Chapter 8, Work and Energy, is necessary to understand or know about the amount of work done and the amount of energy required. Therefore, there exists a relationship between work and energy. The quantity F⋅ dr= F dr cosθ denotes the work done by a force F on a particle during the small displacement dr.
Notably, the change in kinetic energy of a particle is equal to the work done on it. This is called the work-energy theorem. There is a significant difference between work and energy. The work is subsequently calculated as force x displacement x cosine(theta), where theta(θ) is the angle between the force and the displacement vectors. The work done by the resultant force is equal to the sum of the work done by the individual forces.
Energy can be further Classified into potential and Kinetic energy. An object can store energy as a result of its position. Total mechanical energy can be defined as the sum of kinetic energy and potential energy. It remains constant if the system has internal conservative forces and the external forces do not work. This is popularly known as the principle of conservation of energy. However, the total mechanical energy K + U value is not constant if non-conservative forces like friction exist between the system's particles.
The chapter further concentrates on gravitational potential energy. If a block with mass m moves a height h over the Earth's surface (height << the radius of the Earth), the total system's potential energy( i.e., earth+body) increases by mgh, i.e. the product of mass, acceleration due to gravity and height
Let's take all forms of energy into account. First, the generalised law of conservation of energy is considered - Energy can never be created or destroyed. It can only be changed from one form into another.