Work Energy and Power formulas for JEE Main & Advanced

23 formula entries for Work Energy and Power, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Work Done by a Constant Force

W = \vec{F} \cdot \vec{s} = F s \cos θ

When to use. Use when force is constant and displacement is known; calculate work in mechanics problems.

Trap. Forgetting that work is zero if force and displacement are perpendicular ( $θ = 90^{\circ}$ ).

Work Done by a Variable Force

W = \int_{x_{i}}^{x_{f}} F (x) d x

When to use. Use when force depends on position (e.g., spring force, non-uniform fields).

Trap. Forgetting to integrate with respect to the correct variable (e.g., time vs position).

Kinetic Energy

K = \frac{1}{2} m v^{2}

When to use. Use to relate speed and mass in energy conservation or work-energy theorem.

Trap. Using $m v^{2}$ instead of $\frac{1}{2} m v^{2}$ .

Work-Energy Theorem

W_{net} = Δ K = K_{f} - K_{i}

When to use. Use to relate work and speed changes without needing acceleration details.

Trap. Applying only to conservative forces; it holds for all forces (including non-conservative).

Conservative Force

W_{c} = - Δ U

When to use. Use to identify forces where potential energy can be defined (gravity, spring, electrostatic).

Trap. Assuming all forces are conservative; friction is non-conservative.

Non-Conservative Force

W_{n c} = Δ E_{mech}

(negative for dissipation)

When to use. Use when friction, air resistance, or applied forces are present; account for energy loss.

Trap. Thinking non-conservative forces cannot do positive work; they can (e.g., pushing).

Potential Energy

Δ U = - W_{c} = - \int \vec{F} \cdot d \vec{r}

When to use. Use to simplify problems with conservative forces via energy conservation.

Trap. Forgetting that only changes in potential energy are physically meaningful.

Gravitational Potential Energy

U_{g} = m g h

When to use. Use for objects near Earth's surface in energy conservation problems.

Trap. Forgetting that $h$ is measured from a chosen reference (usually ground).

Spring Potential Energy

U_{s} = \frac{1}{2} k x^{2}

When to use. Use for springs, elastic strings, or any Hooke's law system.

Trap. Forgetting the factor $\frac{1}{2}$ ; using $k x^{2}$ is wrong.

Conservation of Mechanical Energy

E_{mech} = K + U = constant

When to use. Use for systems with only conservative forces (e.g., free fall, pendulum, spring-mass).

Trap. Applying when non-conservative forces (friction) are present; then energy is not conserved.

Power

P = \frac{d W}{d t} = \vec{F} \cdot \vec{v}

When to use. Use to compute energy transfer rate in engines, motors, or moving objects.

Trap. Using average power $P = W / t$ when instantaneous power is needed.

Using Work-Energy Theorem with Multiple Forces

W_{gravity} + W_{spring} + W_{friction} + \dots = Δ K

When to use. Use when multiple forces act, especially including non-conservative forces.

Trap. Double-counting work when using potential energy; either use work or potential energy, not both.

Solving with Conservation of Mechanical Energy

K_{i} + U_{i} = K_{f} + U_{f}

When to use. Use for frictionless systems with only conservative forces (e.g., pendulum, spring).

Trap. Forgetting to include all forms of potential energy (e.g., both gravitational and elastic).

Work Done by Friction

W_{friction} = - μ_{k} N d

(where

d

is path length)

When to use. Use when objects slide on surfaces with kinetic friction.

Trap. Using displacement instead of path length; friction work depends on distance traveled.

Variable Force: Spring Force

W_{spring} = - \frac{1}{2} k (x_{f}^{2} - x_{i}^{2})

When to use. Use for any Hooke's law spring in work-energy or conservation problems.

Trap. Forgetting the negative sign; work done by spring is negative when stretching.

Work Done by a Constant Torque (Rotational Work)

W = τ θ

(for constant torque)

When to use. Use for rotational systems with constant torque (e.g., rotating pulleys).

Trap. Using linear work formula for rotation; must use torque and angle.

Rotational Kinetic Energy

K_{rot} = \frac{1}{2} I ω^{2}

When to use. Use for rotating bodies, especially in rolling without slipping problems.

Trap. Forgetting to include both translational and rotational KE in rolling motion.

Energy Conservation in Rolling Motion

m g h = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}

with

v = ω R

When to use. Use for objects rolling down inclines or on surfaces without slipping.

Trap. Forgetting the rolling condition $v = ω R$ .

Elastic and Inelastic Collisions (Energy Aspect)

Elastic:

\sum K_{i} = \sum K_{f}

; Inelastic:

\sum K_{f} < \sum K_{i}

When to use. Use to analyze collisions; check if KE is conserved to determine type.

Trap. Assuming all collisions are elastic; inelastic collisions are common.

Coefficient of Restitution

e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}}

When to use. Use in collision problems to relate velocities and find energy loss.

Trap. Using wrong sign; ensure velocities are along line of impact.

Work-Energy for Systems with Internal Forces

W_{ext} + W_{int} = Δ K_{system}

(all internal forces); equivalently

W_{ext} + W_{int, nc} = Δ K + Δ U_{int}

When to use. Use for multi-object systems with internal friction or springs.

Trap. Internal forces cannot change the CM momentum, but they can change the system's KE (and internal PE).

Graphical Interpretation of Work

W = \int F d x = Area under F (x) vs x

When to use. Use when given a force-displacement graph to find work.

Trap. Forgetting that only component of force along displacement contributes.

Potential Energy Curve and Equilibrium

F = - \frac{d U}{d x}

When to use. Use to analyze motion from potential energy graphs (e.g., diatomic molecules).

Trap. Forgetting that force is zero at equilibrium points.

Values to remember

$g = 9.8 {m/s}^{2}$ Gravitational Potential Energy
$G = 6.67 \times 10^{- 11} {N m}^{2} / {kg}^{2}$ Gravitational Potential Energy

Read the full chapter: Work Energy and Power for JEE, with what JEE asks and the common traps.