Introduction to Work, Power, and Energy for RRB Exams
In the world of competitive exams like RRB NTPC, RRB Group D, and RRB Technician, General Science—specifically Physics—holds a significant position. Among the various chapters in Physics, Work, Power, and Energy is a fundamental topic that forms the backbone of Mechanics. In our daily lives, we use the word 'work' for any mental or physical activity, but in Physics, 'work' has a very specific, mathematical definition. Understanding these concepts is not just about memorizing formulas; it is about understanding how the universe functions and how machines operate.
This guide is designed to provide you with a comprehensive understanding of the definitions, units, types, and inter-relationships between Work, Power, and Energy. Whether you are appearing for the Technician Grade I or III, or aiming for a post in NTPC, this detailed explanation will ensure you can solve even the trickiest conceptual and numerical questions with ease.
Topic Weightage and Importance
For RRB exams, the General Science section usually comprises 20-25 questions in Group D and a substantial portion of the Tier-1 and Tier-2 syllabus in NTPC and Technician exams. Based on previous years' analysis, Work, Power, and Energy typically accounts for 2 to 4 questions. These questions range from direct SI unit identifications to numerical problems based on the Law of Conservation of Energy or the Work-Energy Theorem.
Because these concepts are interrelated with 'Force' and 'Motion', mastering this topic helps you perform better in the entire Physics section. Scoring full marks here is highly achievable if your conceptual foundation is strong.
Key Concepts and Formulas
1. Work (W)
In Physics, work is said to be done when a force acts upon an object to cause a displacement. It is a scalar quantity.
Formula: W = F × s × cosθ
- F: Force applied (Newton)
- s: Displacement (Meter)
- θ: Angle between the direction of force and direction of displacement.
Important Cases of Work:
- Positive Work: When the force and displacement are in the same direction (θ = 0°). Example: Pulling a toy car.
- Negative Work: When the force and displacement are in opposite directions (θ = 180°). Example: Force of friction acting on a moving body.
- Zero Work: When the force is perpendicular to displacement (θ = 90°) or if displacement is zero. Example: A coolie carrying a load on his head and walking on a platform (Force is upward, displacement is horizontal).
SI Unit: Joule (J). 1 Joule = 1 Newton-meter.
2. Energy (E)
Energy is defined as the capacity to do work. Like work, it is a scalar quantity and shares the same SI unit: Joule (J).
Main Types of Mechanical Energy:
- Kinetic Energy (K.E.): The energy possessed by a body by virtue of its motion.
Formula: K.E. = ½ mv² (where m = mass, v = velocity). - Potential Energy (P.E.): The energy possessed by a body by virtue of its position or configuration. The most common type is Gravitational Potential Energy.
Formula: P.E. = mgh (where m = mass, g = acceleration due to gravity, h = height).
Work-Energy Theorem: The net work done on an object is equal to the change in its kinetic energy. (W = ΔK.E.)
Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total mechanical energy (K.E. + P.E.) remains constant in a closed system.
3. Power (P)
Power is defined as the rate of doing work or the rate at which energy is transferred.
Formula: P = Work / Time = W / t
Since W = F × s, then P = (F × s) / t. Because s/t = velocity (v), we can also say P = F × v.
Units of Power:
- SI Unit: Watt (W). 1 Watt = 1 Joule/second.
- Horsepower (hp): 1 hp = 746 Watts (Commonly asked in RRB exams).
- Commercial Unit of Energy: Kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ Joules.
Solved Examples (Step-by-Step)
| Example No. | Problem Statement | Step-by-Step Solution |
|---|---|---|
| 1 | An object of mass 10 kg is lifted to a height of 6 meters. Calculate the work done. (Take g = 10 m/s²) | Step 1: Identify given values: m = 10 kg, h = 6 m, g = 10 m/s². Step 2: Work done in lifting is equal to Potential Energy (mgh). Step 3: W = 10 × 10 × 6 = 600 Joules. Result: 600 J. |
| 2 | A car of mass 1000 kg is moving with a velocity of 20 m/s. What is its Kinetic Energy? | Step 1: Given: m = 1000 kg, v = 20 m/s. Step 2: Use formula K.E. = ½ mv². Step 3: K.E. = ½ × 1000 × (20)² = 500 × 400 = 2,00,000 J. Result: 2 × 10⁵ J or 200 kJ. |
| 3 | An electric bulb of 100W is used for 10 hours a day. How many 'units' (kWh) of energy are consumed in one day? | Step 1: Power (P) = 100 W = 0.1 kW. Time (t) = 10 hours. Step 2: Energy = Power × Time. Step 3: Energy = 0.1 kW × 10 h = 1 kWh. Result: 1 unit. |
| 4 | How much work is done by a force of 50 N acting on a body if the body displaces 10 m at an angle of 60° to the force? | Step 1: Given F = 50 N, s = 10 m, θ = 60°. Step 2: W = Fs cosθ. (cos 60° = 0.5). Step 3: W = 50 × 10 × 0.5 = 250 J. Result: 250 J. |
Common Mistakes to Avoid
- Confusing Mass and Weight: Always check if the question gives mass (kg) or weight (Newton). If weight is given, don't multiply by 'g' again.
- Unit Conversion: Many students forget to convert time into seconds for Power calculations or grams into kilograms for Kinetic Energy. Stick to SI units!
- Cosine Value: Be careful with the angle θ. If the force is perpendicular, the work is ZERO, regardless of the force's magnitude.
- K.E. vs Momentum: Remember K.E. = P² / 2m (where P is momentum). RRB often asks about the relationship when momentum is doubled.
Practice Questions with Solutions
1. If the velocity of a body is tripled, its kinetic energy becomes how many times?
2. A man of mass 50 kg climbs a ladder of 10 m in 20 seconds. Calculate his power. (g = 10 m/s²)
3. What is the work done by the Earth's gravity on a satellite moving in a circular orbit?
4. Find the energy possessed by an object of mass 5 kg when it is at a height of 15 m above the ground. (g = 9.8 m/s²)
5. A machine does 4000 J of work in 2 minutes. What is its power in Watts?
6. If a force of 1 N displaces a body by 1 m in the direction of force, what is the work done?
7. What is the relationship between 1 Horsepower and Watts?
Solutions:
1. Answer: 9 times. (Since K.E. ∝ v², 3² = 9).
2. Answer: 250 W. (Work = mgh = 50×10×10 = 5000 J. Power = Work/Time = 5000/20 = 250 W).
3. Answer: Zero. (The force of gravity is perpendicular to the instantaneous displacement).
4. Answer: 735 J. (P.E. = mgh = 5 × 9.8 × 15).
5. Answer: 33.33 W. (Time = 2 × 60 = 120s. Power = 4000/120).
6. Answer: 1 Joule. (Direct application of W = F × s).
7. Answer: 1 hp = 746 Watts.
Frequently Asked Questions (FAQs)
Q1: Is work a vector or scalar quantity?
A: Work is a scalar quantity because it only has magnitude and no specific direction, even though force and displacement are vectors.
Q2: What happens to Potential Energy as an object falls?
A: As an object falls, its height decreases, so its Potential Energy decreases. However, this energy is converted into Kinetic Energy as its velocity increases.
Q3: What is the commercial unit of electricity?
A: The commercial unit is the Kilowatt-hour (kWh), often simply called a 'unit'. 1 kWh is the energy consumed by a 1000W appliance in one hour.
Q4: Why is no work done when you carry a heavy suitcase and stand still?
A: Because displacement (s) is zero. According to the formula W = F × s, if s = 0, work is 0.
Conclusion and Final Tips
Mastering Work, Power, and Energy is essential for anyone aspiring to crack the RRB NTPC or Group D exams. The key is to visualize the problems—think about the direction of force and the resulting movement. Remember to keep your units consistent (always use kilograms, meters, and seconds) and memorize the relationship between Kinetic Energy and Momentum (K.E. = P²/2m), as it is a favorite for RRB examiners.
Keep practicing numerical problems and stay consistent in your preparation. Physics might seem daunting, but once you grasp the core logic, it becomes the most scoring part of the General Science section. Good luck with your preparation, and aim for those top marks!
