Class 11 Physics · Chapter 5 NotesWork, Energy and Power
Study Class 11 Physics Chapter 5 Work, Energy and Power. Learn work-energy theorem, kinetic and potential energy, power, and collisions with clear explanations.
Work, energy and power are words we use every day, but in physics they have precise meanings. This chapter begins by defining work as the product of the component of force along the displacement and the magnitude of the displacement. It then introduces kinetic energy and proves the work-energy theorem, which states that the change in kinetic energy of a body equals the work done by the net force. The concept of potential energy is developed for conservative forces such as gravity and the spring force, leading to the principle of conservation of mechanical energy. The chapter also explains power as the rate of doing work or transferring energy, and applies the laws of momentum and energy conservation to elastic and inelastic collisions in one and two dimensions. By the end, you will be able to calculate work done by constant and variable forces, analyse energy transformations, and solve collision problems.
What you'll learn
1Define work and calculate it using the scalar product of force and displacement.
2Explain the work-energy theorem and apply it to problems involving constant and variable forces.
3Distinguish between kinetic energy and potential energy, and write expressions for gravitational and spring potential energy.
4State and apply the principle of conservation of mechanical energy for conservative forces.
5Define power and compute average and instantaneous power.
6Analyse elastic and inelastic collisions in one and two dimensions using conservation of momentum and kinetic energy.
Chapter at a glance
01Work: Definition, Calculation, and Examples
02Kinetic and Potential Energy
03Power: Rate of Work and Energy
Detailed chapter notes
01
Work and the Scalar Product
In physics, work is done when a force acts on an object and the object undergoes a displacement. If the force is constant and makes an angle θ with the displacement, the work done is W = F d cos θ. This is the scalar product of the force and displacement vectors, written as W = F·d. Work is a scalar quantity and can be positive, negative or zero. It is positive when the force has a component in the direction of displacement, negative when the component is opposite to the displacement, and zero when the force is perpendicular to the displacement or when there is no displacement. The SI unit of work is the joule (J), which equals one newton-metre.
W = F d cos θ = F·d
Positive work0° ≤ θ < 90°
Negative work90° < θ ≤ 180°
Zero workθ = 90° or d = 0
1 J = 1 N m
02
Kinetic Energy and the Work-Energy Theorem
Kinetic energy is the energy possessed by an object due to its motion. For an object of mass m moving with speed v, the kinetic energy is K = ½ m v². It is a scalar quantity and is always positive. The work-energy theorem states that the change in kinetic energy of a body is equal to the work done by the net force acting on it: Kf – Ki = Wnet. This theorem is derived from Newton's second law and holds for both constant and variable forces. It provides a powerful method to solve problems where the net force or the displacement is known, without directly using acceleration.
K = ½ m v²
Work-energy theoremKf – Ki = Wnet
Valid for constant and variable forces
Work done by net force equals change in kinetic energy
03
Work Done by a Variable Force
Many forces, such as the spring force, vary with position. To calculate work done by a variable force F(x) along the x-axis, we divide the displacement into small intervals Δx. Over each interval, the force is approximately constant, so the work done is ΔW = F(x) Δx. The total work is the sum of these small amounts. In the limit Δx → 0, this sum becomes the definite integral of F(x) from the initial position xi to the final position xf: W = ∫ F(x) dx. Graphically, this work is the area under the force-displacement curve. The work-energy theorem can be extended to variable forces using this integral.
W = ∫ F(x) dx from xi to xf
Work is the area under the force-displacement graph
Examplework done by a spring force Fs = –kx
04
Potential Energy and Conservation of Mechanical Energy
Potential energy is the energy stored in a body due to its position or configuration. For a conservative force, we can define a potential energy function V(x) such that F(x) = –dV/dx. The change in potential energy is the negative of the work done by the conservative force. For gravitational force near the Earth's surface, V(h) = mgh, where h is the height above a chosen reference. For a spring obeying Hooke's law, Fs = –kx, the elastic potential energy is V(x) = ½ kx². The principle of conservation of mechanical energy states that if only conservative forces do work, the total mechanical energy E = K + V remains constant. This principle allows us to relate speeds and positions without knowing the details of the path.
F(x) = –dV/dx
Gravitational potential energyV(h) = mgh
Spring potential energyV(x) = ½ kx²
ConservationKi + Vi = Kf + Vf (if only conservative forces act)
05
Power
Power is the rate at which work is done or energy is transferred. The average power is the total work done divided by the total time taken: Pav = W/t. The instantaneous power is the limiting value of the average power as the time interval approaches zero: P = dW/dt. Since dW = F·dr, we can also write P = F·v, where v is the instantaneous velocity. Power is a scalar quantity and its SI unit is the watt (W), where 1 W = 1 J s⁻¹. Another common unit is the horsepower (hp), with 1 hp = 746 W. The kilowatt-hour (kWh) is a unit of energy, not power, and equals 3.6 × 10⁶ J.
Average powerPav = W/t
Instantaneous powerP = dW/dt = F·v
SI unitwatt (W), 1 W = 1 J s⁻¹
1 hp = 746 W
1 kWh = 3.6 × 10⁶ J
06
Collisions
A collision is a brief interaction between two bodies in which they exert strong forces on each other. In all collisions, the total linear momentum of the system is conserved. Collisions are classified as elastic or inelastic. In an elastic collision, the total kinetic energy is also conserved. In an inelastic collision, some kinetic energy is lost to other forms such as heat, sound or deformation. A completely inelastic collision is one in which the bodies stick together after collision. For a one-dimensional elastic collision between two masses m₁ and m₂, with m₂ initially at rest, the final velocities are v1f = ((m₁ – m₂)/(m₁ + m₂)) v1i and v2f = (2m₁/(m₁ + m₂)) v1i. In two dimensions, momentum conservation gives two equations, and for elastic collisions, kinetic energy conservation provides a third. If the masses are equal and the collision is elastic and glancing, the two bodies move at right angles to each other.
Momentum is conserved in all collisions
Elastic collisionkinetic energy is also conserved
Inelastic collisionsome kinetic energy is lost
Completely inelasticbodies stick together
For equal masses in elastic glancing collision, final velocities are perpendicular
Want the complete chapter resources?Topic notes, quizzes and flashcards for Work, Energy and Power.
Q1. Define work in physics. When is the work done by a force zero? Give one example.
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Model answer
Work is defined as the product of the component of force in the direction of displacement and the magnitude of displacement. Mathematically, W = F d cos θ. Work done is zero when displacement is zero, force is zero, or force and displacement are perpendicular. For example, if a person pushes a wall and the wall does not move, work done is zero.
Sample question3 marks
Q2. State and prove the work-energy theorem for a constant force in one dimension.
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Model answer
The work-energy theorem states that the change in kinetic energy of a particle is equal to the work done on it by the net force. For constant acceleration, from v² - u² = 2as, multiplying by m/2 gives (1/2)mv² - (1/2)mu² = mas = Fs = W. Thus, Kf - Ki = W.
Sample question3 marks
Q3. Define power. Write its SI unit and derive its dimensional formula.
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Model answer
Power is defined as the time rate at which work is done or energy is transferred. Its SI unit is watt (W), where 1 W = 1 J s⁻¹. The dimensional formula of power is [ML²T⁻³], derived from work (force × displacement) having dimensions [ML²T⁻²] divided by time [T].
Sample question3 marks
Q4. A cyclist skids to a stop in 10 m. The road exerts a frictional force of 200 N opposite to motion. Calculate the work done by the road on the cycle and the work done by the cycle on the road.
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Model answer
Work done by road on cycle: W = F d cos θ = 200 × 10 × cos 180° = -2000 J. The negative sign indicates the force opposes motion. Work done by cycle on road is zero because the road undergoes no displacement.
Sample question3 marks
Q5. A raindrop of mass 1.00 g falls from a height of 1.00 km. It hits the ground with a speed of 50.0 m/s. Using the work-energy theorem, find the work done by the resistive force. (Take g = 10 m/s²)
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Model answer
Initial KE = 0, final KE = (1/2)×10⁻³×(50)² = 1.25 J. Work done by gravity Wg = mgh = 10⁻³×10×10³ = 10 J. By work-energy theorem, ΔK = Wg + Wr, so 1.25 = 10 + Wr, giving Wr = -8.75 J.
Want more questions with answers?Get the full practice set for this chapter.
In physics, work is done when a force acts on an object and the object moves. It is defined as the product of the component of the force in the direction of displacement and the magnitude of the displacement: W = F d cos θ. Work is a scalar quantity and its SI unit is the joule (J).
What is the work-energy theorem?
The work-energy theorem states that the change in kinetic energy of a body is equal to the work done by the net force acting on it. Mathematically, Kf – Ki = Wnet, where K = ½ m v². It is valid for both constant and variable forces.
What is the difference between kinetic and potential energy?
Kinetic energy is the energy possessed by an object due to its motion, given by K = ½ m v². Potential energy is the energy stored in an object due to its position or configuration, such as gravitational potential energy mgh or spring potential energy ½ kx². Kinetic energy is always positive, while potential energy can be positive or negative depending on the reference point.
What is the principle of conservation of mechanical energy?
The principle states that the total mechanical energy (kinetic plus potential) of a system remains constant if only conservative forces do work on it. That is, Ki + Vi = Kf + Vf. If non-conservative forces like friction act, mechanical energy is not conserved.
What is power and how is it calculated?
Power is the rate at which work is done or energy is transferred. Average power is W/t, and instantaneous power is dW/dt or F·v. Its SI unit is the watt (W), where 1 W = 1 J s⁻¹. Another unit is horsepower (1 hp = 746 W).
What is the difference between elastic and inelastic collisions?
In an elastic collision, both total linear momentum and total kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not; some kinetic energy is converted into other forms like heat or sound. In a completely inelastic collision, the bodies stick together after impact.