Lecture on Work, Energy, and Forces

Key Concepts

Work (W): Defined as the force applied to an object times the distance over which it is applied. Expressed mathematically as: [ W = F \times d ]
Kinetic Energy (KE): The energy an object possesses due to its motion, calculated as: [ KE = \frac{1}{2} mv^2 ]
- m: mass of the object
- v: velocity of the object
Potential Energy (PE): The energy stored in an object due to its position or height. Specifically, gravitational potential energy is: [ PE = mgh ]
- m: mass
- g: acceleration due to gravity (9.8 m/s²)
- h: height above a reference point

Relation between Work and Kinetic Energy:
- Work done on an object is equal to the change in kinetic energy of the object.
- Example Calculation:
  - A 5 kg object moving at 7 m/s has kinetic energy: [ KE = \frac{1}{2} \times 5 \times 49 = 125 \text{ Joules} ]
  - This means 125 Joules of work has been done to bring it to this speed.

Example of Constant Velocity:
- Elevators moving at constant speed: The upward force equals gravitational force.
- For a 10 kg elevator moving up 100 meters, work done is: [ W = 10 \times 9.8 \times 100 = 9800 \text{ Joules} ]
Potential Energy Concept:
- Work done against gravity is stored as potential energy.
- Potential energy is the capacity to do work due to position.
- Example:
  - A 1 kg object at 10 meters has potential energy: [ PE = 1 \times 10 \times 10 = 100 \text{ Joules} ]

Law of Conservation of Energy:
- Energy cannot be created or destroyed; it transforms from one form to another.
- Example: Object falling from height where potential energy converts to kinetic energy as it descends.
- Potential energy decreases as the object falls, converting it into kinetic energy.

Understanding these principles helps in solving real-world physics problems involving motion and forces.
These principles are foundational in fields like engineering, mechanics, and energy science.

The lecture explains the fundamental relationship between force, work, and energy.
Practical examples help in understanding how energy transformations occur in physical systems.
Emphasizes the importance of the conservation of energy in analyzing systems under various forces.