General Science: Work and Energy (Physics)

📅 Date: 17 December 2025 (Wednesday)

We are now entering the realm of Energy and Power, concepts that run the modern world. In your exam, questions here are often tricky because they play on the difference between the "Physics definition" of work and the "English definition" of work. Here is your dissected study guide for Work and Energy.

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1. WORK: The Scientific Perspective

In everyday language, "work" means effort. In Physics, "Work" is a mathematical relationship between Force and Displacement.

The Two Essential Ingredients

For Work (W) to be non-zero, two things must happen simultaneously:

• Force (F): You must push or pull.
• Displacement (s): The object must actually move.

The Three States of Work (Detailed Analysis)

Examiners love to give you scenarios and ask if the work is Positive, Negative, or Zero.

1. Positive Work (Angle is 0°)

• Scenario: You push a car, and it moves forward.
• Physics: The Force and the Displacement are in the same direction.
• Result: You are adding energy to the object. Its speed increases.

2. Negative Work (Angle is 180°)

• Scenario: You apply brakes to a moving car.
• Physics: The car moves forward, but the force (friction/brakes) acts backward.
• Result: The force is taking energy away from the object. Its speed decreases.
• Another Example: When you lift a book, Gravity does negative work because gravity pulls down while the book moves up.

3. Zero Work (Angle is 90° or Displacement is 0)

This is the most important category for exams.

• Case 1: No Displacement.
  Scenario: Pushing a massive wall.
  Reason: s=0, so W=0.
• Case 2: Perpendicular Force.
  Scenario: A porter (coolie) walking on a horizontal platform with a load on his head.
  Physics: The Force he exerts is Upward. His movement is Forward. The angle is 90°.
  Result: He is doing no work against gravity.
• Scenario: A satellite orbiting Earth. Gravity pulls to the center, but it moves along the tangent. W=0.

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2. ENERGY: The Currency of the Universe

Think of Energy as "money" that allows you to "purchase" Work. If you have Energy, you can do Work. If you do Work, you spend Energy.
Unit: Joule (J).
Law of Conservation: Energy cannot be created or destroyed. It can only be transferred or transformed.

KINETIC ENERGY (KE): The Energy of Motion

This is the energy an object has simply because it is moving.
The Formula: KE = 1/2 mv²

The Work-Energy Theorem:
Work done = Change in Kinetic Energy.
Example: If you want to stop a car, the work done by the brakes must equal the car's Kinetic Energy.

POTENTIAL ENERGY (PE): The Energy of Position

This is "stored" energy. The object isn't moving yet, but it has the potential to move.

1. Gravitational Potential Energy (PEg)

Energy stored by lifting something against gravity.
Formula: PE = m × g × h
(m = Mass, g = Gravity, h = Vertical Height)

The "Path Independence" Rule: If you lift a stone to the 3rd floor using the stairs, or an elevator, or pull it up with a rope—the Work Done and Potential Energy are the SAME. Why? Because 'h' (vertical height) is the same. Gravity only cares about the vertical difference.

2. Elastic Potential Energy

Energy stored when you deform something (stretch a rubber band, compress a spring, draw a bow). When you release it, this PE turns into Kinetic Energy.

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3. POWER: The Rate of Work

Work tells you how much you did. Power tells you how fast you did it.

The Concept: Imagine an old man and a young athlete climbing the same stairs.
Work: Both do the same work (lifting body weight).
Power: The athlete is faster (Time t is less). Therefore, the athlete has more Power.

Formula: Power (P) = Work Done / Time Taken (P = W/t)
Velocity Relation: P = Force × Velocity (P = F × v).
(This explains why a car needs more power to maintain a high speed against air resistance).

Units:

• SI Unit: Watt (W).
• Commercial Unit: Kilowatt-hour (kWh).
• Horsepower (hp): 1 hp = 746 Watts.

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4. The "Kilowatt-hour" (kWh) Trap

This is where students lose marks. Kilowatt-hour is a unit of ENERGY, not Power.

The Logic: Power = Energy / Time. Therefore, Energy = Power × Time.
If you use a 1000 Watt (1 kW) heater for 1 Hour: Energy = 1 kW × 1 hour = 1 kWh.

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5. "Think Like a Physicist" Scenarios

• Scenario A: The Pendulum:
  • Highest point: Velocity 0, KE 0, PE Maximum.
  • Lowest point: Moving fastest, KE Maximum, PE Minimum.
  • Total Energy: Constant at every single point.
• Scenario B: Free Fall: As a stone falls, does it lose energy? No. It loses Potential Energy (height decreases), but gains Kinetic Energy (speed increases). Total Mechanical Energy remains conserved.
• Scenario C: Stopping Distance: Two cars (v and 2v) slam brakes. Car 1 stops in distance 'd'. Car 2 stops in distance '4d' (Because it had 4 times the Kinetic Energy).

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6. Summary Checklist

Can you answer these "Why" questions now?

• Why is no work done when carrying a bag horizontally? (Force ⊥ Displacement).
• Why does a stretched bow possess energy? (Work was done to change its shape, stored as Elastic PE).
• Why is "1 Unit" of electricity equal to 3.6×10⁶ Joules? (Math conversion of kW and Hours).
• Why does a lighter body and a heavier body dropped from the same height strike the ground with different KE? (KE depends on mass; heavier body has more KE, even if they fall at the same speed).

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7. Mentor’s Final Drill (Exam-Ready Questions)