Work, Energy & Power — Introduction

These three concepts form the backbone of mechanics in physics.

• ›Work is done when a force moves an object in its direction.
• ›Energy is the capacity to do work.
• ›Power is the rate at which work is done.

All three are inter-related: energy enables work, and power measures how fast work happens.

They appear frequently in BPSC TRE-4 General Science questions — especially formulas, units, and types of energy.

Work — Definition & Formula

Work is done when a force applied on an object causes displacement in the direction of the force.

Formula: W = F × d × cos θ

• ›W = Work (in Joules, J)
• ›F = Applied Force (in Newtons, N)
• ›d = Displacement (in metres, m)
• ›θ = Angle between force and displacement

Key points:

• ›If θ = 0°, W = F × d (maximum work)
• ›If θ = 90°, W = 0 (no work done — e.g., carrying a bag horizontally)
• ›Work is a scalar quantity

Energy — Types & Formulas

Energy is the ability to do work. SI unit: Joule (J).

Kinetic Energy (KE): Energy of a moving object.

• ›KE = ½ mv²
• ›m = mass, v = velocity

Potential Energy (PE): Stored energy due to position.

• ›PE = mgh
• ›m = mass, g = 9.8 m/s², h = height

Law of Conservation of Energy: Energy can neither be created nor destroyed — only converted from one form to another.

Total mechanical energy = KE + PE = constant (in absence of friction)

Power — Definition & Formula

Power is the rate of doing work.

Formula: P = W / t

• ›P = Power (in Watts, W)
• ›W = Work done (in Joules, J)
• ›t = Time taken (in seconds, s)

Also: P = F × v (force × velocity)

Units of Power:

• ›SI unit: Watt (W) = 1 J/s
• ›Larger unit: Kilowatt (kW) = 1000 W
• ›1 Horsepower (HP) = 746 Watts

Power is a scalar quantity.

The unit kilowatt-hour (kWh) is used to measure electrical energy, not power.

Work-Energy Theorem

The Work-Energy Theorem states:

> The net work done on an object equals the change in its kinetic energy.

W_net = ΔKE = ½mv² − ½mu²

• ›v = final velocity
• ›u = initial velocity
• ›m = mass

Practical meaning: If you push a stationary car and it starts moving, the work done by you equals the KE gained by the car.

This theorem is key for BPSC numerical-type questions involving force, mass, and velocity.

Points to Remember

• ›Work (W) — W = F × d × cos θ; unit = Joule
• ›θ = 90° — Work done is zero (force ⊥ displacement)
• ›Kinetic Energy — KE = ½mv²; depends on mass & speed
• ›Potential Energy — PE = mgh; depends on height
• ›Conservation of Energy — total energy is always conserved
• ›Power (P) — P = W/t; unit = Watt
• ›1 HP — equals 746 Watts
• ›kWh — unit of energy, not power
• ›Work-Energy Theorem — W_net = ΔKE
• ›Exam tip: Students confuse kWh as a unit of power — it is a unit of energy.
• ›Exam tip: When θ = 90° (e.g., a coolie carrying load on head walking forward), many students say work is done — but W = 0 here.