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Work is defined as the energy delivered to or from an item by applying force along with a displacement. It is frequently expressed as the product of force and displacement. If a force contains a component in the direction of the displacement of the site of application (when applied), it is said to produce positive work. The quantity of energy moved or transformed per unit time is referred to as Power.
Power is a scalar quantity while energy is termed as the quantitative attribute that must be transmitted to a body or physical system in order to perform work on it or to heat it. Energy is a conserved quantity, which means that it cannot be generated by transformation.
Read More: Work Energy & Power Important Questions
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Key Terms: Work, Energy, Power, Displacement, Joules, Newton, Force, Distance, Torque, Watt
What is Work?
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Work done on a system is defined as the product of the component of the force in the direction of motion and the distance across which the force operates.
- When a force acts on an object, causing it to move, work is said to be done on the object.
- Work is made up of three main components: force, displacement, and causation.
- There must be a displacement and the force must cause the displacement for a force to qualify as having done work on an object.
- Examples of work: a man carrying a box, a horse pulling a plough, etc.
- A force is applied to each object in the cases listed above, causing it to be move.
Work Done Example
Read More: Work Done by Gravity Formula
SI Unit of Work
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Joule denoted by the letter ‘J’ is the SI Unit of work.
- 1 Joule is defined as the work done by a force of one Newton in moving an object a distance of one meter in the direction of the force.
- Although it is equivalent to a newton metre, the joule should never be referred to as such.
- Nm is the correct unit for measuring Torque (force-displacement product).
Example: When a person does work of 200 J on a moving an object, it indicates that the person applies a force of 200 N to the object, the object is moved by 1 m along the force action line. Despite the fact that both force and displacement are vector values, work is a scalar quantity since it is the dot product of the two.
Work Done to Move an Object
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Factors Affecting Work
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Force is described as a push or a pull that may cause any massed object's velocity and acceleration to alter. The factors affecting work are:
- The amount and direction of force: both are vector quantities.
- If the force acting on an item is zero then no work is done.
- Displacement: a vector quantity that represents the smallest distance between an object's starting and final positions.
- If the resultant displacement in the direction of force is zero, the total work done by a force acting on an item is zero.
- For example, if we push a stiff wall with all our might but still fail to move it, we have done no work on the wall.
Angle between Force and Displacement
Depending on the direction of displacement of the item with regard to the force, the work done by the force might be positive, negative, or zero. Some other points to be considered are as follows:
The work done by the force of friction on an item moving against it is negative. An item experiences zero force when the angle of displacement is perpendicular to the direction of the force. Consider the case of a coolie who is lifting a bulk on his head at a 90-degree angle to the force of gravity. Gravity does no work on the item in this situation.
Also Read: Differences between Acceleration and Velocity
Power and Energy
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To derive the relatiionship between work, energy and power, let us individually understand the coscepts of power and energy in depth.
Power
The quantity work involves a force that causes a displacement. Sometimes the task is completed fast, and other times it is completed more slowly.
Examples of Power
- A rock climber takes an unusually lengthy time to raise her body a few metres up the edge of a cliff.
- A trail hiker, on the other hand, who chooses the simpler way up the mountain, may raise her body a few metres in a short length of time.
- Although the two persons undertake the same amount of work, the hiker completes it in significantly less time than the rock climber.
- The power is defined as a number that has to do with the rate at which a specific amount of work is completed.
- The hiker's power rating is higher than the rock climbers.
Power = Work / Time
Watt is the unit of Power. A unit of power is equal to a unit of work divided by a unit of time.
Watt = Joule/second
Horsepower is used to denote the power of machines One horsepower is roughly 750 Watts.
Power can also be written as:
Power = Force x (Displacement/Time)
Power = Force x Velocity
Read More: Kinetic and Potential Energy Difference
Energy
Energy is described as the "capacity to conduct work," or the "ability to apply a force that causes an item to move."
Potential energy and kinetic energy are two principal forms of energy. Potential energy arises before and kinetic energy occurs during activity.
Example: Consider that you're holding your physics textbook in the air. Because of its lofty elevation, it has the potential to fall. When you drop your textbook, the potential energy is transformed to kinetic energy, which is the energy that drives the movement.
Also Read: Joule's Law
Work, Power, and Energy – Relation
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The relationship of work with the concepts of Power and Energy is elaborated in detail below:
Work and Energy
Work is only done on an item when its kinetic energy changes, according to the work-energy theorem.
- When a force pushes an item from one point to another, the object does work if its kinetic energy changes.
- And only when some components of the applied force are in the same or opposite direction as the object's motion is this kinetic energy shift achievable.
- For example: Lifting a thing up requires work because your force pulls the object up in the opposite direction of the gravitational force dragging it down.
- Work is measure of energy change in an object.
- A force applied is applied in the same or opposite direction as the object's motion causes work to be done.
- Work done give rise to energy when this force is feasible.
- The work-energy theorem asserts that the work done on an item equals the change in that object's kinetic energy.
- Kinetic energy is the energy held by a moving body. Kinetic energy is present when an item moves.
KE = mv2/2
where,
m is the object's mass in kilograms
v is the velocity in meters per second.
Raed More: Speed-Time Graphs
Work Done and Kinetic Energy
Consider an object having a velocity of u at the start. When a force, F, is applied to an object, it is displaced by a distance, s, and accelerates by an amount, a. As a result, a new velocity, v, is generated.
Work Done by a Ball
v2 = u2 + 2as —— 1
v2 – u2 = 2as.-------- 2
Multiply the second equation by the mass, m.
As a result, mv2 – mu2 = 2mas ------ 3
When we divide everything by two, we get: mv2/2 – mu2/2 = mass-------- 4
Work = Force x Distance = Mass
The net force is represented by Force, F.
mv2/2 – mu2/2 = Work done (if mass is replaced with work done in equation 4) -------- 5
The change in the kinetic energy of the item is denoted by mv2/2 – mu2/2 in equation 5.
Therefore it is proved that,
Work done by the force is equal to the change in kinetic energy
Examples of Kinetic Energy
Read More: Angular Velocity Formula
Work and Power
Power is a measurement of quantity of work that can be accomplished in a given length of time. Work (J) divided by time equals power (s). Watt (W) is the SI unit for power, equaling 1 joule of work per second (J/s). When a force (push or pull) is applied to an item, it causes it to move. The capacity to accomplish the job is defined as energy. The work done per unit of time is referred to as power.
Also Read: Difference between Speed and Velocity
Things to Remember
- Work can be defined as the transfer of the energy that happens when an object is moved across a distance by an external force.
- The various factors affecting work are Force, Displacement and the Angle between Force and Displacement.
- Power is defined as the rate at which work is done or energy is transferred.
- Energy can be defined as the ability to do work.
- There are various forms of energy including potential, kinetic, thermal, etc.
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Previous Year Questions
- Calculate the work done by the applied force. [DUET 2011]
- What is the work done to pull the hanging part on the table. [JIPMER 2000]
- What is the work done in taking charge Q once along the loop? [NEET 2005]
- The work done by a given force only depends on? [JKCET 2018]
- Find the unknown angle between the force and displacement vector. [AMUEEE 2011]
- The area under displacement curve gives? [JKCET 2008]
- Calculate the work done by the cord.
- What is the work done by the force of gravity when the particle goes up?
- Calculate the work done by the force in displacing the particle. [KEAM]
- Calculate the work done to accelerate the particle in 10 seconds?
- What is the work done to drag the 60 kg weight.
- Calculate the work done when the spring is stretched from 0.1 to 0.2 m.
Also Read: Relation Between eV And Joule
Sample Questions
Ques. Using the Work-Energy Theorem, explain the relationship between work and energy. Derive its Formula as well. (5 Marks)
Ans. The Work-Energy theorem asserts that the work done by the total of all forces acting on any particle/object is equal to the change in the Kinetic Energy of the particle. With the addition of work of torque and rotating Kinetic Energy, the concept may be extended to rigid bodies.
The force's work W on any particle/object is equal to the change in the particle's kinetic energy.
W=ΔKE =1/2mV2f-1/2mv2i
Here, Vf and Vi are the particle's starting and ultimate speeds after the force is applied, and m is the particle's mass.
To make it easier to understand, consider the instance when the resultant torque T is constant in magnitude and direction, as well as parallel to the particle's motion. The particle moves with constant acceleration down a straight line, according to Newton's second law, and the force and acceleration are proportional. is equal to F=ma.
The particle's displacement is d, which can be calculated as: vf2=vi2+2ad. I heretore, d=vf2-vi22a
The work of a net force is computed by multiplying its magnitude F=ma by the particle's displacement.W=Fd=mavf2-vi2⋅2a=1/2mvf2-1/2mvi2=KEf-KEi=ΔKE
Ques. Explain the concepts of work, energy, and the work-energy principle. (5 Marks)
Ans. Work is defined as the transformation of energy from one form to another. When energy is transmitted to a particle/object, work is said to be done on that particle/object. If one thing transmits energy to another, the first is said to have performed work on the second.
Work is defined as the application of force to an object over a certain distance. Lifting a weight from the ground and placing it on a shelf is a great illustration of completed Work. The force is equal to the weight of the object, and the distance is equal to the shelf's height.
F x d = W
Energy, on the other hand, is the ability to work. The most basic example of mechanical work is when an object is stationary and you use force to move it. Kinetic energy is the energy stored in any moving object.
The Work-Energy Principle is also used to describe the relationship between work and energy. The change in Kinetic Energy of an item equals the net work done on the specified object is how it's defined.
Ques. When a force of 10 KN is applied, a body is displaced 2 metres. Calculate the amount of work that has been done on the body. (3 Marks)
Ans. Work is calculated by multiplying force by displacement. W = F x d
Where F = 10 KN = 10000N and d = 2m, F = 10 KN = 10000N
We obtain W = 10000 x 2 = 20000 Nm or 20000 J by substituting the variables in the formula.
As a result, the body has been subjected to a total of 20000 J of effort.
Ques. With a force of 15 KN, a student pulls a box across an inclined plane. If the body is displaced 3 metres with a 6000 inclination. Calculate the amount of work the student has done on the body. (5 Marks)
Ans. F = 15 KN = 15000 N is the force applied by the pupil to pull a box across the inclined plane.
Because the body is 3 metres away, d = 3 metres. The force and displacement are inclined at an angle of 600 degrees.
W = F x cos x d is the work done formula.
We obtain W = 15000 x cos 600 x 3cos 600 = 12 by substituting the variables in the formula.
As a result, W = 15000 x (1/2) x 3 = -22500 Nm.
Because the learner is tugging the box, the box is working on him. As a result, the job completed is negative. The student's work on the body is worth -22500 J.
Ques. What is the status of work? Use mathematical notation to explain. (3 Marks)
Ans. Work is considered to be done when energy is moved from one form to another. Work is defined as the movement of an item caused by a force.
The work done by a force F operating at an angle to the displacement d is calculated as follows:
W = F x cosθ x d
When θ= 00, the work done is at its maximum.
If the angle θ is equal to 900, the work done is zero.
Ques. How much work is done on the lawn mower by a person if he pushes the mower 25 m on level ground while exerting a continuous force of 75 N at an angle 350 below the horizontal? Convert the quantity of work into kilocalories and compare it to this person's typical daily dietary energy intake of 10,000 kJ (about 2400 kcal). One calorie (1 cal) of heat is equal to 4.184 J and is used to warm 1 g of water by 1oC, but one food calorie (1 kcal) is equal to 4184 J. (3 Marks)
Ans. The work equation is as follows:W=Fdcosθ
When the known values are substituted, the result is
W =(75.0 N)(25.0 m) cos(35.0o) =1536 J=1.54×103 J
The work in joules is converted to kilocalories.
W=(1536J)/(1 kcal =4184 J)=0.367 kcal. The ratio of daily consumption to labour done is
W / 2400kcal = 1.53×10-4
Ques. A 15-meter displacement is produced by pulling a box with a force of 25 N. Find the work done by the force if the angle between the force and the displacement is 30o. (3 Marks)
Ans. F = 25 N,force
d= 15 m displacement
F and dhave a 30o angle θbetween them.
W = Fd cos θ
Ques. As illustrated in the image, an item of mass m=1 kg slides from top to bottom on a frictionless inclined plane with an inclination angle of 30o and a length of 10 m. Calculate the work done on the item by gravitational and normal forces. Assume a gravity acceleration of g = 10 m s-2. (5 Marks)
Ans. We know that the object's acceleration in the inclined plane is gsin θ.
Newton's second law states that the force acting on a mass along an inclined plane is F=mgsinθ. It's worth noting that this force remains constant during the mass's motion.
The effort done by the gravitational force's parallel component ( mgsinθ ) is given by
W=Fdr=F. dr cosθ
where θ is the angle formed by the force (mg) and the motion's direction (dr). The force (mg sinθ) and displacement (dr) are both in the same direction in this situation. As a result, Work done is zero and cosθ=1
W=Fdr=(mgsinθ)(dr)
(dr=length of the inclined place) W=1×10×sin 30×10=100×12=50 J
Ques. A weight lifter raises a load of 250 kg to a height of 5 m with a force of 5000 N. (5 Marks)
(a) What exactly does a weight lifter do?
(b) What is gravity's contribution to the world?
(c) How much net work has been done on the object?
Ans.
- When a weight lifter lifts a weight, the mass, force, and displacement all point in the same direction, resulting in an angle of =0. between them. As a result of the weight lifter's efforts;
Wweight lifter=Fwhcosθ=Fwh(cos0o) = 5000×5×(1)=25,000joule=25 kJ
- Gravity operates downwards while the weight lifter raises the mass, hence the force and displacement are in the opposite direction. As a result, the angle between them is =180
Wgravity =Fghcos=mgh(cos180o) =250×10×5×(-1) =-12,500joule=-12.5 kJ
- The object's net work done (or total work done).
Wnet =Wweight lifter+Wgravity =25 kJ-12.5 kJ=+12.5 kJ
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