Every day, we are involved in countless activities—from lifting a school bag, climbing stairs, or opening a door to pushing a swing in the park. While these tasks may seem different, they all have something in common: they require effort. But what exactly makes something happen when we apply effort? The answer lies in the concept of force and how it brings about movement.
Work is done only when a force moves an object. So, actions like pushing a cart or kicking a ball involve scientific work, but if there is no movement, no work is done.
Work Done in Physics
Work is a physical quantity that occurs when a force causes an object to move or be displaced. The amount of work done is calculated as the product of the force applied and the displacement of the object in the direction of the force. According to physics, if there is no displacement, no work is done—regardless of how much force is applied.
This above image illustrates the concept of work done in physics. It shows a man lifting a weight of 200 Newtons vertically upward to a height of 2 meters.
In physics, work is said to be done when a force is applied to an object and the object moves in the direction of that force. In this case, the man applies an upward force to lift the weight, and the weight moves upward as a result.
This gives us the idea of following conditions necessary for work done
- Force must be applied.
- There must be some amount of displacement.
Hence, according to the definition in physics, work is done only when an object is moved or lifted by an applied force. Although force and displacement are vector quantities, work has no direction, making it a scalar quantity.
Work can vary depending on the context. For instance, when compressing a gas at constant temperature, the work done is the product of pressure and volume change. Work transfers energy to an object, so the amount of work done is directly related to the increase in the object's energy.
If the applied force acts opposite to the direction of motion, the work done is negative, indicating that energy is being taken away from the object.
The Science Behind 'No Work Done' Despite Effort!
Consider the following scenario,
Imagine a waiter carrying a tray high above his head with one arm while walking steadily across a room. At first glance, it seems like he's doing a lot of work—after all, holding and balancing a tray while walking takes effort.
However, in physics, the definition of work is different. Work is only done when a force causes an object to move in the direction of that force.
In this case, the waiter applies an upward force to support the tray, but the tray is moving horizontally as he walks. Since the direction of the force (upward) is not the same as the direction of movement (forward), no work is done on the tray in the scientific sense.
The product of the magnitude of applied force and the distance travelled by the body equals the total work done by this force.
The formula for scientifically completed work will be as follows:
W = F·d
The force acting on the block is constant in this example, but the direction of the force and the direction of displacement impacted by it are not. Force F reacts at an angle θ to the displacement d in this case.
W=∣F∣⋅∣d∣⋅cosθ
where,
W is the work done by the force.
F is the force,
θ is the angle between the force vector and the displacement vector,
d is the displacement caused by the force.
From Newton’s second law:
F=m⋅a
Use kinematic equation:
v^2 = u^2 + 2as ⇒as=\frac{v^2 - u^2}{2}
Multiply both sides by 'm'
mas = \frac{1}{2}mv^2 - \frac{1}{2}mu^2
But F=ma, and work done W=F⋅s, so:
W=F⋅s=mas
Unit of Work
- SI unit of work done is Joule(J).
- Other unit of work done is Newton meter(Nm)
Dimension of Work Done
The dimension of work done is [ML2T–2]. It is defined as the product of the magnitude of displacement d and the component of the force acting in the displacement direction.
Types of Work Done
On the basis of the angle between the force and the displacement work done can be categorized into three types,
- Positive Work
- Negative Work
- Zero Work
1. Positive Work
When a force moves an item in a the direction of force, the work done is considered positive. The motion of a ball falling towards the earth, with the displacement of the ball in the direction of gravity, is an example of this sort of labour.
When force is applied to an item at an angle 0 ≤ θ < 90°, it is said to be positive work done.
2. Negative Work
When force and displacement are in opposite directions, it is considered that the work is negative. For example, if a ball is thrown upwards, the displacement will be upwards; nevertheless, the force due to gravity will be downwards.
When force is applied to an item at an angle of 90° ≤ θ ≤ 180°, it is said to be negative work done.
3. Zero Work Done
The total work done by the force on the item is 0 in the following two cases
Case 1: If the displacement caused by the force is zero. For example, if you push a wall the displacement of wall is zero hence work done is zero
Case 2: If the direction of the force and the displacement are perpendicular to each other. For example if you carry a load on your head and walk straight then the force applied by you in carrying the load is upward and your direction of movement is forward then the angle between force and displacement here is zero.
Work Done by a Constant Force
When a force acts on an item over a long distance, the thing undergoes work. Physically, the work done on an item is the change in energy that the object possesses.
Thus, we can define the work done as the change in the energy of the object(either kinetic or potential). The total energy of the system is always constant and it can be converted to other forms using the work done.
Work Done by the System
When we talk about work, we focus on the impact that the system has on its surroundings. As a result, we consider work to be positive when the system makes an attempt to improve the environment (i.e., energy leaves the system). If work is done on the system, the work is negative (i.e., energy added to the system).
Examples of the work done by the system are,
- The output shaft of a turbine rotating a generator
- A rocket propelling itself upward by expelling gas
- An internal combustion engine powering a vehicle
- A pump pushing water through a pipeline
Factors Affecting Work Done
Various factors affect the work done by an object which are,
- Force applied
- Displacement
- Angle Between Force Vector and Displacement Vector
Let's look at some of the factors that affect the work done by an object.
Force Applied
It is described as a push or a pull that may cause any massed object's velocity and acceleration to alter.
The amount and direction of force are both vector quantities. If the force acting on an item is zero, regardless of whether the object is in a dynamic or static state, the force does not work.
Displacement
It is a vector quantity that represents the smallest distance between an object's starting and final positions. The net work done by a force acting on an item is zero if the resultant displacement in the direction of force is zero.
For example, if we push a hard wall with all our might but still fail to move it, we might say we have done no work on the wall.
Angle Between Force Vector and Displacement Vector
The work done by a force depends on the direction of displacement relative to the force. If the displacement is in the same direction as the force, the work is positive. If it is in the opposite direction, the work is negative, like friction acting against a moving object.
When the displacement is perpendicular to the direction of the applied force, the work done is zero. For example, in circular motion, the force is toward the center, but the object moves along the path—so no work is done.
Relation between Work and Energy
Work and energy are closely related concepts in physics. Their relationship can be understood through the following key points:
- Energy is defined as the ability to do work.
- Work is defined as the transfer of energy from one object or form to another.
- When an object gains or loses energy, it’s due to work being done.
Work-Energy Theorem:
W = \Delta E = E_{\text{final}} - E_{\text{initial}}
Hence,
Work = Change in Energy = Energy Transferred
Rate of Work Done
The rate at which work is done or energy is transferred per unit time is called Power.
The physical quantity that measures the rate of work done is called Power.
It is given by the formula,
P = W/t
Solved Examples on Work Done
Example 1: The rope pulls the box along the floor, creating a 30° angle with the horizontal surface. The box is dragged for 20 meters, with a force of 90 N applied by the rope. Where can I find the force's final work?
Solution:
Here,
The angle between force and displacement, θ = 30°
The displacement of the box, d = 20 m
The force applied on the box, F = 90 N
So, total work done by the force is,
W = F .d cosθ = 90 × 20 × 0.866 J
= 1558.8 J ≈ 1560 J
Hence, the work done by the force is 1560 J.
Example 2: With Force 10 N engaged at an angle of 60° from the horizontal, a girl thrusts a toy car from the stationary state on the horizontal floor. The toy car weighs 4 kg. In 10 seconds, can you find the girl's work?
Solution:
Initially, we can resolve the force into two components such as horizontal and vertical component;
Horizontal component = 10 cos60° = 5 N
Vertical component = 10 sin60° = 8.66 N
Now we need to figure out how much work we've done and how far we've travelled.
Horizontal force will now be the sole source of acceleration for that toy cart.
Acceleration, a = F/m = 5 N /4 kg = 1.25 m/s²
We can obtain displacement from the formula:
s = u t + 1/2 a t² = 0 + 0.5 × 1.25 × 10² m = 62.5 m
So, the work done will be:
W = F × s
= 5 × 62.5 J
= 312.5 J
Hence, the work done by the car is 312.5 J
Example 3: Calculate the Work Done on the Body when a force pg 50 N displaces it by 5m
Solution:
Formula for the work done is,
W = F × d
Given,
F = 50 N
d = 5m
Substituting these values in the above formula we get
W = 50 × 5
W = 250 Joule
Thus, the work done on the body is 250 J.
Example 4: A Box is pulled over an inclined plane with a force of 5 KN. If the displacement of the box is 5 m and the inclination of the plane is 30°. Find the work done (neglecting the weight of the box and friction between the plane and the box)
Solution:
Force applied on the box is 5 KN = 5000 N.
As the box is placed on an inclined plane with an angle of 30° the two components of the forces are, F cos 30° and F sin 30°.
The force which displace the body is F cos 30°= 5000 × (√3 / 2)
= 2500√3
Displacement of the box is 5 m.
Work done is given by the formula,
W = F × d
= 2500√3 × 5
= 12500√3 Joule
Thus, the work done is 12500√3 J
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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