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Work -Definition, Formula, Examples, FAQs

Work -Definition, Formula, Examples, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:41 PM IST

What is Work?

The term work in everyday life is used to indicate that whenever an activity is done physically we simply say that the body has done some work. When a body moves from its initial position to some distance we simply say this activity of a body as work done by the body.

What is work done in Physics?

In physics, Work done is simply the amount of energy a body needs to move it from its initial position to the final position.

Work Done Definition:

The standard work done definition states that “ The work done by a body is equal to the dot product between the force applied on the body and displacement covered by the body”.

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This Story also Contains
  1. What is Work?
  2. S.I Unit and Dimensional formula of work done.
  3. Examples of Work done by a body:
Work -Definition, Formula, Examples, FAQs
Work

Work Done Formula:

If a body is applied by some amount of force F and the body covers some displacement S then the work done by the body is written mathematically as W=F.S where W is denoted for work done.

Work Done Formula

(Source: Self-Drawn Using Geogebra)

S.I Unit and Dimensional formula of work done.

Mathematically, work done is the product of the force applied on the body and displacement covered by it, and since force has a SI unit of Kgms-2 and displacement has a SI unit of m so, work done will have a SI unit of Kgm2s-2 and standard notation for SI unit of Work done is known as Joules which is denoted as J and it was named after by scientist James Joules.

So, The SI unit of work done is Joules and the dimensional formula of work done is ML2T-2

Meaning of work definition Physics

Consider a block lying horizontally on the table and now it’s affected by some amount of applied force in a particular direction F and let this block gets moved to some displacement in specific direction S and the angle between the force vector and the displacement vector be then the work done by the body in order to cover this displacement is defined as W=F.S and since it’s the dot product between force vector and displacement vector so, Work done is written as W=FScos

Work Done

(Source: Self Drawn using Geogebra)

Hence, the meaning of work done is simply that, the amount of work done by a body in order to cover a displacement of S when applied with some force of magnitude F and having an angle between force and displacement vector is calculated as W=FScos

Various Factors on which Work done by a body depends.

Some of the factors which affect the work done by a body are listed as:

  1. Force. So, Work done on a body depends upon force and it’s directly proportional to the force acting on a body. On increasing the magnitude of force, the magnitude of work done is also gets increased while On decreasing the magnitude of force, the work done by a body also gets decreased.
  2. Displacement. Work done by a body depends upon displacement and it’s directly proportional to the displacement covered by the body. When a body covers greater displacement the work done by the body is also greater while when the body covers less displacement, the work done by the body is also very less.

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Variation of work done by a body on varying the value of “Angle between Force and Displacement vector”

Since Work done is directly proportional to the cosine of the angle between force vector and displacement vector which can be seen from the work done formula as W=FScos and we know that decreases while going from zero to degree ninety. So, the value of work done by a body gets decreased when the angle between displacement and force gets increased from zero.

Different cases of variation of work done by varying the angle are listed as:

  1. When a body is acted by some force and it covers some displacement and the angle between the force vector and displacement vector lies in the range of 0≤θ<90o Then, work done by the body is said to be positive.
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  1. When a body is acted by some force and it covers some displacement and the angle between force vector and displacement vector lies in the range of 180≤θ<90o Then, work done by the body is said to be negative.
  1. The maximum work done by the body is when the angle between force vector and displacement vector is zero θ=0 such that value of maximum work done is W=FScos 0=FS
  1. Work done by a body is zero only when Force vector and displacement vector are perpendicular to each other θ=90° such that W=FScos90°=0

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Examples of Work done by a body:

Some of the most common examples of work done by a body in our everyday life are listed as:

  1. When we apply some force on a table to change its position in our home, then we lose some of our mechanical energy and this energy is used by the table to perform work done in order to change its position.
  1. Work done by a body moving in a circular path is always zero because the force vector and displacement vector are always perpendicular to each other.
  1. When a person carries a load of some weight over his head and walks horizontally straight then, work done by the force of gravity is always zero because the direction of the force of gravity is downward and the direction of displacement is horizontal which shows both force and displacement are perpendicular to each other, which makes work done by force of gravity is zero.
  1. When a cricketer hits the ball with his bat, he loses some mechanical energy and this energy is used by the bat which is then transferred to the ball, and hence then work done by the ball helps it to move further on the ground.

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NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. Define Work Done definition in Physics?

In physics, work done by a body is simply the amount of energy it needs to cover some displacement, and mathematically work done is defined as the dot product between force vector and displacement vector which is further written as W=F.S . For example, if a body is acted by some amount of force having magnitude F and body covers some displacement having magnitude S and the angle between force and displacement is  then, the amount of work done performed by the body will be W=FScos  

2. What is work done by a body that covers a displacement of 5m when due to a force of magnitude 8N?

Work done by a body is simply defined as the product of the force applied on the body and displacement covered by the body, here we have given that F=8N  and S=5m and work done is W=FS on putting the values, we get W=8×5=40Joules hence, work done by the body is 40J.

3. What is the nature of work meaning?

Mathematically, work done is defined as the dot product between force vector and displacement vector, and it’s written as, work done be W=FScos   now, the nature of work meaning is that, if the value of cos   is positive then the nature of work done will be positive and is the value of cos   is negative, then the nature of work done will be negative. As well as if the force vector and displacement vector are perpendicular to each other, then the nature of work done will be zero.

4. What is work done by frictional force always?

The frictional force acts between two bodies between the surface of contact between them, and frictional force opposes the relative motion between two bodies in contact so, the frictional force is opposing force, hence if the body moves forward so friction force will act in the opposite direction which is backward hence, the angle between the friction force vector and displacement vector is always θ=180° which makes work done by frictional force always negative as W=FScos180°=-FS Hence, work done by the frictional force is always negative.

5. What is work done by force of gravity on a moving block horizontally on the ground?

Since work done is the product between force vector and displacement vector between two bodies. And the force of gravity acts on an object in a downward direction towards the ground and if a block is moving horizontally on the ground then, it covers displacement in a horizontal direction whereas the force of gravity acts in a vertically downward direction, which makes the force of gravity vector and displacement vector perpendicular to each other which makes work done by the moving block is zero as W=FScos90°=0 Hence, work done by force of gravity is zero.

6. Can work be negative?
Yes, work can be negative. This occurs when the force applied is in the opposite direction of the object's motion. For example, friction does negative work on a moving object because it opposes the motion.
7. Can work be done without a change in kinetic energy?
Yes, work can be done without changing kinetic energy. For example, when lifting an object at constant speed, work is done against gravity, increasing the object's potential energy without changing its kinetic energy.
8. How does the angle between force and displacement affect work?
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 parallel to displacement (θ = 0°), work is maximized. When perpendicular (θ = 90°), no work is done.
9. How is work calculated?
Work is calculated using the formula W = F * d * cos(θ), where W is work, F is the applied force, d is the displacement of the object, and θ is the angle between the force and displacement vectors. When the force is parallel to the displacement, cos(θ) = 1, simplifying the formula to W = F * d.
10. What is the work-energy theorem?
The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Mathematically, it's expressed as W_net = ΔKE, where W_net is the net work and ΔKE is the change in kinetic energy.
11. What are the SI units of work?
The SI unit of work is the joule (J). One joule is equal to the work done when a force of one newton causes a displacement of one meter in the direction of the force.
12. What is the relationship between work and power?
Power is the rate at which work is done or energy is transferred. Mathematically, power is work divided by time (P = W / t). This means work is power multiplied by time (W = P * t).
13. Can work be done on a system without changing its energy?
In a closed system, work done on the system always changes its energy. However, if we consider an open system, work can be done without changing the system's energy if an equal amount of energy is simultaneously transferred out of the system.
14. What is the concept of net work?
Net work is the total work done on an object by all forces acting on it. It's the sum of positive and negative work done by different forces and determines the overall change in the object's energy.
15. How does work relate to conservation of energy?
The work-energy principle is a consequence of the conservation of energy. When work is done on a system, it changes the system's energy. The total energy before and after the work is done remains constant, but it may be transformed between different forms.
16. What is work in physics?
In physics, work is the transfer of energy that occurs when a force acts on an object and causes it to move in the direction of the force. It's a way to quantify how much energy is transferred to or from an object through the application of force over a distance.
17. Is lifting an object and holding it stationary considered work?
No, holding an object stationary does not constitute work in physics, even if it requires effort. Work requires both force and displacement in the direction of the force. When holding an object still, there is force but no displacement.
18. What's the difference between work and energy?
Work is the process of transferring energy, while energy is the capacity to do work. Work is a measure of energy transfer, whereas energy is a state property of a system.
19. What's the difference between work and force?
Force is a push or pull exerted on an object, measured in newtons (N). Work is the energy transferred when a force moves an object over a distance, measured in joules (J). Force is a vector quantity, while work is a scalar quantity.
20. Can zero work be done when a force is applied?
Yes, zero work can be done even when a force is applied. This happens when there's no displacement in the direction of the force, such as when pushing against a stationary wall or when a force acts perpendicular to the motion.
21. How does relativistic motion affect the calculation of work?
In relativistic scenarios (speeds approaching the speed of light), the classical work equation must be modified. The relativistic work-energy theorem relates work to changes in relativistic energy, which includes rest mass energy and kinetic energy.
22. What is the significance of path independence in conservative forces?
Path independence in conservative forces means that the work done is only dependent on the initial and final positions, not the path taken. This property allows for the definition of potential energy and simplifies many calculations in physics.
23. How does the concept of work apply in quantum mechanics?
In quantum mechanics, work is often described in terms of changes in expectation values of energy. The quantum work-energy theorem relates the work done on a quantum system to changes in its energy expectation value.
24. How does the concept of work apply in quantum field theory?
In quantum field theory, work can be understood in terms of changes in the energy of quantum fields. This might involve the creation or annihilation of particles, or changes in the energy states of fields, connecting the concept of work to fundamental particle physics.
25. How does the concept of work apply in astrophysics?
In astrophysics, work is crucial in understanding stellar processes, galaxy formation, and cosmic evolution. For example, gravitational work plays a key role in stellar collapse, while work done by radiation pressure is important in stellar stability.
26. How does the concept of work relate to the uncertainty principle?
The uncertainty principle in quantum mechanics limits the precision with which certain pairs of physical properties can be known. While work itself is not directly subject to the uncertainty principle, the energy and time over which work is done are subject to quantum uncertainties.
27. How does the concept of work apply in relativistic scenarios?
In relativistic scenarios, the classical definition of work must be modified. The work-energy theorem in special relativity relates work to changes in relativistic energy, which includes both rest mass energy and kinetic energy. This leads to effects like the increase in mass with velocity.
28. How does the concept of work relate to information theory?
In information theory, work is related to the manipulation and erasure of information. The Landauer principle connects the erasure of information to a minimum amount of work that must be done, linking concepts from information theory to thermodynamics and computation.
29. How does gravity affect work?
Gravity can do positive or negative work depending on the situation. When an object falls, gravity does positive work, increasing its kinetic energy. When lifting an object, we do work against gravity, increasing the object's gravitational potential energy.
30. How does friction affect work?
Friction typically does negative work on a moving object because it opposes the motion. This negative work reduces the object's kinetic energy, converting it to thermal energy (heat).
31. What is the difference between conservative and non-conservative forces in terms of work?
Work done by conservative forces (like gravity) is path-independent and can be recovered, while work done by non-conservative forces (like friction) is path-dependent and cannot be fully recovered. Conservative forces conserve mechanical energy, non-conservative forces don't.
32. How does work relate to potential energy?
Work done against a conservative force (like gravity) increases the potential energy of an object. For example, when you lift an object, you do work against gravity, increasing the object's gravitational potential energy.
33. Can work be done by a centripetal force?
No, a centripetal force does not do work. Although it causes circular motion, the force is always perpendicular to the direction of motion. Since work is calculated using the component of force parallel to displacement, centripetal force does zero work.
34. 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 angle between the force and displacement vectors. It ensures that only the component of force parallel to the displacement contributes to work done.
35. How does the concept of work apply in simple machines?
In ideal simple machines, the work input equals the work output (neglecting friction). Machines don't create energy but can change the magnitude or direction of forces, making tasks easier by trading force for distance or vice versa.
36. What is the relationship between work and torque?
While work involves linear forces and displacements, torque involves rotational forces and angular displacements. The work done by a torque is equal to the torque multiplied by the angular displacement (W = τ * θ).
37. How does the concept of work apply in thermodynamics?
In thermodynamics, work is one way energy can be transferred into or out of a system. It often involves changes in volume against a pressure, such as the work done by an expanding gas (W = -P * ΔV).
38. Can work be done on a quantum scale?
Yes, the concept of work applies at the quantum scale, but it's often described in terms of changes in energy states rather than classical force and displacement. Quantum work is related to changes in the energy levels of particles or systems.
39. What is the role of work in the First Law of Thermodynamics?
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 (ΔU = Q - W). Work is a key component in this energy balance equation.
40. How does work relate to the concept of force fields?
In force fields (like gravitational or electric fields), work is related to the potential energy of the field. The work done to move an object in a force field is equal to the negative change in the potential energy of the object in that field.
41. How does the concept of work apply in fluid dynamics?
In fluid dynamics, work can be done by or on a fluid through changes in pressure, volume, or flow. For example, the work done by a fluid expanding against a piston or the work done to pump a fluid through a pipe.
42. What is the relationship between work and impulse?
While work relates force to displacement (W = F * d), impulse relates force to time (I = F * t). Both concepts involve force, but work results in energy transfer, while impulse results in momentum change.
43. How does the concept of virtual work apply in physics?
Virtual work is a principle used in mechanics to analyze equilibrium conditions. It states that for a system in equilibrium, the virtual work done by applied forces for any virtual displacement is zero. This principle is particularly useful in analyzing complex mechanical systems.
44. Can work be done in a vacuum?
Yes, work can be done in a vacuum. Many forms of work, such as gravitational work or work done by electromagnetic forces, do not require a medium. However, some forms of work, like those involving fluid pressure, would not be possible in a perfect vacuum.
45. How does work relate to the concept of energy landscapes in chemistry and biology?
In chemistry and biology, energy landscapes represent the potential energy of a system as a function of its configuration. Work is done when the system moves from one point to another on this landscape, changing its potential energy.
46. What is the significance of work in statistical mechanics?
In statistical mechanics, work is related to changes in the accessible microstates of a system. The work done on a system can change its entropy by altering the number of available microstates, linking the concept of work to fundamental principles of thermodynamics.
47. What is the role of work in the Carnot cycle?
In the Carnot cycle, an idealized thermodynamic cycle, work is done by the system during the expansion phases and on the system during compression phases. The net work output of the cycle is used to define the maximum possible efficiency of heat engines.
48. How does work relate to the concept of free energy in thermodynamics?
Free energy (like Gibbs free energy) represents the maximum work that can be extracted from a thermodynamic system at constant temperature and pressure. The change in free energy determines the spontaneity of processes and the work available from chemical reactions.
49. What is the significance of negative work in physics?
Negative work indicates that energy is being removed from a system rather than added to it. It occurs when the force opposes the motion, such as when friction slows down a moving object or when compressing a spring.
50. How does the concept of work apply in electromagnetism?
In electromagnetism, work is done when charges move in electric fields or when currents flow in magnetic fields. The work done in moving a charge through an electric potential difference defines the volt, a fundamental unit in electricity.
51. What is the relationship between work and heat in thermodynamics?
Work and heat are two methods of energy transfer in thermodynamics. While work involves macroscopic forces and displacements, heat involves microscopic energy transfer due to temperature differences. Both contribute to changes in a system's internal energy.
52. What is the role of work in the formation of chemical bonds?
Work is involved in the formation and breaking of chemical bonds. Energy must be supplied (work done on the system) to break bonds, while energy is released (work done by the system) when bonds form. This relates work to concepts of bond energy and enthalpy.
53. What is the significance of PV work in thermodynamics?
PV work, or pressure-volume work, is a common form of work in thermodynamics. It occurs when a system changes volume against an external pressure, such as in the expansion or compression of gases. The work is calculated as W = -P * ΔV.
54. What is the role of work in the concept of exergy?
Exergy is the maximum useful work that can be extracted from a system as it reaches equilibrium with its surroundings. It combines concepts of energy and entropy to quantify the quality of energy in a system, relating work to the second law of thermodynamics.
55. What is the significance of work in non-equilibrium thermodynamics?
In non-equilibrium thermodynamics, work plays a crucial role in understanding irreversible processes and the production of entropy. The concept of work helps describe how systems evolve towards equilibrium and how energy is dissipated in real-world processes.

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