Work and Energy
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
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Work Done by a Force
Constant Force
W = F ⋅ d = Fd cos θ
Variable Force
W = ∫ F ⋅ dr
Work from Graph
W = Area under
F-x graph
F-x graph
Units & Dimensions
SI Unit: Joule (J)
Dimension: [ML²T⁻²]
Dimension: [ML²T⁻²]
Work by Gravity
W₉ = -mgΔh
Δh = h₂ - h₁
Δh = h₂ - h₁
Work by Spring
Wₛ = -½ k(x₂² - x₁²)
Kinetic Energy & Work-Energy Theorem
Kinetic Energy (KE)
K = ½ mv²
Work-Energy Theorem
Wnet = ΔK = Kf - Ki
The most powerful tool in this chapter. Applies to ALL forces (conservative & non-conservative).
KE & Momentum (p)
K = p² / 2m
p = √(2mK)
p = √(2mK)
Crucial for ratio-based questions involving K and p.
BITSAT Hotspots
If momentum (p) increases by x%, KE increases by approx. 2x% (for small x).
If KE increases by x%, momentum (p) increases by approx. x/2% (for small x).
Work-Energy Theorem is universal. Use it when forces and displacements are known, but time is not.
Work done by centripetal force in uniform circular motion is always ZERO as F ⊥ v.
If a light and a heavy body have the same momentum, the lighter body has more KE.
Power
Average Power
Pavg = ΔW / Δt
Instantaneous Power
P = dW/dt = F ⋅ v
Units
SI: Watt (W)
1 hp = 746 W
1 hp = 746 W
Potential Energy & Conservative Forces
Potential Energy (PE)
ΔU = Uf - Ui = -Wconservative
Force from PE
F = -dU/dr
Force acts in the direction of decreasing potential energy.
Gravitational PE
U = mgh
(near Earth's surface)
(near Earth's surface)
Elastic PE (Spring)
U = ½ kx²
Conservation of Mechanical Energy
Principle
If Wnon-cons = 0,
then ΔE = ΔK + ΔU = 0
then ΔE = ΔK + ΔU = 0
Core Equation
Ki + Ui = Kf + Uf
With Non-Cons. Forces
Wnon-cons = ΔE
= (Kf + Uf) - (Ki + Ui)
= (Kf + Uf) - (Ki + Ui)
Force Types at a Glance
| Property | Conservative Force | Non-Conservative Force |
|---|---|---|
Work Done | Path independent | Path dependent |
Work in a Closed Loop | Zero | Not necessarily zero |
Potential Energy | Can be defined (U = -∫F·dr) | Cannot be defined |
Examples | Gravity, Spring Force, Electrostatic | Friction, Air Drag, Viscous Force |