Work by Constant Force
W = Fd cosθ — see the horizontal component pull the block while F is applied at angle θ.
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Class 11 · Notes
Work, Energy & Power— Notes, Formulas & Revision
Complete revision notes and formulas for Work, Energy & Power (Class 11). Curated for JEE, NEET, AP Physics, SAT, and CUET. Tap any topic to open the live simulation and full PYQ set.
Work–Energy Theorem
W_net = ΔKE — apply a force and watch kinetic energy change exactly by the work done.
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Kinetic Energy
KE = ½mv² — see KE scale quadratically with velocity via a live curve and ball.
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Gravitational PE (Near Earth)
U = mgh — drop a ball from height h and watch PE convert to KE.
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Spring Potential Energy
U = ½kx² — stretch a spring and see the parabolic U–x curve with live reading.
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Conservation of Energy
Roller-coaster track — E = PE + KE stays constant; bars show the exchange.
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Power Delivered
P = F·v — see instantaneous and average power grow as velocity increases.
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Work by Variable Force
W = ∫F dx — see area under F(x) for linear, quadratic, or sinusoidal forces.
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Elastic Collision (1D)
Both KE and momentum conserved — live v₁', v₂' from standard formulas.
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Inelastic Collision
Balls stick together — momentum conserved, KE lost to heat/deformation.
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Coefficient of Restitution
Drop a ball — each bounce loses energy; heights scale as h₀·e^(2n).
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Spring-Mass SHM
Visualize simple harmonic motion with a spring-mass system. Watch energy transform between kinetic and potential forms.
01
The Work-Energy Theorem states: Net work done on a body equals the change in its kinetic energy (W_net = ΔKE).
02
Work done by a constant force: W = F·d·cos θ, where θ is the angle between force and displacement.
03
Conservative forces (gravity, spring) have associated potential energy. Non-conservative forces (friction) dissipate energy as heat.
04
For a spring: PE = ½kx², where k is the spring constant and x is the displacement from equilibrium.
05
In SHM (spring-mass system), energy continuously converts between KE and PE. Total mechanical energy is conserved.
06
Power is the rate of doing work: P = dW/dt = F·v (instantaneous power).
07
The area under a Force-displacement graph gives the work done.
08
At equilibrium position in SHM: KE is maximum and PE is minimum. At extreme positions: KE = 0, PE = maximum.
Work Done
Work by a constant force at angle θ to displacement.
Work-Energy Theorem
Net work equals change in kinetic energy.
Spring PE
Potential energy stored in a spring displaced by x.
SHM Period (Spring)
Time period of oscillation for spring-mass system.
SHM Velocity
Velocity at displacement x, where A is amplitude.
Power
Instantaneous power.
Work done by gravity is path-independent (conservative). Work by friction is path-dependent (non-conservative).
For a spring-mass SHM: ω = √(k/m), frequency f = ω/2π.
Total energy in SHM = ½kA² = constant (A is amplitude).
At x = A/√2, KE = PE (energy is equally divided).
Negative work by friction reduces mechanical energy. This 'lost' energy becomes heat.
In JEE, energy methods are often faster than force methods for solving kinematics problems.
Positive vs Negative Work
Switch force angle: 0° → +W, 180° → −W (friction), 90° → 0. See the sign change.
01
W = F·d cosθ. Sign depends entirely on the angle between force and displacement.
02
θ = 0° → +W (force aids motion). θ = 180° → −W (force opposes motion, e.g. friction).
03
θ = 90° → W = 0 (centripetal force, normal force on a horizontal floor — perpendicular).
Work
Sign of cosθ determines sign of W.
Friction always does negative work on a sliding object (relative to ground).
Tension in a string passing over a smooth pulley does zero net work on the system.
Energy Loss to Friction
Block slides on rough floor — KE drops as heat: see d_stop = v₀²/(2μg).
01
Block sliding on rough floor decelerates; KE is dissipated as heat by friction.
02
Stopping distance d = v₀²/(2μg) — independent of mass.
03
Total heat generated = initial KE = ½mv₀².
Stopping distance
When friction is the only horizontal force.
Work–energy
Friction work equals KE loss.
Doubling v₀ quadruples the stopping distance.
Heat = μ × N × d (kinetic friction × distance).
Work, Energy & Power on sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs). Free physics revision for Class 11, JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT Subject Physics, and CUET-UG.