Work and energy are fundamental concepts in physics that explain how force, motion, and transfer of energy are connected. These concepts are not only important for understanding natural phenomena but also play a major role in day-to-day life.
What is Work?
In everyday language, we say “work” when someone does physical or mental effort. But in physics, the meaning of work is specific and different.
Definition of Work
Work is said to be done when a force is applied on an object and the object is displaced in the direction of the applied force.
Conditions for Work
- A force must be applied.
- The object must be displaced.
- The displacement should have a component in the direction of the force.
Mathematical Expression of Work
Work (W) = Force (F) × Displacement (S) × cosθ
- F = magnitude of force
- S = displacement of the object
- θ = angle between force and displacement
If θ = 0° (force and displacement in same direction), W = F × S
If θ = 90° (force perpendicular to displacement), W = 0 (no work done).
Positive and Negative Work
- Positive Work: When force and displacement are in the same direction (e.g., a man pushes a moving car forward).
- Negative Work: When force and displacement are in opposite directions (e.g., friction acts on a moving object).
Energy
Energy is the capacity to do work. It exists in many forms, such as mechanical, heat, chemical, electrical, nuclear, etc. The SI unit of energy is the Joule (J), same as that of work.
Kinetic Energy
Kinetic energy is the energy possessed by a body due to its motion.
Expression: KE = ½ mv²
- m = mass of the body
- v = velocity of the body
Derivation is based on the work-energy theorem.
Potential Energy
Potential energy is the energy possessed by a body due to its position or configuration.
Expression: PE = mgh
- m = mass of the body
- g = acceleration due to gravity
- h = height of the body above ground
Work-Energy Theorem
Work done on an object is equal to the change in its kinetic energy.
W = ΔKE = KE₂ – KE₁
Power
Power is the rate of doing work.
Expression: Power = Work done / Time
The SI unit of power is Watt (W). 1 watt = 1 joule of work done per second.
Commercial Unit of Energy
The unit of energy used in households and industries is the kilowatt-hour (kWh).
1 kWh = 1 kilowatt × 1 hour = 1000 watt × 3600 seconds = 3.6 × 106 joules
Law of Conservation of Energy
Energy can neither be created nor destroyed; it can only change from one form to another. The total energy of an isolated system remains constant.
Examples of Transformation of Energy
- In a simple pendulum: Potential energy ↔ Kinetic energy
- In hydroelectric plants: Potential energy of water → Kinetic energy → Electrical energy
- In electric bulbs: Electrical energy → Light energy + Heat energy
Important Numerical Examples
- Example 1: A force of 10 N displaces an object by 5 m in the direction of force. Work = 10 × 5 = 50 J
- Example 2: A 2 kg body is raised to a height of 5 m. Potential energy = mgh = 2 × 9.8 × 5 = 98 J
- Example 3: A body of mass 4 kg moving at 3 m/s. Kinetic energy = ½ mv² = ½ × 4 × 9 = 18 J
Key Points to Remember
- Work is done only when displacement occurs.
- If force is perpendicular to displacement, work = 0.
- Kinetic energy depends on mass and square of velocity.
- Potential energy depends on mass, gravity, and height.
- Total mechanical energy (TME) = Kinetic Energy + Potential Energy.
- Energy is always conserved in any system.
Practice Questions
- Define work. State the conditions necessary for work to be done.
- Differentiate between positive work and negative work with examples.
- Derive the expression for kinetic energy.
- A body of mass 5 kg is lifted to a height of 10 m. Calculate its potential energy.
- What is the commercial unit of energy? Convert 5 kWh into joules.
Conclusion
Work and energy are closely related physical quantities. Work is the transfer of energy, and energy is the capacity to do work. The principle of conservation of energy is one of the most fundamental laws of nature and applies to all physical and chemical processes.
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