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CBSE Class 11 · Physics

Work, Energy and Power

Official NCERT chapter from Physics Part I–II (book code keph1). ExamMaster notes are original teaching at CBSE Class 11 depth.

This lesson follows the official chapter “Work, Energy and Power” in Physics Part I–II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 11
  • Medium level
  • 10 concepts

1Notions of work and kinetic energy : The work-energy theorem

The work–energy theorem: net work on a body equals the change in kinetic energy. 8 N along 3 m on a 2 kg that started at 1 m/s: W=24 J, ΔK=24 J. Work is F along s (or the integral-story if variable); tiredness of a still hold is not this work.

Holding 8 N still for a minute is not 24 J.

Figure. Net work equals the kinetic energy the cart gains. A 4 kg cart from rest to 3 m/s stores ½×4×9 = 18 J, so W_net is 18 J. The two bars are the same height because the theorem is an equality, not a sketch.

How it works

  1. Name F_net along the displacement, and sThe given.
  2. Write W_net = ΔKThe theorem.
  3. Keep the jouleThe link.

2Work

Work at this class is F s cosθ when F is constant, or “along” when θ=0. 6 N at 60° through 4 m is 12 J. A force perpendicular to the move does zero this work.

Using 6×4 with a 90° force is a miss.

Figure. Work is F s cosθ along a straight displacement. F = 20 N at 60° to s = 4 m gives W = 20×4×½ = 40 J. The force arrow is drawn at a true 60° in this 2:1 frame. The 20 N arrow and 4 m span are not one scale.

How it works

  1. Name F, s, and the angle between themThe given.
  2. Write W = F s cosθThe work.
  3. Zero when they are perpendicularThe caution.

6 N at 60° through 4 m

Find the work.

  • cos 60°1/2
  • W6×4×1/2=12 J
  • ReadAlong-component only

Pro tip. Constant F; the perpendicular part does no this work.

3Kinetic energy

Kinetic energy is ½ mv². A 2 kg at 3 m/s has 9 J. K is a scalar store of motion; it is not momentum. Doubling v quadruples K.

Using mv as if it were K is the heading-steal.

Figure. Kinetic energy is ½mv², so speed is squared. A 2 kg cart at 4 m/s stores 16 J; at 8 m/s it stores 64 J. The second bar is drawn 4× the first because doubling v quadruples KE.

How it works

  1. Write m and vThe given.
  2. Compute ½ mv²K.
  3. Keep the joule, not kg·m/sEnergy, not p.

4Work done by a variable force

A variable force’s work is the area under an F-versus-s graph (as taught), not F_avg guessed by eye. A triangle of height 8 N and base 3 m is 12 J. The theorem still says that work equals ΔK if it is the net force.

Using the end-value 8 N × 3 m when the graph rose from 0 is a miss.

Figure. Work by a variable force is the area under F against x. F falls linearly from 12 N to 0 over 3 m, so the area is a triangle: ½×3×12 = 18 J. The triangle is not shaded — the vocabulary has no fill — the three corners fix the area a student would compute.

How it works

  1. Read the F–s graphThe variable F.
  2. Take the area as WThe work.
  3. Then ΔK = that W if F was the netThe theorem still.

5The work-energy theorem for a variable force

The work–energy theorem for a variable force is the same sentence — net work (now an area) equals ΔK. It is not a new law. A spring that rises in F still pays ΔK with the area.

Saying the theorem “only works for constant F” skips this heading.

Figure. The work-energy theorem still holds when F changes: the 18 J area under that falling force is the KE the 4 kg cart gains from rest. ½×4×3² = 18 J, so v = 3 m/s. The two bars are equal because W_net = ΔK.

How it works

  1. Compute W as the area (or the taught integral-story)The net work.
  2. Set it equal to K_after − K_beforeThe theorem.
  3. Keep one sentence for constant and variableSame link.

6The concept of potential energy

Potential energy is a stored-by-position write: mgh for a height-store near Earth as taught; a spring-store later in this chapter. PE is a pair with a zero you choose. A height 2 m for 3 kg is 60 J if g=10 m/s² as a school number.

A PE without a named zero is a floating number.

Figure. Gravitational potential energy at this class is mgh from a chosen floor. A 2 kg block 5 m above the floor stores 2×10×5 = 100 J. The 5 m bracket is schematic: the block is not 5 m tall.

How it works

  1. Name the zero and the positionThe store.
  2. Write mgh or the taught formPE.
  3. Change in PE is what the work-against-the-field paidThe concept.

7The conservation of mechanical energy

Mechanical energy (K+PE) stays when only conservative forces do work, as taught. A throw-up trades K for PE; the sum holds if air is ignored. A friction-slide spends mechanical into heat — not conserved in that pair.

Adding a chemical-store into “mechanical” without the lesson is a steal.

Figure. Mechanical energy stays 100 J when only gravity does work. At the shelf the 2 kg block holds 100 J as PE; at the floor that same 100 J is KE. The two bars are drawn the same height because E is unchanged.

How it works

  1. Write K + the taught PEThe pair.
  2. Ask whether only conservative work ranThe gate.
  3. If yes, the sum stays; if friction, it dropsConserve or not.

8The potential energy of a spring

A spring’s PE is ½ kx² as taught, with x the stretch from the unstretched zero. k=200 N/m, x=0.10 m → 1 J. The force is kx back; the store is the area under that line.

Using kx as if it were the joules is the heading-steal.

Figure. A spring's applied force is F = kx, a straight line through the origin. At x = 0.25 m and k = 80 N/m the force is 20 N, so stored energy is the triangle ½×0.25×20 = 2.5 J, also ½kx². The triangle is not shaded.

How it works

  1. Name k and the stretch xThe given.
  2. Write ½ kx²The store.
  3. Keep F=kx as the force, not the energyTwo writings.

9Power

Power is work (or energy-change) per time: P=W/t, and P=F v when F is along v, as taught. 24 J in 3 s is 8 W. Power is a rate, not “strength”.

A slow crane with huge W can be low P.

Figure. Instantaneous power is F·v. A 15 N pull along a 4 m/s velocity delivers 15×4 = 60 W. The two arrows share a direction, so cosθ = 1. The 15 N and 4 m/s arrows are not one scale.

How it works

  1. Name W and t (or F and v)The given.
  2. Divide, or multiply F vP.
  3. Keep the wattThe rate.

10Collisions

A collision is a short bang: momentum of the system if F_ext≈0; kinetic energy stays only if the lesson called it elastic. 4 kg at 3 m/s hitting 2 kg at rest elastically is not the same v as the stick-case. Name elastic or inelastic before you keep K.

Using K-conserve on a stick-together bang is a miss.

Figure. A 1-D elastic hit of equal masses swaps the velocities. Before: 2 kg at 6 m/s meets 2 kg at rest. After: the first block is at rest and the second carries 6 m/s. Momentum 12 kg m/s and KE 36 J are both kept. Blocks are rectangles — the vocabulary has no circle.

How it works

  1. Name the system and elastic/inelasticThe sort.
  2. Write p-conserve; write K-conserve only if elasticThe pair.
  3. Solve; the stick-case shares one vThe collision.
A still 8 N hold for a minute does
  1. No work in this story — no displacement
  2. 480 J
  3. 8 W always

Tiredness is not the joule.

Notes

  • Mapped to the official NCERT chapter “Work, Energy and Power”. Original teaching only — no textbook sentences.
  • Science here is Physics, Chemistry and Biology ideas at this class, never a language or social-science chapter.

Formulas

  • W=Fs cosθ (constant F)
  • K=½mv²
  • PE_spring=½kx²
  • P=W/t

Recap

Hold these pegs from the official chapter “Work, Energy and Power”. The wording is ExamMaster’s teaching, not a textbook recap.

Notions of work and kinetic energy : The work-energy theorem
The work–energy theorem: net work on a body equals the change in kinetic energy.
Work
Work at this class is F s cosθ when F is constant, or “along” when θ=0.
Kinetic energy
Kinetic energy is ½ mv². A 2 kg at 3 m/s has 9 J. K is a scalar store of motion; it is not momentum. Doubling v quadruples K.
Work done by a variable force
A variable force’s work is the area under an F-versus-s graph (as taught), not F_avg guessed by eye.
The work-energy theorem for a variable force
The work–energy theorem for a variable force is the same sentence — net work (now an area) equals ΔK.
The concept of potential energy
Potential energy is a stored-by-position write: mgh for a height-store near Earth as taught; a spring-store later in this chapter.

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