WORK, ENERGY AND POWER is a chapter in the CBSE Class 11 Physics syllabus from Physics Part - I. This chapter hub brings together revision notes, practice questions, worksheets, flashcards, formula sheet to help students learn, practice, and revise WORK, ENERGY AND POWER effectively.

Scroll down to find WORK, ENERGY AND POWER notes, practice questions, worksheets, and revision resources — all in one place. Use the sidebar to jump to any section, or browse the full page below.

WORK, ENERGY AND POWER

NCERT Class 11 Physics Chapter 5: WORK, ENERGY AND POWER (Pages 71–91)

Class 11 CBSE hub Physics chapters Physics Part - I

WORK, ENERGY AND POWER at a Glance

Board

CBSE

Class

Class 11

Subject

Physics

Book

Physics Part - I

Chapter

Pages

71–91

Resources

7 study resources

WORK, ENERGY AND POWER Revision Guide

Download the WORK, ENERGY AND POWER revision guide with key points, summaries, and quick revision notes for CBSE Class 11 Physics.

Key Points

Work is defined as W = F.d cos(θ).

Work is the product of force, displacement, and the cosine of the angle between them. If θ is 0°, work is positive; if it's 90°, no work is done.

Average power is defined as P = W/t.

Power measures how quickly work is done, calculated as total work done (W) divided by the time interval (t). The SI unit is the watt (W).

Kinetic Energy: K = 1/2 mv².

The kinetic energy of an object is dependent on its mass (m) and the square of its velocity (v). It's a scalar quantity that represents the work the object can perform due to its motion.

Work-Energy Theorem: ΔK = W.

The change in kinetic energy (ΔK) of a particle is equal to the net work done on it. This theorem applies to scenarios with varying forces.

Gravitational Potential Energy: V = mgh.

The potential energy (V) stored in an object due to its height (h) above a reference point is the product of its mass (m), gravitational acceleration (g), and height (h).

The conservation of mechanical energy states: K + V = constant.

In the absence of non-conservative forces, the total mechanical energy (sum of kinetic and potential energy) in a closed system remains constant.

Elastic and Inelastic Collisions.

In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved, but kinetic energy is not.

Positive and Negative Work.

Work can be positive (force and displacement in the same direction) or negative (force and displacement in opposite directions).

Work done by a variable force requires integration.

For a varying force, work done is calculated as W = ∫ F(x) dx, which sums incremental work over displacement using calculus.

The Scalar Product: A·B = |A||B| cos(θ).

The dot product results in a scalar. It's dependent on the magnitudes of two vectors and the cosine of the angle between them.

Units of Work/Energy: 1 J = 1 N·m.

Work and energy share the same SI unit, joule (J), which is equivalent to one newton of force exerted over one meter of distance.

The spring force follows Hooke’s Law: F = -kx.

In ideal springs, the force (F) exerted by the spring is directly proportional to its extension (x) from its equilibrium position, where k is the spring constant.

Power has units of watts, where 1 W = 1 J/s.

Power quantifies the rate of energy use or work done, calculated via dividing work by time, highlighting efficiency and energy transfers.

Work done against friction is always negative.

Frictional forces oppose motion, leading to a decrease in kinetic energy, thus resulting in negative work being done on an object.

The work-energy theorem incorporates all forces.

This theorem states that the total work done by all forces acting on an object equals its change in kinetic energy, highlighting the connection between force and motion.

In closed systems, total momentum is conserved.

During collisions, the total momentum before and after remains constant, demonstrating a key principle in mechanics.

Terminal velocity is reached when forces balance.

An object in free fall stops accelerating when gravitational force equals resistive forces (like drag), leading to constant velocity.

Energy cannot be created or destroyed, only transformed.

The law of conservation of energy asserts that energy can change forms (like from potential to kinetic) but the total energy remains unchanged.

Friction converts kinetic energy to thermal energy.

In physical systems, kinetic energy is lost to friction, and this energy is often transformed into heat, affecting overall energy calculations.

Work done is path-independent for conservative forces.

In conservative fields, the work done on an object is only dependent on its initial and final positions, irrespective of the path taken.

WORK, ENERGY AND POWER Practice Questions & Answers

Practice important questions and exam-style problems from WORK, ENERGY AND POWER. These questions cover key topics from the CBSE Class 11 Physics syllabus.

How to practice: Start with the questions below to test your understanding of WORK, ENERGY AND POWER. Use the revision guide to review concepts you find difficult, then come back and retry the questions for better retention.

What is the correct definition of 'work' in physics?

Single Answer MCQ

Q-00057247

View explanation

How is 'energy' defined in relation to work?

Single Answer MCQ

Q-00057248

View explanation

Which of the following correctly describes 'power'?

Single Answer MCQ

Q-00057249

View explanation

If a person lifts a box to a height with a constant force, what is true about the work done by that person?

Single Answer MCQ

Q-00057250

View explanation

Which statement is true regarding the scalar product of two vectors?

Single Answer MCQ

Q-00057251

View explanation

What is a characteristic of the scalar product of vectors?

Single Answer MCQ

Q-00057252

View explanation

An archer releases an arrow. What kind of energy is primarily involved as the arrow flies?

Single Answer MCQ

Q-00057253

View explanation

If a horse performs 1500 joules of work in 30 seconds, what is the power output of the horse?

Single Answer MCQ

Q-00057254

View explanation

View all 173 WORK, ENERGY AND POWER questions

Which of the following best explains why work can be zero even if a force is applied?

Which phenomenon best describes the energy transformation in a moving pendulum?

Why is mechanical energy conserved in an ideal system?

In the context of work, what does the angle between force and displacement determine?

What scenario involves the force and displacement in opposite directions?

A variable force acts on an object. Under which condition would the work done be maximized?

What is the definition of work in physics?

If a force does no work on an object, which of the following must be true?

Which of the following illustrates the work-energy theorem?

An object is lifted to a height. If its weight is 400 N and it is raised 5 m, how much work is done against gravity?

What happens to the kinetic energy of an object if its speed is doubled, assuming constant mass?

A cyclist, traveling at a constant speed, comes to a skidding stop in 10 m. What does this imply about the work done by friction?

What is the unit of work and energy in the SI system?

For an object experiencing a constant force, which of the following equations is used to determine the work done by that force?

If a 5 kg block is pushed with a force of 20 N over a distance of 3 m, ignoring friction, what is the work done on the block?

Which scenario depicts positive work being done?

Which of the following statements is true regarding the work-energy principle?

A truck pushes a car stuck in mud, doing 5000 J of work on it. If the truck does not accelerate, how much work is done on the truck?

What is the work done when lifting a weight of 60 N vertically 2 m?

A ball is thrown vertically upwards and reaches a maximum height before coming back down. What happens to its kinetic energy at the peak?

What is the scalar product of two vectors A and B represented as?

If the angle between two vectors A and B is 90 degrees, what is the value of their scalar product?

Which of the following statements about the scalar product is true?

What does the scalar product A.B give geometrically?

In which case is the scalar product A.B negative?

If vectors A and B are represented as A = 3i + 4j and B = 2i + 5j, what is their dot product?

The scalar product of unit vectors i and j is equal to:

Which of the following is a property of scalar products?

If A = 5i + 3j and B = 4i - 2j, what is A.B?

What happens to the scalar product if one of the vectors is a zero vector?

If the vectors A and B have magnitudes |A| = 6 and |B| = 8, and the angle θ between the vectors is 60 degrees, what is the value of A.B?

How many components are involved in the calculation of the scalar product in a three-dimensional vector space?

In the scalar product formula A.B = AB cos(θ), what does θ represent?

In which of the following cases is the scalar product maximized?

Given two vectors A (2i - 3j) and B (i + 4j), find their scalar product.

What is the formula for kinetic energy (KE)?

If the speed of an object is doubled, what happens to its kinetic energy?

An object of mass 3 kg is moving with a velocity of 4 m/s. What is its kinetic energy?

When an object collides elastically, what happens to its kinetic energy?

If two objects collide and stick together, what type of collision occurred?

Which of the following scenarios would increase the kinetic energy of an object?

Which of the following best describes kinetic energy at the point of maximum height for a projectile?

A 2 kg object moving at 3 m/s collides with a stationary 2 kg object. If they collide elastically, what is the final velocity of the first object after the collision?

In an inelastic collision, what happens to the total kinetic energy?

Which unit is appropriate for measuring kinetic energy?

Why is kinetic energy never negative?

If an object's mass is halved but its speed is doubled, what happens to its kinetic energy?

Which of the following statements about kinetic energy is incorrect?

In a system of two colliding objects, how does momentum compare to kinetic energy?

What is the work done by a constant force acting on an object when it moves in the direction of the force?

When is the work done by a force considered zero?

The work done by a variable force can be calculated by which method?

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

If a block slides down a frictionless incline, what type of force is primarily doing work?

What is the work done against friction when an object moves at a constant speed?

A spring is compressed by 0.5 m, and the spring constant is 200 N/m. What is the work done in compressing the spring?

If you lift an object vertically at a constant velocity, what is true about the work done by you and the weight of the object?

In which scenario is work done on an object positive?

Which of the following statements about work is true?

If a car travels in a circular path at constant speed, what is the work done by the centripetal force?

A box is pulled with a force of 50 N over a distance of 10 m at an angle of 30 degrees to the horizontal. What is the work done?

When lifting a heavy object, if the lifting force is applied at an angle, how does this affect the work done?

If a person carries a box along a horizontal path and does not lift it at all, what can be said about the work done by the gravitational force?

What is the work done by a variable force when displacement approaches zero?

If a varying force is represented graphically, how is the total work done calculated?

In the equation W = ∫ F(x) dx, what does 'x' represent?

A particle moves under the influence of a variable force F(x) = kx, where k is a constant and x is the displacement. What is the work done from x = 0 to x = a?

An object is moved by a variable force described by the equation F(x) = ax^2 + b, where a and b are constants. Which of the following describes how to calculate the work done over a distance from x = 1 to x = 2?

In calculations of work done by a variable force, what happens to the accuracy of the result as the intervals of displacement become smaller?

Before performing work calculations with a variable force, it is necessary to determine what aspect of the force?

The work done by a variable force over a displacement can be approximated through which method?

If a graph of force versus displacement is linear, what type of work function is used?

What is the formula for gravitational potential energy?

A student incorrectly applies a formula for constant force to find the work done by a variable force. What is likely the source of error?

If a ball is lifted to a height of 5 meters, what happens to its potential energy?

How can one derive the relationship between work done and kinetic energy using variable forces?

What conceptual principle explains the conversion of potential energy to kinetic energy?

When considering a non-constant force applied to an object, which integral expression best represents the work done from position x1 to x2?

The potential energy of a lifted object is considered relative to what?

A variable force acting on an object changes from 10 N to 30 N over a total displacement of 10 m. What method would provide an approximate work done?

If a rock is dropped from a height of 15 m, what happens to its potential energy as it falls?

If a force varies linearly with position, such as F(x) = mx + b, what is the first step to determine work done from a to b?

Which of the following correctly describes a conservative force?

How does gravitational potential energy change if both the height and mass of the object are doubled?

When an object is at its highest point in projectile motion, its potential energy is...

In a closed system, if potential energy decreases, what must happen to kinetic energy?

What is the relationship between potential energy and conservative forces?

Which scenario exemplifies potential energy being converted to kinetic energy?

A hydraulic lift uses potential energy to raise cars. What principle does this represent?

How is potential energy calculated when multiple forces act on an object?

Calculating potential energy involves understanding the path taken. What statement describes this relationship?

What does the work-energy theorem state?

If a variable force F(x) does work on an object moving from position x1 to x2, how is the work calculated?

A box is pushed across a rough surface with a varying force. If the force decreases linearly, how would you graph the work done over distance?

An object moves under the influence of a variable force described by F(x) = 3x^2. What is the work done from x = 1 to x = 2?

What happens to the kinetic energy of a particle if the net work done on it is zero?

In which scenario does the work-energy theorem not apply?

If the force F(x) is represented by a curve above the x-axis from x1 to x2, what can be said about the work done?

Which of the following statements best describes the law of conservation of mechanical energy?

What is the unit of work done in the SI system?

A 2 kg object is dropped from a height of 10 m. What is its potential energy at the height of 10 m?

A force varies as F(x) = kx, where k is a constant. How does the work vary with displacement?

If an object falls freely from a certain height, what happens to its mechanical energy?

How can you determine the work done by a variable force graphically?

An object at rest is pushed up a hill. If it reaches a height of 5 m, which energy type increases the most?

What is the significance of the area under the curve when force is plotted against displacement?

A 1 kg ball is thrown upwards with an initial speed of 20 m/s. What is its maximum height?

Which of the following equations represents the work-energy theorem mathematically?

How does the presence of air resistance affect mechanical energy during a free fall?

If a particle is subject to a varying force that increases with displacement, what can we infer about its kinetic energy?

When a spring is compressed, which of the following statements is true regarding energy transformation?

A car accelerates from rest under a constant variable force for a short period. How does this affect its kinetic energy?

A pendulum swings to its highest point. At this moment, which type of energy is at its maximum?

If the force acting on an object is not conservative, what can we deduce about the work-energy theorem?

What is the relationship between kinetic energy and potential energy in a closed system?

In the absence of air resistance, if a ball is thrown upwards, what happens to its total mechanical energy?

A car moving at a speed of 30 m/s applies brakes and comes to a stop after covering a certain distance. Which type of energy is lost during this process?

If a spring's initial extension is halved, what happens to its potential energy at this position?

If a block slides down a frictionless incline, what remains constant throughout its motion?

At what point in a projectile's trajectory is its kinetic energy maximum?

Which of the following is NOT an example of a conservative force?

A ball thrown up reverses its direction at its peak. What can be said about its mechanical energy at this point?

What is the SI unit of power?

If a machine does 500 J of work in 10 seconds, what is its power output?

Which of the following scenarios represents the highest power output?

A 100 W light bulb is on for 5 hours. How much energy does it consume?

A motor provides a constant power of 1500 W. If it runs for 2 hours, how much work is done?

Which of the following represents how power is related to work and time?

An electric motor is rated at 200 W efficiency. After running for 1 hour, what amount of work can it do?

If two machines provide the same amount of work but one takes twice as long, which has greater power?

What happens to the power consumed when work done is kept constant but the time taken is halved?

A person exerts a force of 50 N to lift a box 2 meters in 4 seconds. What is the power exerted?

In a system where mechanical energy is conserved, what can be said about the power input?

If a cyclist maintains an average power output of 200 W, how long will they take to climb a hill requiring 3000 J of work?

A block slides down a frictionless incline converting potential energy into kinetic energy. What does this say about power in the system?

What is the relationship between instantaneous power and velocity at a given moment?

What is the formula for the potential energy stored in a spring?

If a spring is compressed by 4 cm, what is the potential energy stored in the spring if the spring constant is 200 N/m?

If the spring constant of a spring is doubled, how does the potential energy change for the same compression distance?

Which statement about potential energy in a spring is true?

A spring with a spring constant of 50 N/m is compressed by 0.1 m. What is the potential energy stored in the spring?

What happens to the potential energy when a compressed spring is released?

A 0.5 kg object is attached to a spring that follows Hooke's law. If the spring constant is 100 N/m, what is the maximum potential energy when the object is displaced by 0.2 m?

A spring with a spring constant of 120 N/m is stretched by 0.15 m. What work done in stretching the spring?

Which factor affects the potential energy in a spring the most?

A spring is compressed and then released. What type of energy conversion occurs?

Which of these statements is true about potential energy in a spring?

If a spring is compressed by a distance of 0.3 m and the spring constant is 150 N/m, what is the potential energy?

What is the effect of increasing the spring constant 'k' on the potential energy for a given displacement?

What type of force does a spring exert when extended or compressed?

If the potential energy of a spring is maximum, what can be said about the speed of the attached object?

What is conserved in all types of collisions?

In an elastic collision, which of the following statements is true?

What type of collision occurs when two objects stick together after colliding?

When can we say that a collision is perfectly elastic?

In a one-dimensional collision, if a moving object collides with a stationary object and they move together post-collision, how is the final velocity calculated?

If two objects collide elastically, what happens to the kinetic energy of the system?

Which of the following is an example of an inelastic collision?

What is the fractional loss of kinetic energy during a collision where the two colliding bodies move together after impact?

In a two-dimensional collision, how is the momentum computed in each direction?

What happens to the total mechanical energy in an inelastic collision?

What is the equation used to describe momentum conservation for two colliding bodies?

If object A of mass 2kg moving at 4m/s collides elastically with object B of mass 3kg at rest, what is the recoil speed of object B after the collision?

How does increasing mass affect momentum during a collision?

In a completely elastic two-dimensional collision, which quantities can change direction?

Single Answer MCQ

Q-00057437

View explanation

WORK, ENERGY AND POWER Practice Worksheets

Download and practice WORK, ENERGY AND POWER worksheets to improve problem-solving accuracy and speed for CBSE Class 11 Physics exams.

WORK, ENERGY AND POWER - Practice Worksheet

This worksheet covers essential long-answer questions to help you build confidence in WORK, ENERGY AND POWER from Physics Part - I for Class 11 (Physics).

Practice

Questions

Define work in physics. Discuss how the concept of work applies in different scenarios, including lifting a weight and pushing a box across a surface. Include the equation for work and its units.

In physics, 'work' is defined as the product of the force applied to an object and the displacement of the object in the direction of the force: W = F.d.cos(θ), where W is work, F is the force, d is the displacement, and θ is the angle between the force and the displacement vector. Work is measured in joules (J). For instance, if a person lifts a weight vertically (θ = 0), all the applied force contributes to the work done against gravity. Alternatively, if a box is pushed horizontally on the ground (with friction), the work done might be less than calculated as the force vector would need to overcome friction too.

Explain the work-energy theorem. How does it relate work done to changes in kinetic energy? Provide a mathematical expression and an example.

The work-energy theorem states that the work done by all forces acting on an object is equal to the change in its kinetic energy: W = ΔK = K_f - K_i. Here, K_f and K_i are final and initial kinetic energies. For example, if a car accelerates from rest (K_i = 0) to a final speed v, the work done to accelerate the car equals the change in its kinetic energy: W = (1/2)mv^2, where m is the mass of the car.

Differentiate between kinetic energy and potential energy. Provide their formulas and describe situations in which each type of energy is crucial.

Kinetic energy (KE) is the energy of an object due to its motion, defined by KE = (1/2)mv^2, where m is mass and v is velocity. Potential energy (PE) is stored energy based on an object's position or configuration, commonly gravitational potential energy defined as PE = mgh, where h is the height above a reference level. An example of kinetic energy is a moving car, whereas potential energy is exemplified by water stored in a dam at height.

What is the principle of conservation of mechanical energy? Illustrate it using an example of a pendulum.

The principle of conservation of mechanical energy states that the total mechanical energy (kinetic + potential) in a closed system remains constant if only conservative forces act. For a pendulum, when it swings, at its highest point all energy is potential, and at its lowest point, all energy is kinetic. The energy converts back and forth but the total remains constant assuming no air resistance.

Describe how work is done by a variable force. What mathematical approach can be used to calculate work done in this scenario?

For a variable force, work done can be calculated with the integral of the force over the path of displacement: W = ∫ F(x) dx from x_i to x_f. This is often necessary when forces change magnitude or direction, as seen in spring forces or forces experienced by an object moving through a non-uniform medium. An example might involve a spring, where force varies with compression or extension, necessitating integration to find total work.

Examine the concept of power. How is it related to work and energy? Provide formulas and practical examples.

Power is defined as the rate at which work is done or energy is transferred, expressed as P = W/t, where P is power, W is work, and t is time in seconds. It is measured in watts (1 W = 1 J/s). For instance, if a machine does 100 J of work in 5 seconds, its power output is 20 watts. Practical examples include electrical appliances, where higher wattage indicates more energy consumption per unit time.

Discuss the role of friction in work and energy. How does it affect the energy conversion of systems?

Friction acts as a non-conservative force that converts mechanical energy into thermal energy, thus reducing the total mechanical energy available in a system. For example, when a sliding block on a surface experiences friction, not all the work done by the applied force results in kinetic energy; some energy is lost as heat. Thus, the work done is less than the initial potential or applied energy due to frictional losses.

Analyze the concept of potential energy in a spring system. Derive the expression for elastic potential energy and discuss its implications.

The potential energy stored in a spring is given by U = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position. This expression illustrates that potential energy increases with the square of the displacement, meaning that a double displacement results in four times the stored energy. This principle enables applications such as in shock absorbers and mechanical springs.

What are elastic and inelastic collisions? Explain the differences in terms of energy conservation and provide real-world scenarios.

In an elastic collision, both momentum and kinetic energy are conserved (e.g., two billiard balls colliding). In contrast, during inelastic collisions, momentum is conserved, but kinetic energy is not (e.g., a car crash). The key difference lies in the energy transformations; some kinetic energy is converted to other forms such as heat or sound in inelastic collisions, while elastic collisions conserve all kinetic energy in the interacting bodies.

WORK, ENERGY AND POWER - Mastery Worksheet

This worksheet challenges you with deeper, multi-concept long-answer questions from WORK, ENERGY AND POWER to prepare for higher-weightage questions in Class 11.

Mastery

Questions

A 2 kg object is thrown upwards with an initial velocity of 20 m/s. Calculate the maximum height it reaches. Discuss the energy transformations at various points in its flight.

The maximum height h can be calculated using the equation: K.E. initial = P.E. at height h. 1/2 * m * v² = m * g * h. Therefore, h = (v²)/(2g) = (20²)/(2*9.8) = 20.4 m.

Discuss the work-energy theorem and apply it to a case where a 5 kg block is moved 10 m across a frictionless surface by a constant force of 30 N. What is the change in kinetic energy?

Work done W = Force × distance = 30 N × 10 m = 300 J. According to the work-energy theorem, the change in kinetic energy (ΔK.E.) = W = 300 J.

An object is dropped from a height of 50 m. Calculate the work done by gravity when it reaches the ground, and what will be its velocity just before impact?

Work done by gravity W = mgh. If m = 1 kg, then W = 1 * 9.8 * 50 = 490 J. Using K.E. = 1/2 mv², we find the velocity before impact: 490 = 1/2 * 1 * v², giving v = 31.3 m/s.

A spring with a spring constant k = 200 N/m is compressed by 0.5 m. Calculate the potential energy stored in the spring. If it is released, calculate the maximum velocity of a 2 kg mass attached to it.

Potential energy stored, PE = 1/2 kx² = 1/2 * 200 * (0.5)² = 25 J. Using conservation of energy, 25 J = 1/2 mv², thus, v = sqrt(25*2/2) = 5 m/s.

Explain the process of energy conservation in a pendulum swing. Discuss its kinetic and potential energy at the highest and lowest points.

At the highest point, potential energy is maximum and kinetic energy is zero; at the lowest point, kinetic energy is maximum and potential energy is zero. Total energy remains constant throughout.

A cyclist skids to a stop over a distance of 40 m, applying a braking force that does 800 J of work. Calculate the average frictional force exerted on the cyclist.

Work done = Force × Distance, thus, 800 J = F * 40 m. Average frictional force F = 800 J / 40 m = 20 N.

When two ice skaters push off from each other, one skater moves in the opposite direction. If skater A has a mass of 60 kg and skater B has a mass of 40 kg, find the ratio of their velocities if they result from the same push-off force.

By conservation of momentum, 60v_A = 40v_B. Therefore, v_A/v_B = 40/60 = 2/3.

A 1 kg ball is thrown straight up with an initial velocity of 15 m/s. How high will it go? Calculate the time it takes to reach this height.

Height h = (v²)/(2g) = (15²)/(2*9.8) ≈ 11.5 m. Time to reach max height: t = v/g = 15/9.8 ≈ 1.53 s.

A car of mass 1000 kg accelerates from rest to a speed of 20 m/s. What is the work done by the engine? Assume the force provided is constant and find the distance covered during this acceleration.

Using work-energy theorem: Work done W = ΔK.E. = 1/2 m v² = 1/2 * 1000 * (20)² = 200,000 J. The distance can be found using v² = u² + 2as.

An object of mass 3 kg is attached to a spring and compressed by 0.4 m. Determine the spring potential energy and the velocity of the object if it were released and moves vertically.

Spring potential energy PE = 1/2 kx²; for k = 50 N/m, PE = 1/2 * 50 * (0.4)² = 4 J. If released, the potential energy converts to kinetic energy, thus 4 = 1/2*3*v² gives v ≈ 2.58 m/s.

WORK, ENERGY AND POWER - Challenge Worksheet

The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for WORK, ENERGY AND POWER in Class 11.

Challenge

Questions

Evaluate the implications of the work-energy theorem in real-life contexts, such as a vehicle coming to a stop due to friction.

Discuss the relationship between work done by non-conservative forces and the final kinetic energy. Consider examples like vehicles of different masses and stopping distances.

Analyze the factors affecting the potential energy of a spring and derive an equation for the potential energy when stretched or compressed.

Include considerations on energy storage and how it depends on displacement. Compare the potential energy in various scenarios.

Discuss the difference between elastic and inelastic collisions, providing specific examples from sports or daily life.

Evaluate energy conservation in both types of collisions, using equations to express momentum and kinetic energy before and after collisions.

Evaluate how the concept of work done varies with direction of forces and displacement in non-linear motion.

Apply the formula for work to different scenarios; analyze forces acting on an object along a non-linear path.

Explore how conservation of mechanical energy applies when an object moves in gravitational fields of varying strengths.

Illustrate how potential energy shifts to kinetic energy during different phases of motion, including edge cases.

Investigate the work done by multiple forces acting on an object and resulting motion on a frictional surface.

Employ the work-energy theorem to calculate frictional effects and total work done in motion.

Evaluate the applications of power in various human activities, discussing how it affects performance in daily tasks.

Analyze the calculation of power in scenarios such as lifting weights and running, comparing effectiveness.

Analyze collision types based on conservation principles, discussing scenarios where energy is transformed into heat.

Use mathematical models to derive outcomes in different types of collisions and the energy lost.

Evaluate the environmental impact of energy conservation in a system using examples of conservation across mechanical energy.

Discuss real-life implications of energy transfer efficiency in devices like engines or electric cars.

Examine the role of work done on an object during its interaction with conservative and non-conservative forces.

Differentiate between the outcomes of work done by conservative forces and those that are non-conservative, providing examples.

WORK, ENERGY AND POWER Formula Sheet

Use this Class 11 Physics WORK, ENERGY AND POWER Formula Sheet for quick revision before school exams and CBSE exams. It brings together the important formulas, key concepts, and worked examples in one place so students can revise faster and download a printable PDF for offline study.

Important Formulas

W = F · d · cos(θ)

W is work (in joules), F is the applied force (in newtons), d is the displacement (in meters), and θ is the angle between the force and displacement vectors. This formula calculates work done by a constant force acting over a distance.

K = (1/2) mv²

K represents kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). This shows the energy due to motion of an object.

W = ΔK

This states that the work done (W) by the net force on an object is equal to the change in kinetic energy (ΔK) of the object.

V(h) = mgh

V(h) denotes gravitational potential energy (in joules) at height h (in meters), m is mass (in kg), and g is the acceleration due to gravity (≈9.81 m/s²). This shows the energy stored due to an object's height.

P = W / t

P represents power (in watts), W is work done (in joules), and t is the time (in seconds) over which the work is done. It indicates the rate at which work is performed.

K = (1/2) kx²

K is the elastic potential energy (in joules) stored in a spring, k is the spring constant (N/m), and x is the displacement from equilibrium (in meters). This signifies the energy stored in a spring when compressed or stretched.

W = ∫F(x) dx

This represents the work done by a variable force F(x) as it moves from position xi to xf, calculated as an integral of the force over the displacement.

ΔK + ΔV = 0

This expresses the principle of conservation of mechanical energy, stating that the sum of the changes in kinetic energy (ΔK) and potential energy (ΔV) is zero when only conservative forces act.

v² = u² + 2as

This equation connects initial velocity (u), final velocity (v), acceleration (a), and displacement (s). It relates kinematic quantities for an object undergoing constant acceleration.

F = ma

This is Newton's second law, where F is the net force (in newtons), m is mass (in kg), and a is acceleration (in m/s²). It describes the relationship between force, mass, and acceleration.

Worked Examples

W_total = W_g + W_r

This equation relates the total work (W_total) done on a system to the work done by gravitational force (W_g) and the work done by resistive forces (W_r).

K_final - K_initial = W_net

This equation illustrates that the change in kinetic energy is equal to the work done by the net force acting on the object.

V = K + U

This states that the total mechanical energy (V) is the sum of the kinetic energy (K) and potential energy (U) of an object.

P_avg = ΔE / Δt

This defines average power (P_avg) as the change in energy (ΔE) divided by the time interval (Δt) over which the change occurs.

F_s = -kx

This is Hooke's law, stating that the spring force (F_s) acts in the opposite direction of the displacement (x) and is proportional to the displacement amount, where k is the spring constant.

F_net = ma

This equation states that the net force (F_net) acting on an object is equal to the product of its mass (m) and acceleration (a).

mgh = (1/2) mv² + (1/2) kx²

This equation represents energy conservation, expressing that gravitational potential energy (mgh) converts to kinetic energy and elastic potential energy when falling.

W = ∫F·dx

This describes the work done by a force (F) along a path (dx) as an integral, useful for non-constant forces.

F · d = W

This signifies that the work done by a force (F) on an object while it displaces through a distance (d) is equal to the dot product of the force and displacement vectors.

K = W

Indicates that the work done on an object is equal to its kinetic energy, illustrating the work-energy principle.

Explore More WORK, ENERGY AND POWER Resources

Explore more chapter resources to strengthen your understanding and prepare for exams.

Practice Questions Worksheets Revision Notes Flashcards Download PDFs

WORK, ENERGY AND POWER Frequently Asked Questions

Explore the fundamental concepts of work, energy, and power in Class 11 Physics. Understand scalar products and their implications for mechanical systems. Enhance your knowledge with detailed explanations and examples.

QWhat is the definition of work in physics?

In physics, 'work' is defined as the measure of energy transfer that occurs when an object is moved over a distance by an external force. Specifically, work is calculated as the product of the force applied to the object and the distance moved in the direction of the force. The formula is W = F × d × cos(θ), where θ is the angle between the force and the displacement direction.

QHow is energy related to work?

Energy is defined as the capacity to do work. In physics, energy is involved in performing work whenever a force acts upon an object to cause displacement. The work done on an object results in a change in its energy, particularly kinetic or potential energy. Thus, energy is considered a measure of the ability to perform work or to produce changes in the physical system.

QWhat is the scalar product of vectors?

The scalar product, or dot product, of two vectors is a mathematical operation that results in a scalar number. It is calculated by multiplying the magnitudes of the vectors and the cosine of the angle between them. The formula for the scalar product A . B is A . B = |A| |B| cos(θ), which indicates how much of one vector acts in the direction of another.

QWhat does the term 'power' mean in physics?

In physics, 'power' refers to the rate at which work is done or energy is transferred over time. It quantifies how quickly energy is used, calculated as the work done divided by the time taken. The formula for power is P = W / t, where P is power, W is work, and t is time. Power is measured in watts (W), where one watt equals one joule per second.

QHow is kinetic energy defined?

Kinetic energy is the energy possessed by an object due to its motion. It is defined by the formula KE = 1/2 mv^2, where m represents the mass of the object, and v is its velocity. This relationship illustrates that an object's kinetic energy increases with the square of its velocity and directly with its mass.

QWhat is potential energy, and how is it calculated?

Potential energy is the stored energy of an object based on its position or configuration. The most common form is gravitational potential energy, calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above a reference point. This energy can be converted into kinetic energy when the object is allowed to move.

QWhat does the work-energy theorem state?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as W = ΔKE, where W is work done, and ΔKE is the change in kinetic energy (final KE minus initial KE). This theorem emphasizes the relationship between the forces acting on an object and its resulting motion.

QWhat is mechanical energy conservation?

The principle of conservation of mechanical energy states that if only conservative forces are acting on a system, the total mechanical energy (sum of potential and kinetic energy) will remain constant over time. This implies that energy can transform from one form to another but cannot be created or destroyed in isolated systems.

QWhat role does the angle θ play in work calculations?

The angle θ in work calculations determines how much of the applied force contributes to the displacement. The work is maximized when θ is 0° (force and displacement are aligned) and zero when θ is 90° (force is perpendicular to displacement). Hence, cos(θ) plays a crucial role in quantifying the effective force component in the direction of movement.

QHow do you find the work done by a variable force?

To find the work done by a variable force, you need to use the integral of the force function over the distance moved. The work done is calculated as W = ∫ F(x) dx from the initial position to the final position. This integral approach accounts for the changing magnitude of the force across the distance moved.

QWhat is the significance of the scalar product in physics?

The scalar product is significant in physics as it provides a way to calculate relationships between vectors, especially in situations involving work, energy, and projections. It allows for quantifying how much one vector influences another in terms of energy transfer or movement, enhancing our understanding of vector interactions.

QWhat is the relationship between work, energy, and power?

Work, energy, and power are interconnected concepts in physics. Work is the transfer of energy, and energy is the capacity to perform work. Power represents how quickly work is being done or energy is being converted. Thus, understanding these relationships helps analyze motion and energy transformations in physical systems.

QHow does the conservation of mechanical energy apply to springs?

The conservation of mechanical energy applies to springs as their potential energy when compressed or stretched converts to kinetic energy during motion. The potential energy stored in a spring is given by the formula PE = 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position. This explains energy transformation in spring-based systems.

QWhat are unit vectors, and how do they relate to the scalar product?

Unit vectors are vectors with a magnitude of one that are used to indicate direction. In the context of the scalar product, unit vectors simplify calculations by allowing us to focus on the directional components of vectors. The dot product of unit vectors provides valuable information about the angle between them, essential in physics applications.

QWhy is the scalar product commutative?

The scalar product is commutative, meaning that A . B = B . A for any vectors A and B. This property holds because the multiplication of their magnitudes is independent of the order, and the cosine of the angle between them is the same regardless of the vector order. This feature simplifies many calculations in vector analysis.

QWhat is a variable force?

A variable force is one whose magnitude and/or direction changes with position or time. Unlike constant forces, variable forces require more complex methods, such as calculus, to determine the work done over a distance. Examples include gravitational force acting on a falling object or spring forces that vary with displacement.

QHow do we determine when two vectors are perpendicular \(A . B = 0\)?

Two vectors A and B are considered perpendicular when their scalar product equals zero (A . B = 0). This occurs when the angle θ between them is 90 degrees, meaning that the auxiliary forces acting on them do not contribute to the work in a given direction, signifying independence in their directional components.

QHow can power be increased in a mechanical system?

Power in a mechanical system can be increased by either increasing the amount of work done in a given time or decreasing the time taken to do the same amount of work. This can be achieved by applying greater forces, improving mechanical efficiency, or utilizing mechanisms that facilitate faster motion.

QWhat is the role of friction in work and energy?

Friction plays a critical role in work and energy dynamics as it transforms kinetic energy into thermal energy, opposing motion. When work is done against friction, it requires additional energy input to achieve the same displacement; thus, it influences overall energy efficiency in mechanical systems and must be accounted for in work-energy calculations.

QHow does energy transformation occur in practical situations?

Energy transformation occurs in practical situations when energy changes from one form to another. For example, when an object falls, gravitational potential energy is converted into kinetic energy. Similarly, in a bow, stored elastic potential energy is transformed into kinetic energy when the arrow is released. Understanding these transformations is essential for analyzing energy systems.

QWhat is the work done in circular motion?

In circular motion, if the force acting on the object is always directed toward the center (centripetal force), the work done by this force is zero because the direction of the force and the displacement are perpendicular. However, work is done when tangential forces are applied, influencing the object's speed along the circular path.

QHow can we visualize work through graphs?

We can visualize work through graphs by plotting force against distance. The area under the force-distance graph represents the work done. For variable forces, the graph will show curves, and calculating areas under these curves, using integral calculus, provides the total work done across the distance.

Reviewed & Verified by Edzy Expert

Academically Reviewed

Dr. Meera Nair

CBSE Physics & Chemistry Reviewer

Senior Physics and Chemistry educator with 15+ years of experience in CBSE senior secondary curriculum and competitive exam content.

Ph.D. ChemistryM.Sc. Physics

WORK, ENERGY AND POWER PDF Downloads

Download worksheets, revision guides, formula sheets, and the official textbook PDF for WORK, ENERGY AND POWER.

WORK, ENERGY AND POWER Official Textbook PDF

Download the official NCERT/CBSE textbook PDF for Class 11 Physics.

Official PDFEnglish EditionNCERT Source

Download PDF

WORK, ENERGY AND POWER Revision Guide

Use this one-page guide to revise the most important ideas from WORK, ENERGY AND POWER.

Best for1-page chapter recap

Download PDF

WORK, ENERGY AND POWER Formula Sheet

Download the WORK, ENERGY AND POWER formula sheet PDF with important formulas, worked examples, and quick revision support for exam preparation.

Best forImportant formulas for quick revision

Download Formula Sheet PDF

WORK, ENERGY AND POWER Practice Worksheet

Solve basic and application-based questions from WORK, ENERGY AND POWER.

Best forCore practice set

Download PDF

WORK, ENERGY AND POWER Mastery Worksheet

Work through mixed WORK, ENERGY AND POWER questions to improve accuracy and speed.

Best forMixed difficulty set

Download PDF

WORK, ENERGY AND POWER Challenge Worksheet

Try harder WORK, ENERGY AND POWER questions that test deeper understanding.

Best forFor deeper problem solving

Download PDF

WORK, ENERGY AND POWER Question Bank

Download important questions and exam-style prompts from WORK, ENERGY AND POWER.

Best forPrintable question set

Download PDF

WORK, ENERGY AND POWER Flashcards

Revise key terms and definitions from WORK, ENERGY AND POWER with interactive flashcards. Quick recall practice for CBSE Class 11 Physics.

These flash cards cover important concepts from WORK, ENERGY AND POWER in Physics Part - I for Class 11 (Physics).

1/18

What is the definition of work in physics?

1/18

In physics, work is defined as the product of the force applied on an object and the displacement of that object in the direction of the force. Formula: W = F × d × cos(θ), where θ is the angle between the force and displacement vectors.

How well did you know this?

Not at allPerfectly

2/18

What is the SI unit of work?

2/18

The SI unit of work is the Joule (J). One Joule is defined as the work done when a force of one newton displaces an object by one meter in the direction of the force.

How well did you know this?

Not at allPerfectly

Active

3/18

What is energy in physics?

Active

3/18

Energy is the capacity to do work. It exists in various forms such as kinetic energy, potential energy, thermal energy, etc.

How well did you know this?

Not at allPerfectly

4/18

What is the formula for kinetic energy?

4/18

The formula for kinetic energy (KE) is KE = (1/2)mv², where m is mass and v is the velocity of the object.

5/18

Define potential energy.

5/18

Potential energy is the energy possessed by an object due to its position or configuration. For gravitational potential energy: PE = mgh, where m is mass, g is acceleration due to gravity, and h is height above a reference point.

6/18

What does the work-energy theorem state?

6/18

The work-energy theorem states that the work done by the net force acting on an object is equal to the change in its kinetic energy.

7/18

How is power defined in physics?

7/18

Power is defined as the rate at which work is done or energy is transferred. Formula: Power = Work done / Time taken.

8/18

What is the SI unit of power?

8/18

The SI unit of power is the Watt (W). One Watt is equal to one Joule per second.

9/18

What is the scalar product of two vectors?

9/18

The scalar product (or dot product) of two vectors A and B is given by A · B = |A||B| cos(θ), where θ is the angle between the vectors. It results in a scalar quantity.

10/18

What is the commutative property of the scalar product?

10/18

The scalar product follows the commutative property: A · B = B · A.

11/18

State the distributive property of the scalar product.

11/18

The distributive property states: A · (B + C) = A · B + A · C.

12/18

What is the scalar product of two perpendicular vectors?

12/18

If two vectors A and B are perpendicular, then A · B = 0.

13/18

How to calculate work done in lifting an object?

13/18

The work done in lifting an object is calculated using W = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height lifted.

14/18

What is the principle of conservation of energy?

14/18

The principle states that energy cannot be created or destroyed, only transformed from one form to another.

15/18

What is the difference between work and energy?

15/18

Work is the transfer of energy through force applied over a distance, while energy is the capacity to perform work.

16/18

Provide an example illustrating power.

16/18

Running up the stairs quickly requires more power than walking up because power is the rate of doing work; more work is done in less time.

17/18

Is work done when force is applied but no movement occurs?

17/18

No, work is only done when an object moves in the direction of the applied force. If there is no displacement, work done is zero.

18/18

What is the relation between work and energy?

18/18

Work done on an object results in a transfer of energy to that object, changing its kinetic energy or potential energy.

Practice WORK, ENERGY AND POWER with Interactive Duels

Live Academic Duel

Master WORK, ENERGY AND POWER via Live Academic Duels

Challenge your classmates or test your individual retention on the core concepts of CBSE Class 11 Physics (Physics Part - I). Compete in speed-recall question rounds matched explicitly to the latest syllabus milestones for WORK, ENERGY AND POWER.

CBSE-aligned questions

Instant speed-recall rounds

Quick, competitive practice on WORK, ENERGY AND POWER with zero setup.