Work, Energy & Power — Complete Formula

Work

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Work Done (Constant Force)	[W = \vec{F} \cdot \vec{s} = Fs\cos\theta]	[W] = work, [F] = force, [s] = displacement, [\theta] = angle between F and s	J	Only component along displacement does work ⭐
Work (Variable Force)	[W = \int \vec{F} \cdot d\vec{s}]	[d\vec{s}] = small displacement	J	Area under F–s graph ⭐
Work by Gravity	[W = mg(h_1 – h_2)]	[m] = mass, [g] = gravity, [h] = height	J	Depends only on height difference
Work by Spring	[W = \dfrac{1}{2}k(x_1^2 – x_2^2)]	[k] = spring constant, [x] = extension	J	Negative when stretching ⚠️

💡 Memory Hint:
Work = force × displacement in same direction

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Kinetic Energy	[K = \dfrac{1}{2}mv^2]	[K] = kinetic energy, [m] = mass, [v] = velocity	J	Depends on square of velocity ⭐
Work-Energy Theorem	[W = \Delta K]	[\Delta K] = change in KE	J	Very important ⭐

💡 Memory Hint:
Work done = change in kinetic energy

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Gravitational PE	[U = mgh]	[U] = potential energy, [h] = height	J	Reference level matters ⚠️
Spring PE	[U = \dfrac{1}{2}kx^2]	[k] = spring constant, [x] = extension	J	Always positive
Change in PE	[\Delta U = mg(h_2 – h_1)]	—	J	Depends on final – initial

💡 Memory Hint:
PE = energy due to position

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Total Mechanical Energy	[E = K + U]	[E] = total energy	J	Sum of KE and PE
Conservation of Energy	[K_1 + U_1 = K_2 + U_2]	subscripts = initial & final	J	Valid if no non-conservative force ⭐

💡 Memory Hint:
No friction → energy conserved

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Average Power	[P = \dfrac{W}{t}]	[P] = power, [t] = time	W	Rate of doing work
Instantaneous Power	[P = \vec{F} \cdot \vec{v}]	[v] = velocity	W	Very important ⭐

💡 Memory Hint:
Power = how fast work is done

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Hooke’s Law	[F = -kx]	[F] = restoring force, [k] = spring constant, [x] = displacement	N	Negative sign = opposite direction ⭐
Energy Stored in Spring	[U = \dfrac{1}{2}kx^2]	—	J	Used in oscillation problems

💡 Memory Hint:
Spring force always opposes displacement

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Elastic Collision	[K_{initial} = K_{final}]	[K] = kinetic energy	J	Energy conserved ⭐
Inelastic Collision	[K_{initial} \neq K_{final}]	—	J	Energy lost as heat/sound ⚠️

💡 Memory Hint:
Elastic → KE conserved
Inelastic → KE not conserved

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