Physics · Mechanics and Waves

Work Energy and Power formulas for JEE

Every Work Energy and Power formula you need for JEE, grouped by concept.

FormulasRevision notes
29 formulas3 concepts
01Work and Work-Energy Theorem02Potential Energy and Conservative Forces03Power and Collisions
01

Work and Work-Energy Theorem

6 formulas

Kinetic Energy

K=12mv2K = \frac{1}{2}mv^2

Energy possessed by a body due to its motion.

energykinetic

Momentum-Kinetic Energy Relation

K=p22m  ⟺  p=2mKK = \frac{p^2}{2m} \iff p = \sqrt{2mK}

Relationship between linear momentum and kinetic energy.

energymomentumjee-advanced

Scalar (Dot) Product

A⋅B=ABcos⁡θ\mathbf{A} \cdot \mathbf{B} = AB \cos\theta

Definition of the scalar product between two vectors.

vectorsdot-product

Work by Constant Force

W=F⋅d=Fdcos⁡θW = \mathbf{F} \cdot \mathbf{d} = F d \cos\theta

Work done by a constant force over a displacement.

applies whenConstant force only.
workconstant-force

Work-Energy Theorem

Wnet=ΔK=Kf−KiW_{net} = \Delta K = K_f - K_i

Net work done on a particle equals the change in its kinetic energy.

applies whenValid in non-inertial frames only if work by pseudo-forces is included.
work-energy-theorem

Work by Variable Force

W=∫xixfF(x)dxW = \int_{x_i}^{x_f} F(x) dx

Work done by a force varying with position in 1D.

applies whenForce depends on position.
workintegrationvariable-force
02

Potential Energy and Conservative Forces

10 formulas

Stable Equilibrium Condition

d2Vdx2>0\frac{d^2V}{dx^2} > 0

Condition indicating that a point of equilibrium is stable.

applies whenNet force is zero (dV/dx=0dV/dx = 0).
equilibriumpotential-energyjee-advanced

Force from Potential Energy

F(x)=−dVdxF(x) = -\frac{dV}{dx}

Conservative force derived from the negative gradient of potential energy.

applies whenConservative forces only.
forcepotential-energyderivative

Hooke's Law

Fs=−kxF_s = -kx

Restoring force exerted by an ideal spring.

applies whenSpring is within its elastic limit.
springforce

Kinetic Energy

K=12mv2K = \frac{1}{2}mv^2

Energy possessed by a body due to its motion.

energykinetic

Conservation of Mechanical Energy

Ki+Vi=Kf+VfK_i + V_i = K_f + V_f

Total mechanical energy is constant if only conservative forces do work.

applies whenWork done by non-conservative forces is zero.
conservationenergy

Gravitational Potential Energy

V(h)=mghV(h) = mgh

Potential energy of a mass near the Earth's surface.

applies whenHeight h≪REarthh \ll R_{Earth}.
energypotentialgravity

Spring Potential Energy

V(x)=12kx2V(x) = \frac{1}{2}kx^2

Energy stored in a spring deformed by distance x from equilibrium.

applies whenEquilibrium position chosen as zero potential energy.
springpotential-energy

Vertical Circular Motion Minimum Speeds

vlowest≥5gL,vhighest≥gLv_{lowest} \ge \sqrt{5gL}, \quad v_{highest} \ge \sqrt{gL}

Minimum speeds required to complete a vertical circle without string slackening.

applies whenMass attached to a light string.
circular-motionenergy-conservation

Work by Non-Conservative Forces

Wnc=ΔE=Ef−EiW_{nc} = \Delta E = E_f - E_i

Work done by non-conservative forces equals the change in total mechanical energy.

worknon-conservativefriction

Work Done by Spring

Ws=12kxi2−12kxf2W_s = \frac{1}{2}kx_i^2 - \frac{1}{2}kx_f^2

Work done by the spring force between two extensions.

springwork
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03

Power and Collisions

13 formulas

Glancing Elastic Collision Angle

θ1+θ2=90∘\theta_1 + \theta_2 = 90^{\circ}

When two equal masses undergo a glancing elastic collision with one at rest, they separate at right angles.

applies whenElastic collision, equal masses, target initially at rest.
collision2djee-advanced

Elastic Velocity 1 (Target at Rest)

v1f=m1−m2m1+m2v1iv_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_{1i}

Final velocity of incident mass in a 1D elastic collision with a stationary target.

applies whenTarget initially at rest, 1D elastic collision.
collisionelastic

Elastic Velocity 2 (Target at Rest)

v2f=2m1m1+m2v1iv_{2f} = \frac{2m_1}{m_1 + m_2} v_{1i}

Final velocity of stationary target mass in a 1D elastic collision.

applies whenTarget initially at rest, 1D elastic collision.
collisionelastic

Energy Loss in General 1D Collision

ΔK=12m1m2m1+m2(v1i−v2i)2(1−e2)\Delta K = \frac{1}{2}\frac{m_1 m_2}{m_1 + m_2}(v_{1i} - v_{2i})^2 (1 - e^2)

Loss of kinetic energy in a collision with coefficient of restitution e.

applies when1D collision.
collisionenergy-lossjee-advanced

General Final Velocity in 1D Collision

v1f=(m1−em2m1+m2)v1i+((1+e)m2m1+m2)v2iv_{1f} = \left(\frac{m_1 - e m_2}{m_1 + m_2}\right)v_{1i} + \left(\frac{(1+e)m_2}{m_1 + m_2}\right)v_{2i}

Final velocity of mass 1 after a collision characterized by coefficient of restitution e.

applies when1D collision.
collisionrestitutionjee-advanced

Kinetic Energy Loss (Completely Inelastic)

ΔK=12m1m2m1+m2(v1i−v2i)2\Delta K = \frac{1}{2} \frac{m_1 m_2}{m_1 + m_2} (v_{1i} - v_{2i})^2

Loss of kinetic energy in a perfectly inelastic head-on collision.

applies whenObjects stick together (e = 0).
collisioninelasticenergy-loss

Kinematics under Constant Power

v=(2Pm)1/2t1/2,x∝t3/2v = \left(\frac{2P}{m}\right)^{1/2} t^{1/2}, \quad x \propto t^{3/2}

Velocity and displacement relationships for a body starting from rest under constant power.

applies whenConstant power, initial velocity zero.
powerkinematics

Power of Fluid Flow

P=12ρAv3P = \frac{1}{2}\rho A v^3

Power available from a continuous fluid stream (e.g., wind over a windmill).

applies whenConstant flow velocity and fluid density.
powerfluidwind

Linear Momentum Conservation

m1v1i+m2v2i=m1v1f+m2v2fm_1 \mathbf{v}_{1i} + m_2 \mathbf{v}_{2i} = m_1 \mathbf{v}_{1f} + m_2 \mathbf{v}_{2f}

Total linear momentum of a system is conserved during a collision.

applies whenNet external impulsive force is zero.
momentumcollision

Instantaneous Power

P=dWdt=F⋅vP = \frac{dW}{dt} = \mathbf{F} \cdot \mathbf{v}

Instantaneous rate of work done as dot product of force and velocity.

powerinstantaneousdot-product

Average Power

Pav=WtP_{av} = \frac{W}{t}

Average rate at which work is done.

poweraverage

Coefficient of Restitution

e=v2f−v1fv1i−v2ie = \frac{v_{2f} - v_{1f}}{v_{1i} - v_{2i}}

Ratio of relative velocity of separation to relative velocity of approach.

applies when1D head-on collision.
collisionrestitutionjee-advanced

Thrust Force (Variable Mass)

Fthrust=vreldmdt\mathbf{F}_{thrust} = \mathbf{v}_{rel} \frac{dm}{dt}

Force acting on an object due to the continuous loss or gain of mass.

applies whenMass varies with time (e.g., rocket propulsion, leaking sand).
variable-massthrustjee-advanced
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