Work, Energy and Power

Work is done when a force moves a body through a distance: W = Force x Displacement x cos(theta). When force and displacement are in the same direction, W = F x s. SI unit of work and energy is Joule (J); 1 J = 1 N.m. Energy is the capacity to do work. Kinetic energy (KE) = (1/2)mv squared (energy of motion). Potential energy (PE) = mgh (energy due to height). Memory aid: 'KE is for moving, PE is for position'. The Law of Conservation of Energy states energy can neither be created nor destroyed, only transformed from one form to another.

If two trucks deliver the same load to the same destination but one finishes in half the time, the faster truck has greater power — even though the work done by both is the same. Power is the physics that distinguishes a sprint from a marathon, a 1000-watt geyser from a 2000-watt geyser, and an electric scooter from a petrol motorcycle. For RPF General Science, this concept anchors at least one direct numerical every year.

Definition: Power is the rate of doing work, or equivalently the rate at which energy is transferred from one form to another. In symbols, Power = Work / Time, or P = W / t. The SI unit is the watt (W), where 1 watt equals one joule per second.

The core formula and its units

The defining formula P = W / t says nothing more than "how fast is the work being done?" If a worker lifts 100 J of grocery bags in 5 seconds, the power is 20 watts. If a hydraulic crane does the same work in 0.5 seconds, the power is 200 watts — ten times more, because the energy was delivered ten times faster.

Watt is a small unit. To talk about real machines we use larger ones:

• Kilowatt (kW) = 1000 watts. Used for room heaters, microwave ovens, electric kettles.
• Megawatt (MW) = 10^6 watts. Used for power station outputs.
• Horsepower (HP) = 746 watts approximately, or roughly 0.746 kW. Used for engines, motors, pumps.

The "approximately" matters: the value 746 W is the metric horsepower most commonly quoted in Indian textbooks. Different industries use 735.5 W (metric "PS") or 745.7 W (mechanical HP), but for RPF and NCERT, 1 HP = 746 W is the standard.

The quick-estimation trick the question setters love: HP is roughly three-quarters of a kW. So a 1 HP pump is about 0.75 kW, a 5 HP motor is about 3.75 kW. Master this in your head and you cut every HP-to-kW conversion to two seconds.

The kilowatt-hour: the commercial unit

The unit you actually pay your electricity company for is the kilowatt-hour (kWh), popularly called "one unit". It is the energy consumed by a 1 kW device running for 1 hour. Convert to joules: 1 kWh = 1000 W x 3600 s = 3.6 x 10^6 J = 3.6 MJ.

The shortcut every Class 10 NCERT chapter on electricity teaches:

Energy (kWh) = Power (kW) x Time (hours)

This single line is the basis of the electricity bill. A 1.5 kW air conditioner running for 4 hours consumes 1.5 x 4 = 6 kWh = 6 units. At Rs 8 per unit (a typical Indian tariff), that is Rs 48 per day, Rs 1440 per month. The arithmetic is small but the physics is the same as RPF questions in 2024 and 2023.

The P = F v form — power as force times velocity

There is a second, equally important formula for power: P = F v, where F is the force applied and v is the velocity in the direction of the force. To see why it is true, note that work W = Fs (force times displacement) and dividing both sides by t gives W/t = F (s/t) = F v.

This form unlocks problems where the motion is steady. A car moving at constant velocity v against a friction force F requires engine power F v just to overcome friction. A pump lifting water at a constant rate of m kilograms per second to a height h has power output (m/t) g h.

Real-world example: An Indian Railways WAP-7 electric locomotive is rated at about 6125 kW (over 8200 HP). If it pulls a passenger train at 130 km/h (about 36 m/s) against air drag and rolling resistance, the average tractive force it must overcome is roughly P/v = 6125000 / 36 ≈ 170 kN — about 17 tonnes-force. That is why goods trains hauled by the same locomotive cap out at much lower speeds: at lower v, F per unit power can be much higher, but acceleration takes longer.

Why it matters: Almost every Indian appliance is rated in watts, every engine in horsepower, every electricity bill in units. The same three relationships — P = W/t, P = Fv, and energy = P x time — explain all three. Once you internalise them, RPF Physics numericals on power become arithmetic problems with units, not physics puzzles.

Worked example — power from work and time

Question: A water pump lifts 1500 kg of water to a tank 20 m above the ground in 5 minutes. Find the power of the pump. Take g = 10 m/s^2.

Solution:

Step 1: Compute the work done against gravity. W = mgh = 1500 x 10 x 20 = 3,00,000 J.

Step 2: Convert time to SI units. t = 5 minutes = 300 s.

Step 3: Apply P = W / t = 3,00,000 / 300 = 1000 W = 1 kW.

Conclusion: The pump's output power is 1 kW, or about 1.34 HP.

Worked example — energy bill

Question: A household uses a 2 kW geyser for 1 hour daily, a 100 W bulb for 5 hours, and a 1.5 kW air conditioner for 8 hours. At Rs 8 per unit, find the daily electricity bill.

Solution:

Step 1: Compute units. Geyser: 2 x 1 = 2 kWh. Bulb: 0.1 x 5 = 0.5 kWh. AC: 1.5 x 8 = 12 kWh.

Step 2: Total = 2 + 0.5 + 12 = 14.5 units per day.

Step 3: Daily cost = 14.5 x 8 = Rs 116.

Conclusion: The daily bill is Rs 116, the monthly bill about Rs 3480.

Worked example — engine output as force-velocity

Question: A car travels at a constant speed of 72 km/h on a level road against a total resistive force of 500 N. Find the engine output power.

Solution:

Step 1: Convert 72 km/h to m/s. v = 72 x 5/18 = 20 m/s.

Step 2: Apply P = F v = 500 x 20 = 10000 W = 10 kW.

Step 3: Convert to HP if needed: 10 kW / 0.746 ≈ 13.4 HP.

Conclusion: The engine must deliver 10 kW (about 13.4 HP) at this speed.

Common misconception: Students treat "power" and "energy" as the same thing. Energy is the total fuel in the tank; power is how fast you burn it. Two devices can deliver the same energy yet differ enormously in power (think of a slow drip filling a bucket versus a fire-hose).

Example 1: A body of mass 2 kg moves at 4 m/s. KE = (1/2)(2)(4 squared) = (1/2)(2)(16) = 16 J. Example 2: An object of mass 5 kg is raised to height 10 m (g = 10). PE = mgh = 5 x 10 x 10 = 500 J. Example 3: A 100 W bulb runs for 10 hours daily for 30 days. Energy = (100/1000) kW x 10 x 30 = 30 kWh = 30 units. Tip: For KE problems square the velocity first, then multiply. For electricity, always convert watts to kilowatts by dividing by 1000.

Cover the answer, recall, then check. 12 cards on work, energy and power for RPF Constable.

Q1. Define work and give its formula and SI unit.
A1. Work = force × displacement in the direction of force (W = F·s). SI unit is joule (J). 1 J = 1 N·m.

Q2. When is the work done by a force zero?
A2. When displacement is zero, or when force is perpendicular to displacement (e.g. carrying a bag horizontally, or a body in circular motion — centripetal force does no work).

Q3. Define energy and give its SI unit.
A3. Energy is the capacity to do work. SI unit is the joule (J), same as work.

Q4. Write the formula for kinetic energy.
A4. KE = ½mv², where m = mass and v = velocity. It is the energy of a body due to its motion.

Q5. Write the formula for gravitational potential energy.
A5. PE = mgh, where m = mass, g = acceleration due to gravity, h = height. It is the energy due to position.

Q6. State the law of conservation of energy.
A6. Energy can neither be created nor destroyed; it only changes from one form to another. Total energy remains constant.

Q7. Define power and give its formula and SI unit.
A7. Power = work done / time taken (P = W/t). SI unit is the watt (W). 1 W = 1 J/s.

Q8. How many watts is 1 horsepower (HP)?
A8. 1 HP = 746 W (approximately 750 W).

Q9. What is the commercial unit of electrical energy?
A9. The kilowatt-hour (kWh), also called 1 "unit". 1 kWh = 3.6 × 10⁶ J = 3.6 MJ.

Q10. Name the main forms of energy.
A10. Mechanical (kinetic + potential), heat, light, sound, electrical, chemical, and nuclear energy.

Q11. In a freely falling body, how does energy change?
A11. Potential energy decreases and kinetic energy increases, but the total mechanical energy stays constant (conservation of energy).

Q12. A 2 kg body is lifted 5 m (g = 10 m/s²). Find the work done against gravity.
A12. W = mgh = 2 × 10 × 5 = 100 J. This equals the potential energy gained.

Work, energy and power is one of the most predictable physics topics in the RPF Constable exam. General Science forms a steady share of the 50-question General Awareness section, and this chapter is pure formula-and-unit recall — the fastest marks to bank. The joule and watt, the KE and PE formulae, and the kilowatt-hour appear again and again.

Must-know facts and laws

• Work = force × displacement in the direction of force (W = F·s); SI unit joule (J), 1 J = 1 N·m.
• Work is zero when displacement is zero or force is perpendicular to motion (carrying a load horizontally; circular motion).
• Kinetic energy KE = ½mv² (energy of motion).
• Potential energy PE = mgh (energy of position/height).
• Conservation of energy: energy is neither created nor destroyed, only converted from one form to another.
• Power = work/time (P = W/t); SI unit watt (W), 1 W = 1 J/s. 1 horsepower = 746 W.
• Commercial unit of energy = kilowatt-hour (kWh); 1 kWh = 3.6 × 10⁶ J.

Formulae and units at a glance

Quantity	Formula	SI unit
Work	F × s	joule (J)
Kinetic energy	½mv²	joule (J)
Potential energy	mgh	joule (J)
Power	W / t	watt (W)
Commercial energy	—	kilowatt-hour (kWh)

Exam Tricks & Tips

• 🎯 "WEP all use the joule" — work, and every form of energy, share the SI unit joule; only power switches to the watt.
• 🎯 Remember 1 watt = 1 joule/second and 1 HP = 746 W — both are frequent one-mark questions.
• 🎯 KE has the square (v²), PE does not — a classic trick is to swap the two formulae.
• 🎯 1 unit of electricity = 1 kWh = 3.6 × 10⁶ J — links physics to your electricity bill; examiners like this crossover.
• 🎯 A coolie carrying luggage on a level platform does zero work on the load (force vertical, motion horizontal) — favourite trap.
• ❌ Common mistake: calling the kilowatt-hour a unit of power. It is a unit of energy (power × time); the watt is power.

Expected exam pattern

Direct one-liners: "SI unit of work/power," "1 HP = ? watts," "formula for kinetic/potential energy," or a numerical such as work = mgh. Occasionally a concept question on when work is zero.

Quick recap

Work = F × s (joule); KE = ½mv²; PE = mgh; power = W/t (watt, 1 W = 1 J/s, 1 HP = 746 W). Energy is conserved. The commercial unit of energy is the kWh (1 kWh = 3.6 × 10⁶ J). Watch the KE-vs-PE swap and the "zero work" trap.