90 = zero.

3. Outline one watt.

One Watt: the ability of an agent is one watt if it will work on the object is one joule per second. One watt=(1 joule)/(1 second)

4. State Work-Energy Theorem.

Work-Energy Theorem states that the work done by cyber web force performing on the body is adequate to the modification created within the mechanical energy of the body.

5. Outline one joule of work energy and power.

One joule of work is claimed to be done once a force of 1 Newton displaces a body through a distance of one meter in its own direction.

6. Can work be negative?

If the displacement is in the opposite direction of the applied force, then the work done will be negative.

7. Why work and energy are important?

There is no force without energy; without force there is no work done, and there will be no power without work done.

8. Why work is scalar quantity?

Work done is the product of force (vector) and displacement (vector). We don't focus on the direction of work done; we mainly focus on the amount of energy transferred during the work done.

9. Why is the unit of work (joule) the same as the unit of energy?

The unit of work (joule) is the same as the unit of energy because work is a form of energy transfer. When 1 joule of work is done, exactly 1 joule of energy is transferred from one object or system to another. This equivalence reflects the fundamental relationship between work and energy.

10. What is the relationship between work and potential energy?

Work and potential energy are closely related. The work done against a conservative force, like gravity, is stored as potential energy. For example, when you lift an object, the work done against gravity is stored as gravitational potential energy. This potential energy can later be converted back into kinetic energy or other forms of energy.

11. How is work related to energy?

Work and energy are closely related concepts in physics. Work is the process by which energy is transferred from one object or system to another. When work is done on an object, its energy changes. The work-energy theorem states that the net work done on an object equals its change in kinetic energy.

12. What is the work-energy theorem, and why is it important?

The work-energy theorem states that the net work done on an object equals its change in kinetic energy. Mathematically, it's expressed as W_net = ΔKE. This theorem is important because it provides a powerful way to analyze the motion of objects without needing to consider the details of their path or the forces acting on them at each point.

13. What is the difference between conservative and non-conservative forces in terms of work?

Conservative forces, like gravity, do work that is independent of the path taken and depends only on the initial and final positions. The work done by conservative forces is reversible. Non-conservative forces, like friction, do work that depends on the path taken and is not fully reversible. The work done by non-conservative forces often results in energy dissipation as heat.

14. How is power related to force and velocity?

Power is related to force and velocity through the equation P = F * v, where P is power, F is force, and v is velocity. This equation shows that power is the rate at which work is done, as it represents the force applied multiplied by the speed at which the object moves.

15. Can you explain the concept of power in terms of energy transfer rate?

Power is the rate at which energy is transferred or converted. It's measured in watts, where 1 watt equals 1 joule per second. High power means energy is being transferred or converted quickly, while low power means the process is slower. For example, a 100W light bulb converts electrical energy to light and heat energy faster than a 60W bulb.

16. How does the concept of power apply to electrical systems?

In electrical systems, power is the rate at which electrical energy is transferred. It's calculated as P = VI, where V is voltage and I is current. This shows that electrical power increases with both voltage and current. Understanding electrical power is crucial for designing circuits and managing energy consumption in devices.

17. What is the difference between energy and power?

Energy is the capacity to do work, while power is the rate at which work is done or energy is transferred. Energy is measured in joules (J), while power is measured in watts (W), which are joules per second (J/s). Power tells us how quickly energy is being used or transferred.

18. How does air resistance affect the work done on a moving object?

Air resistance is a non-conservative force that always opposes motion. It does negative work on a moving object, converting some of the object's kinetic energy into heat. This is why objects slow down in air unless another force (like a motor) continually does positive work to maintain their speed.

19. How does the concept of work apply to lifting an object vertically?

When lifting an object vertically, work is done against gravity. The work done is equal to the force required to lift the object (which is equal to its weight) multiplied by the vertical distance it is lifted. This work increases the object's gravitational potential energy by the same amount.

20. How does the angle between force and displacement affect the work done?

The angle between force and displacement affects work through the cosine term in the work equation: W = F * d * cos(θ). When the force is in the same direction as the displacement (θ = 0°), cos(θ) = 1, and maximum work is done. When the force is perpendicular to the displacement (θ = 90°), cos(θ) = 0, and no work is done.

21. Why doesn't holding a heavy object stationary count as work in physics?

Holding a heavy object stationary doesn't count as work in physics because there is no displacement. Although you're exerting a force to hold the object against gravity, the object isn't moving in the direction of the force. Work requires both force and displacement in the same direction.

22. How does the concept of work apply to machines and mechanical advantage?

In machines, work input equals work output (ignoring friction). Machines can provide a mechanical advantage by changing the magnitude of the force or the distance over which it's applied. For example, a lever can allow a small force applied over a large distance to lift a heavy weight over a small distance, but the work done remains the same.

23. How does the concept of work apply to springs and elastic potential energy?

When a spring is stretched or compressed, work is done to deform it. This work is stored as elastic potential energy in the spring. The work done is equal to the area under the force-displacement curve for the spring, which for an ideal spring is W = ½kx², where k is the spring constant and x is the displacement from equilibrium.

24. What is work in physics, and how is it different from the everyday meaning of work?

In physics, work is defined as the transfer of energy that occurs when a force acts on an object and causes it to move in the direction of the force. This differs from the everyday meaning of work, which often refers to any effortful activity. In physics, work only occurs when there's both a force and displacement in the same direction.

25. Can you do work on an object without moving it?

No, you cannot do work on an object without moving it. Work requires both a force and a displacement in the direction of that force. If you apply a force to an object but it doesn't move, no work is done, regardless of how much effort you exert.

26. Why is work a scalar quantity and not a vector?

Work is a scalar quantity because it represents the amount of energy transferred, which is a single value without direction. Although force and displacement are vectors, work is calculated using their scalar product (dot product), resulting in a scalar value.

27. What is the formula for work, and what do its components represent?

The formula for work is W = F * d * cos(θ), where W is work, F is force, d is displacement, and θ is the angle between the force and displacement vectors. This formula shows that work depends on the magnitude of the force, the distance moved, and the direction of the force relative to the motion.

28. Can work be negative? If so, what does it mean?

Yes, work can be negative. Negative work occurs when the force applied is in the opposite direction of the object's motion. This means energy is being removed from the system rather than added to it. For example, friction does negative work on a moving object, slowing it down.

29. What is the significance of the dot product in the work equation?

The dot product in the work equation (W = F · d) accounts for the directional relationship between force and displacement. It ensures that only the component of force parallel to the displacement contributes to work. This mathematical operation is crucial for correctly calculating work in three-dimensional space and for understanding why perpendicular forces do no work.

30. How does the concept of work apply to rotational motion?

In rotational motion, work is done when a torque causes an angular displacement. The formula for rotational work is W = τ * θ, where τ is torque and θ is the angular displacement. This is analogous to the linear work formula, with torque replacing force and angular displacement replacing linear displacement.

31. What is the relationship between work and heat in thermodynamics?

In thermodynamics, work and heat are two ways of transferring energy between a system and its surroundings. Work involves the organized motion of particles, while heat involves their random motion. The first law of thermodynamics states that the change in internal energy of a system equals the heat added to the system minus the work done by the system.

32. What is the difference between instantaneous power and average power?

Instantaneous power is the power at a specific moment in time, while average power is the total energy transferred divided by the time interval. Instantaneous power can vary moment to moment, especially in systems with changing forces or velocities. Average power gives an overall measure of energy transfer rate over a period of time.

33. How does the work-energy principle apply to a roller coaster?

The work-energy principle is perfectly illustrated by a roller coaster. As the coaster climbs, work is done against gravity, increasing its gravitational potential energy. As it descends, this potential energy is converted to kinetic energy. The total mechanical energy (potential + kinetic) remains constant in an ideal system, neglecting friction and air resistance.

34. What is the significance of the area under a force-displacement graph?

The area under a force-displacement graph represents the work done. This is because work is the product of force and displacement, and the area under the curve gives the sum of force multiplied by small displacement intervals. This graphical interpretation is particularly useful for calculating work when the force is not constant.

35. How does the concept of work apply to chemical reactions?

In chemical reactions, work can be done by or on the system through changes in volume or pressure. For example, in a reaction that produces gas, the expanding gas can do work on its surroundings. The work done in chemical reactions is often related to changes in enthalpy and internal energy of the system.

36. What is the relationship between work and energy in quantum mechanics?

In quantum mechanics, work and energy are still related, but the concepts become more abstract. Energy is quantized, meaning it can only exist in discrete levels. Work in quantum systems often involves transitions between these energy levels. The work-energy theorem still holds, but it's applied to expectation values and probability distributions rather than classical trajectories.

37. How does the concept of virtual work apply to equilibrium systems?

Virtual work is a principle used in mechanics to analyze equilibrium systems. It states that for a system in equilibrium, the virtual work done by applied forces during any virtual displacement is zero. This principle is powerful for solving complex statics problems and understanding the stability of mechanical systems.

38. What is the significance of the work function in the photoelectric effect?

The work function in the photoelectric effect represents the minimum energy required to remove an electron from a material's surface. It's a form of work done against the binding forces holding the electron in the material. Understanding the work function is crucial for explaining why light below a certain frequency cannot cause electron emission, regardless of its intensity.

39. How does the concept of work apply to adiabatic processes in thermodynamics?

In an adiabatic process, no heat is exchanged with the surroundings, so any change in the system's internal energy must be due to work. The work done in an adiabatic process can change the temperature of the system. This concept is important in understanding phenomena like the heating of air in a bicycle pump or the cooling of gas as it expands in the upper atmosphere.

40. What is the relationship between work and free energy in biochemical systems?

In biochemical systems, the maximum work that can be extracted from a process at constant temperature and pressure is equal to the change in Gibbs free energy. This relationship is crucial for understanding energy transformations in living organisms, where many processes occur at roughly constant temperature and pressure.

41. How does the concept of power apply to human physiology and exercise?

In human physiology, power is a measure of the rate at which work is done or energy is expended. During exercise, power output can be measured in activities like cycling or weightlifting. Understanding power in this context is important for assessing athletic performance, designing training programs, and studying human energy metabolism.

42. What is the significance of the power factor in AC electrical systems?

The power factor in AC systems is the ratio of real power (which does useful work) to apparent power. A low power factor indicates that a significant portion of the apparent power is not doing useful work, leading to inefficiencies. Understanding and improving power factor is crucial for optimizing electrical power transmission and reducing energy waste in industrial settings.

43. How does the concept of work apply to quantum tunneling?

In quantum tunneling, particles can pass through energy barriers that they classically shouldn't be able to overcome. While no work is done in the classical sense, the concept of work is related to the energy of the tunneling particle and the height and width of the potential barrier. Understanding this helps explain phenomena like alpha decay and certain types of chemical reactions.

44. What is the relationship between work and entropy in irreversible processes?

In irreversible processes, some work is always "lost" to increasing entropy. This means that not all the work done on a system can be recovered as useful work. The relationship between work and entropy is described by the second law of thermodynamics and is crucial for understanding the limitations of real-world energy conversions and the concept of efficiency.

45. How does the concept of work apply to cosmological expansion?

In cosmology, the expansion of the universe can be thought of as work done against gravitational forces. As the universe expands, it does work against its own gravity, which affects its energy content. This concept is crucial for understanding the evolution of the universe and phenomena like dark energy.

46. What is the significance of negative work in damped oscillations?

In damped oscillations, negative work is done by the damping force, which opposes the motion. This negative work reduces the system's mechanical energy over time, converting it to heat. Understanding this helps explain why oscillations in real systems eventually die out, and is crucial in designing systems like shock absorbers.

47. How does the concept of power apply to information theory and computation?

In information theory and computation, power can be thought of as the rate at which information is processed or transmitted. This concept is crucial in designing efficient computing systems and communication networks. It relates to ideas like computational complexity and channel capacity, helping to set theoretical limits on information processing and transmission rates.

48. What is the relationship between work and gauge transformations in field theories?

In field theories, gauge transformations are changes in the mathematical description of a system that don't affect observable quantities. The concept of work is invariant under these transformations, meaning the work done in a process should be the same regardless of the gauge chosen. This invariance is a fundamental principle in modern physics, crucial for theories like quantum electrodynamics and general relativity.

49. How does the concept of work apply to phase transitions in materials?

During phase transitions, work can be done on or by a system as it changes from one phase to another. For example, in the melting of ice, work is done against intermolecular forces to separate molecules. Understanding this helps explain phenomena like latent heat and is crucial in fields like materials science and chemical engineering.

50. What is the significance of the work-energy theorem in relativistic mechanics?

In relativistic mechanics, the work-energy theorem still holds, but the definitions of work and energy are modified to account for the effects of special relativity. The kinetic energy term includes the rest mass energy, and the relationship between force and acceleration becomes more complex. This relativistic version is crucial for understanding high-energy particle physics and astrophysical phenomena.

51. How does the concept of power apply to renewable energy systems?

In renewable energy systems, power is a crucial concept for assessing the energy output and efficiency of different technologies. For example, the power output of solar panels or wind turbines varies with environmental conditions. Understanding these power variations is essential for designing reliable and efficient renewable energy systems and integrating them into existing power grids.

52. What is the relationship between work and quantum entanglement?

While work in the classical sense doesn't directly apply to quantum entanglement, the energy required to create or maintain entangled states can be considered a form of work. Understanding this relationship is crucial in quantum information theory and the development of quantum technologies, where entanglement is a key resource.

53. How does the concept of work apply to protein folding in biology?

Protein folding involves work done by and against various molecular forces. The work done during folding contributes to the protein's final conformation and stability. Understanding this process in terms of work and energy is crucial for predicting protein structures, designing new proteins, and understanding diseases related to protein misfolding.

54. What is the significance of the power spectrum in signal processing and astronomy?

The power spectrum in signal processing and astronomy represents the distribution of power (or energy) across different frequencies in a signal. It's crucial for analyzing complex signals, identifying periodic components, and understanding the energy content of various phenomena, from radio waves to cosmic background radiation.

55. How does the concept of work apply to the formation and evolution of stars?

In stellar physics, work is done as gravity compresses gas, heating it up and triggering nuclear fusion. The balance between gravitational work and the outward pressure from fusion reactions determines a star's structure and evolution. Understanding this balance is crucial for modeling stellar lifecycles and explaining phenomena like