Class 11 · Chapter 5

Work, Energy & Power

Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.

Work, Energy & Power Formula Sheet

11 formulas across 4 topics in Work, Energy & Power.

2 min read

Updated 2026-07-03 · v1.0.0

Work Done by a Force

Work is force times displacement along the force. The angle between them decides everything — including whether work is positive, negative, or zero.

W = F s cosθ

Work by a constant force

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
W	work done	J	[ML²T⁻²]
F	magnitude of the force	N	[MLT⁻²]
s	magnitude of displacement	m	[L]
θ	angle between force and displacement	rad (or °)	[M⁰L⁰T⁰]

Valid when

Constant force only — for variable force, integrate

Common mistakes

Work by friction is not always negative — on the lower block of a stacked pair, friction does POSITIVE work
Normal force and centripetal force do zero work (θ = 90°), no matter how large they are

Read the concept →

W = ∫ F dx (area under the F–x graph)

Work by a variable force

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Summing F·dx over infinitesimal displacements

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
F	force as a function of position	N	[MLT⁻²]
dx	infinitesimal displacement	m	[L]

Valid when

Area below the x-axis counts as negative work

Common mistakes

Plugging the final x into W = Fx for a variable force — you must integrate or take graph area

Read the concept →

Worth remembering

Work is a scalar but carries a sign — the sign tells whether energy flows into or out of the body
Work depends on the frame of reference: the same force can do different work in different frames

Kinetic Energy & the Work-Energy Theorem

The work-energy theorem is the fastest route in mechanics — it skips time and acceleration entirely and connects force directly to speed.

K = ½mv²

Kinetic energy

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
K	kinetic energy	J	[ML²T⁻²]
m	mass	kg	[M]
v	speed	m/s	[LT⁻¹]

Valid when

Always non-negative
Frame-dependent

Read the concept →

K = p²/2m, p = √(2mK)

Kinetic energy ↔ momentum relation

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Substituting v = p/m into K = ½mv²

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
p	linear momentum	kg·m/s	[MLT⁻¹]
K	kinetic energy	J	[ML²T⁻²]

Common mistakes

If momentum doubles, KE becomes FOUR times — students often say two times
Two bodies with equal KE do NOT have equal momentum unless masses are equal — the heavier one has more momentum

Read the concept →

W(net) = ΔK = K(f) − K(i)

Work-energy theorem

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Integrating F = ma over displacement using a = v dv/dx

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
W(net)	work done by ALL forces	J	[ML²T⁻²]
K(f), K(i)	final and initial kinetic energies	J	[ML²T⁻²]

Valid when

W must include EVERY force: gravity, friction, normal, applied, tension

Common mistakes

Using only the applied force's work — the theorem needs the NET work
It holds even for variable forces and curved paths — students wrongly restrict it to constant force

Read the concept →

Worth remembering

Choose the work-energy theorem when the question gives distances and speeds but not time

JEE Advanced applies the theorem on curved and rough paths where F = ma is painful — recognising when to switch tools is the real skill tested.

Potential Energy & Conservation of Mechanical Energy

Potential energy exists only for conservative forces. When only such forces act, K + U stays constant — the most powerful shortcut in mechanics.

U = mgh

Gravitational potential energy (near Earth)

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
U	potential energy relative to the chosen reference	J	[ML²T⁻²]
h	height above the reference level	m	[L]
g	acceleration due to gravity	m/s²	[LT⁻²]

Valid when

Valid for h ≪ Earth's radius
Only CHANGES in U are physical — the zero level is your free choice

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U = ½kx²

Elastic potential energy of a spring

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Work done against the spring force: ∫kx dx from 0 to x

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
k	spring constant	N/m	[MT⁻²]
x	extension or compression from natural length	m	[L]

Valid when

x is measured from NATURAL length, never from the equilibrium position of a hanging load

Common mistakes

Energy stored going from stretch x₁ to x₂ is ½k(x₂² − x₁²), NOT ½k(x₂ − x₁)²

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F = −dU/dx

Conservative force from potential energy

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
F	conservative force along x	N	[MLT⁻²]
U	potential energy function	J	[ML²T⁻²]

Valid when

Equilibrium where dU/dx = 0
Stable if U is a minimum (d²U/dx² > 0), unstable if a maximum

Common mistakes

Dropping the minus sign — force points from HIGH potential energy toward LOW

Read the concept →

K(i) + U(i) = K(f) + U(f)

Conservation of mechanical energy

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Work-energy theorem when only conservative forces act

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
K	kinetic energy	J	[ML²T⁻²]
U	total potential energy (all forms)	J	[ML²T⁻²]

Valid when

ONLY when non-conservative forces (friction, air drag) do zero work
With friction: K(i) + U(i) = K(f) + U(f) + heat generated

Common mistakes

Applying it across a collision — collisions generally destroy mechanical energy unless stated perfectly elastic

Read the concept →

Worth remembering

Work by a conservative force over any closed loop is zero — that is the defining test
In a vertical circle (string), the √(5gr) result of Laws of Motion comes from combining energy conservation with the top-point condition

Power

Power is the rate of doing work. The F·v form is the exam favourite — it connects engines, pumps, and vehicles to forces directly.

P(avg) = W / t

Average power

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
P(avg)	average power	W	[ML²T⁻³]
W	work done	J	[ML²T⁻²]
t	time taken	s	[T]

Read the concept →

P = F v cosθ

Instantaneous power

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P = dW/dt with dW = F·ds

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
P	instantaneous power	W	[ML²T⁻³]
F	force	N	[MLT⁻²]
v	instantaneous speed	m/s	[LT⁻¹]
θ	angle between force and velocity	rad (or °)	[M⁰L⁰T⁰]

Common mistakes

A car at TOP speed has engine force = resistive force, so P = F(resistive) × v(max) — the classic pump/vehicle question
Pump problems: P = (dm/dt)gh for lifting, plus ½(dm/dt)v² if the water leaves with speed v

Read the concept →

Worth remembering

1 horsepower = 746 W; 1 kWh = 3.6 × 10⁶ J (a unit of ENERGY, not power — NEET one-liner)

NEET repeats the pump-lifting-water calculation almost every alternate year; JEE Main prefers constant-power motion, where v ∝ √t and x ∝ t³ᐟ².

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