Work, Energy and Power — Study Notes

Overview

Work, Energy and Power form a foundational chapter in physics that appears regularly in Railway Group D exams. This topic tests your understanding of how forces cause displacement, how energy transforms from one form to another, and how quickly work is done. Expect 2–3 questions from this chapter, often integrated with other mechanics topics like motion or simple machines.

The exam focuses on three areas: conceptual definitions (what counts as work versus what doesn't), quantitative problems (calculating work done or kinetic energy), and practical applications (energy conversions in everyday devices). You must master the basic formulas, recognize different forms of energy, and understand the law of conservation of energy—that energy cannot be created or destroyed, only transformed. Questions often involve real-world scenarios: a person lifting a load, a moving train, hydroelectric power generation, or household appliances converting electrical energy to other forms.

The key to scoring well is distinguishing between similar concepts (work vs. energy vs. power), applying the correct formula for each scenario, and remembering that energy transformations are never 100% efficient in practice due to heat loss and friction. This topic connects directly to other chapters like force, motion, heat, and electricity, so understanding it strengthens your overall physics foundation.

Key Concepts

• **Work** is done when a force causes displacement in the direction of the force. If there's no displacement or the displacement is perpendicular to the force, work done is zero. Example: carrying a bag horizontally does no work against gravity.

• **Energy** is the capacity to do work. It exists in multiple forms and is measured in the same unit as work (joules). An object possesses energy if it can exert a force through a distance.

• **Power** measures the rate of doing work or transferring energy. High power means work is done quickly; low power means the same work takes longer. A 100-watt bulb uses energy faster than a 40-watt bulb.

• **Kinetic Energy (KE)** is the energy of motion. Any moving object—from a speeding train to a falling raindrop—possesses kinetic energy proportional to its mass and the square of its velocity.

• **Potential Energy (PE)** is stored energy due to position or configuration. Gravitational PE depends on height; elastic PE is stored in compressed springs or stretched rubber bands.

• **Law of Conservation of Energy** states that the total energy in an isolated system remains constant. Energy transforms between forms but the sum never changes. A pendulum continuously converts PE to KE and back.

• **Energy conversions** occur in every device we use. Batteries convert chemical energy to electrical; motors convert electrical to mechanical; solar panels convert light to electrical; our bodies convert chemical (food) energy to mechanical and heat.

• **Efficiency** of any machine or process is always less than 100% because some energy is inevitably lost as heat due to friction, air resistance, or other dissipative forces.

Formulas / Key Facts

**Work = Force × Displacement × cos θ** (θ is angle between force and displacement; when θ = 0°, Work = F × s)

**1 Joule = 1 Newton × 1 metre** (One joule is the work done when a force of 1 N moves an object 1 m)

**Kinetic Energy = ½ × mass × velocity²** (KE = ½mv²; energy of motion doubles with mass, quadruples with velocity)

**Gravitational Potential Energy = mass × gravity × height** (PE = mgh; where g = 10 m/s² approximately; height is measured from reference level)

**Power = Work / Time** (P = W/t; also Power = Force × velocity when force and velocity are in same direction)

**1 Watt = 1 Joule per second** (Standard unit; 1 kilowatt = 1000 watts; 1 horsepower ≈ 746 watts)

**1 kilowatt-hour (kWh) = 3.6 million joules** (Commercial unit of energy used in electricity bills; 1 kWh = 1000 W × 3600 s)

**Law of Conservation: Total Energy (initial) = Total Energy (final)** (In free fall: PE at top = KE at bottom; in pendulum: PE + KE = constant)

Worked Examples

**Example 1: Calculate work done** A porter lifts a 20 kg suitcase through a vertical height of 1.5 m. Find the work done against gravity (g = 10 m/s²).

*Solution:* Work = Force × Displacement Force needed = Weight = mg = 20 × 10 = 200 N Displacement = 1.5 m (vertical) Work = 200 × 1.5 = **300 J**

Note: When lifting vertically, force and displacement are in the same direction, so cos θ = 1.

**Example 2: Kinetic energy calculation** A train of mass 50,000 kg is moving at 20 m/s. What is its kinetic energy?

*Solution:* KE = ½mv² KE = ½ × 50,000 × (20)² KE = ½ × 50,000 × 400 KE = 25,000 × 400 KE = **10,000,000 J = 10 MJ**

If the velocity doubles to 40 m/s, KE becomes 40 MJ—four times larger.

**Example 3: Power and time relationship** A pump does 6000 J of work in 30 seconds to lift water. If a more powerful pump does the same work in 20 seconds, compare their power.

*Solution:* First pump: P₁ = Work/Time = 6000/30 = **200 W** Second pump: P₂ = 6000/20 = **300 W**

The second pump is more powerful (50% more) because it completes the same work in less time.

Common Mistakes

**Mistake:** Thinking that carrying a bag while walking horizontally involves work against gravity. **Fix:** Work requires displacement *in the direction* of force. Gravity acts downward; horizontal walking has zero vertical displacement, so no work is done against gravity. Work is done against friction to move forward.

**Mistake:** Confusing energy with power, or using kilowatt-hour as a unit of power. **Fix:** Energy is capacity to do work (measured in joules or kWh); power is rate of energy use (measured in watts). A 100 W bulb running for 10 hours uses 1 kWh of *energy*, not power.

**Mistake:** Forgetting that kinetic energy depends on velocity *squared*. **Fix:** Doubling velocity quadruples KE, not doubles it. If a vehicle's speed increases from 10 m/s to 20 m/s, its KE increases four times, requiring four times more braking work to stop.

**Mistake:** Claiming energy is "lost" or "destroyed" when a ball bounces lower each time. **Fix:** Energy is *converted* (not lost) to heat and sound due to air resistance and inelastic collision. Total energy is conserved; mechanical energy decreases as it transforms to non-mechanical forms.

**Mistake:** Using g = 9.8 m/s² when the problem states a simpler value like 10 m/s². **Fix:** Railway Group D problems often use g = 10 m/s² for easier calculation. Always use the value provided in the question or use 10 m/s² if not specified.

Quick Reference

• **Work done = 0 when:** force ⊥ displacement, or displacement = 0, or force = 0
• **Energy unit:** 1 J = 1 N·m = 1 kg·m²/s²; commercial unit: 1 kWh = 3.6 MJ
• **PE and KE swap:** In free fall or pendulum, PE converts to KE and vice versa; total remains constant
• **Power unit:** 1 W = 1 J/s; 1 HP ≈ 746 W; higher power = faster work completion
• **Energy forms:** Mechanical (KE + PE), thermal (heat), chemical, electrical, light, sound, nuclear
• **Common conversions:** Electric motor (electrical → mechanical), generator (mechanical → electrical), battery (chemical → electrical), sun (nuclear → light and heat)