Work, Energy and Power Notes for NEET and JEE Main 2027 with PDF

Work, Energy and Power is Chapter 5 of NCERT Class 11 Physics and Unit 4 of both the NEET UG and JEE Main syllabi. These notes cover the scalar product, work by constant and variable forces, kinetic and potential energy, the work-energy theorem, conservation of mechanical energy, spring energy, power and collisions, with key facts and a free PDF.

Work, Energy and Power Notes for NEET and JEE Main

Section-wise key points from NCERT Chapter 5, formula and collision tables, high-yield facts and common mistakes for 2027 revision.

Work, Energy and Power at a Glance

The topic list follows the NEET UG 2026 syllabus released by the National Medical Commission (NMC) on 22 December 2025 and the JEE Main 2026 syllabus published by the National Testing Agency (NTA). Both stay the reference until the 2027 syllabi are out. Full lists: NEET syllabus and JEE Main syllabus.

Scalar Product of Two Vectors

The scalar (dot) product of A and B is A·B = AB cos θ, a scalar, where θ is the angle between them. It equals the magnitude of one vector times the component of the other along it.

• Commutative: A·B = B·A. Distributive: A·(B + C) = A·B + A·C; and A·(λB) = λ(A·B).
• î·î = ĵ·ĵ = k̂·k̂ = 1 and î·ĵ = ĵ·k̂ = k̂·î = 0.
• A·B = AₓBₓ + A_yB_y + A_zB_z, and A·A = A².
• A·B = 0 when A and B are perpendicular.
• NCERT Example 5.1: for F = 3î + 4ĵ − 5k̂ and d = 5î + 4ĵ + 3k̂, F·d = 16 and cos θ = 0.32.

Work: Definition, Sign and Units

Work done by a constant force is the component of force along the displacement times the magnitude of the displacement: W = (F cos θ)d = F·d.

• No work is done if the displacement is zero (pushing a rigid wall, a weightlifter holding a load steady), if the force is zero (a block sliding on a smooth table), or if force and displacement are perpendicular (gravity on that block, or on the moon in an assumed circular orbit).
• Work is positive for 0° ≤ θ < 90° and negative for 90° < θ ≤ 180°; friction usually does negative work (θ = 180°).
• Work and energy have dimensions [M L² T⁻²]; the SI unit is the joule (J), after James Prescott Joule.
• Though forces between two bodies are equal and opposite, the work done on each need not be: a road does −2000 J on a skidding cycle, but the cycle does no work on the road because the road does not move.

Kinetic Energy and the Work-energy Theorem

Kinetic energy K = ½mv² is a scalar and measures the work a body can do because of its motion. The work-energy (WE) theorem says the change in kinetic energy equals the work done by the net force: K_f − K_i = W.

• For a constant force it follows from v² − u² = 2as multiplied by m/2.
• Work by a variable force: W = ∫F(x)dx from x_i to x_f, the area under the force-displacement curve; area below the x-axis counts as negative.
• For a variable force, dK/dt = Fv gives dK = F dx, which integrates to K_f − K_i = ∫F dx.
• The WE theorem is an integral form of Newton’s second law. It is a scalar relation, so the time and direction information of the second law is lost.
• NCERT Example 5.4: a 50.0 g bullet at 200 m s⁻¹ (1000 J) that keeps only 10% of its kinetic energy emerges at 63.2 m s⁻¹, a speed drop of about 68%, not 90%.
• NCERT Example 5.5: with 100 N for 10 m, then a force falling linearly to 50 N over 10 m, the woman does 1750 J while friction of 50 N does −1000 J.

Potential Energy and Conservative Forces

Potential energy is energy stored because of the position or configuration of a body. It is defined only for forces where the work done against the force is stored, and F(x) = −dV/dx.

• Gravitational potential energy near the earth’s surface: V(h) = mgh (h much smaller than the earth’s radius), with F = −dV/dh = −mg.
• A ball dropped from height h reaches the ground with ½mv² = mgh, that is v = √(2gh).
• An object sliding from rest down a smooth incline of height h reaches the bottom with speed √(2gh), whatever the angle.
• The change in potential energy for a conservative force is the negative of the work done by the force: ΔV = −F(x)Δx.
• The zero of potential energy is arbitrary, but once chosen it must be kept throughout a problem.

Friction is non-conservative: the work it does depends on the path, and it does not store energy as potential energy.

Conservation of Mechanical Energy and the Vertical Circle

The total mechanical energy K + V of a system is conserved if the forces doing work on it are conservative: K_i + V(x_i) = K_f + V(x_f).

• Ball dropped from a cliff of height H: E = mgH at the top, mgh + ½mv_h² on the way and ½mv_f² at the ground, giving v_f = √(2gH) and v_h² = 2g(H − h).
• With a non-conservative force such as friction, the change in mechanical energy equals the work done by that force: E_f − E_i = W_nc.

Motion in a Vertical Circle (NCERT Example 5.7)

A bob of mass m on a light string of length L is given speed v₀ at the lowest point A so that the string goes slack only at the top C. The tension does no work, so mechanical energy is conserved.

Potential Energy of a Spring

The spring force is a variable, conservative force that obeys Hooke’s law, F_s = −kx, where k (unit N m⁻¹) is the spring constant: large k means a stiff spring.

• Work done by the spring force when stretched or compressed by x_m: W_s = −½kx_m²; the external force does +½kx_m².
• From x_i to x_f: W_s = ½kx_i² − ½kx_f², which depends only on the end points; over a cycle it is zero.
• Potential energy of a spring: V(x) = ½kx², taking V = 0 at the unstretched position.
• Energy is exchanged between kinetic and potential forms: ½kx_m² = ½kx² + ½mv². The speed is maximum at x = 0: v_m = x_m√(k/m).
• NCERT Example 5.8: a 1000 kg car at 18 km/h hitting a spring of k = 5.25 × 10³ N m⁻¹ compresses it by 2.00 m; with μ = 0.5 (Example 5.9), the compression falls to 1.35 m.

Power

Power is the time rate at which work is done or energy is transferred. Average power P_av = W/t; instantaneous power P = dW/dt = F·v.

• Power is a scalar with dimensions [M L² T⁻³]. The SI unit is the watt (1 W = 1 J s⁻¹), after James Watt.
• 1 horse-power (hp) = 746 W.
• The kilowatt hour (kWh) is a unit of energy, not power: 1 kWh = 3.6 × 10⁶ J. A 100 W bulb on for 10 hours uses 1 kWh.
• NCERT Example 5.10: an elevator of total mass 1800 kg moving up at 2 m s⁻¹ against 4000 N of friction needs at least 44000 W, about 59 hp.

Collisions

In all collisions the total linear momentum is conserved, because the impulses on the two bodies are equal and opposite. Kinetic energy is conserved only in elastic collisions.

Collisions in One Dimension (m₂ at Rest)

• Neutron moderators (NCERT Example 5.11): in a head-on elastic collision a neutron gives about 8/9 of its kinetic energy to deuterium but only 28.4% to carbon. Heavy water and graphite are used as moderators.
• A one-dimensional or head-on collision has initial and final velocities along one line.

Collisions in Two Dimensions

• Momentum is conserved along x and along y separately: m₁v₁ᵢ = m₁v₁f cos θ₁ + m₂v₂f cos θ₂ and 0 = m₁v₁f sin θ₁ − m₂v₂f sin θ₂.
• Even for an elastic collision, one of the four unknowns (for example θ₁) must be known to solve the problem.
• When two equal masses collide elastically and one was at rest, they move at right angles after a glancing collision: θ₁ + θ₂ = 90° (NCERT’s billiard example gives θ₁ = 53° for θ₂ = 37°).
• When particles interact at a distance without touching (a comet near the sun, an alpha particle near a nucleus), the event is called scattering.

Most-asked Facts for NEET and JEE Main: Work, Energy and Power

Revise these one-line facts from the chapter just before the exam.

• W = F·d = Fd cos θ; no work when force and displacement are perpendicular.
• Work by a variable force = area under the F-x graph.
• Work-energy theorem: W_net = K_f − K_i.
• F = −dV/dx for a conservative force.
• Work by a conservative force over a closed path is zero.
• Spring: F = −kx, V = ½kx², v_max = x_m√(k/m).
• Vertical circle with a string: minimum speed √(gL) at the top and √(5gL) at the bottom.
• P = F·v; 1 hp = 746 W; 1 kWh = 3.6 × 10⁶ J.
• Momentum is conserved in every collision; kinetic energy only in elastic ones.
• Equal masses in a 1D elastic collision exchange velocities.
• Equal masses in a 2D elastic collision (one at rest) move off at 90° to each other.
• Deuterium takes about 8/9 of a neutron’s kinetic energy in a head-on elastic collision.

Common Mistakes to Avoid

Watch for these mix-ups when you answer questions on this chapter.

• Assuming equal and opposite forces do equal and opposite work. The work depends on each body’s own displacement.
• Calling kWh a unit of power. It is a unit of energy.
• Forgetting that the spring force does negative work when the spring is stretched or compressed from its natural length.
• Using conservation of mechanical energy when friction acts. Use E_f − E_i = W_nc or the work-energy theorem instead.
• Thinking kinetic energy is conserved in every collision. Only momentum is always conserved.
• Assuming a 10% kinetic energy left means a 10% speed left. Speed scales with the square root of kinetic energy.
• Counting tension as doing work in a vertical circle. Tension is perpendicular to the motion of the bob and does no work.

Work, Energy and Power Notes PDF and Related Pages

Download the AglaSem notes for Work, Energy and Power (key notes and important questions with answers) free: View PDF

• All chapters: Physics notes for NEET and JEE Main
• Full topic lists: NEET syllabus and JEE Main syllabus
• Practice: NEET question papers and JEE Main question papers
• Source text: NCERT Chapter 5 (NCERT, Class 11 Physics Part I)

Physics Notes for NEET and JEE Main: All Chapters

• Units and Measurement
• Motion in a Straight Line
• Motion in a Plane
• Laws of Motion
• Work, Energy and Power
• Systems of Particles and Rotational Motion
• Gravitation
• Mechanical Properties of Solids
• Mechanical Properties of Fluids
• Thermodynamics
• Kinetic Theory of Gases
• Oscillations
• Waves
• Thermal Properties of Matter
• Electric Charges and Fields
• Electrostatic Potential and Capacitance
• Current Electricity
• Moving Charges and Magnetism
• Magnetism and Matter
• Electromagnetic Induction
• Electromagnetic Waves
• Ray Optics and Optical Instruments
• Wave Optics
• Dual Nature of Radiation and Matter
• Atoms
• Nuclei
• Semiconductor Electronics

All chapters with key points and notes PDFs are on the Physics notes for NEET and JEE Main page.

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