Work, Energy and Power – Complete Physics Notes | Mechanics (Bsc)
Work, Energy and Power – Complete Notes (Mechanics)
The study of Work, Energy and Power forms a fundamental part of classical mechanics. This chapter explains how forces cause motion, how energy is transferred or transformed, and how fast work is done. These concepts are essential for understanding motion, machines, engines, and natural phenomena.
1. Concept of Work
In everyday language, we say work is done when someone is tired after an activity. However, in physics, work has a precise scientific meaning.
Work is said to be done when a force acting on a body produces displacement in the direction of the force.
1.1 Mathematical Definition of Work
If a constant force F acts on a body and produces a displacement s in the same direction, then the work done W is:
W = F × s
If the force makes an angle θ with the direction of displacement, then:
W = F s cosθ
1.2 SI Unit of Work
The SI unit of work is joule (J).
1 joule is the work done when a force of 1 newton produces a displacement of 1 metre in its direction.
1.3 Special Cases of Work
- Positive Work: When force and displacement are in the same direction (pushing a box).
- Negative Work: When force acts opposite to displacement (friction).
- Zero Work: When displacement is zero or force is perpendicular to motion (centripetal force).
2. Energy
Energy is the capacity of a body to do work. A body having energy can perform work on another body.
Energy exists in various forms and can be transformed from one form to another.
2.1 SI Unit of Energy
The SI unit of energy is also joule (J).
3. Kinetic Energy
Kinetic energy is the energy possessed by a body due to its motion.
Any moving object, whether it is a car, a flowing river, or a rotating fan, possesses kinetic energy.
3.1 Expression for Kinetic Energy
The kinetic energy K of a body of mass m moving with velocity v is:
K = ½ mv²
3.2 Factors Affecting Kinetic Energy
- Kinetic energy is directly proportional to the mass of the body.
- Kinetic energy is proportional to the square of velocity.
This means doubling the velocity increases kinetic energy four times.
4. Work–Energy Theorem
The work–energy theorem states that:
The net work done on a body is equal to the change in its kinetic energy.
Mathematically:
W = ΔK = Kfinal − Kinitial
This theorem connects the concepts of force, work, and motion.
5. Potential Energy
Potential energy is the energy possessed by a body due to its position or configuration.
A raised object, a stretched spring, or water stored in a dam has potential energy.
5.1 Gravitational Potential Energy
When a body of mass m is raised to a height h against gravity, the gravitational potential energy is:
U = mgh
where g is acceleration due to gravity.
5.2 Zero Level of Potential Energy
The zero level of potential energy is arbitrary and can be chosen for convenience. Only changes in potential energy are physically meaningful.
6. Conservative and Non-Conservative Forces
6.1 Conservative Forces
A force is called conservative if the work done by it depends only on the initial and final positions, not on the path followed.
Examples: Gravitational force, spring force.
6.2 Non-Conservative Forces
A force is non-conservative if the work done depends on the path taken.
Example: Friction.
7. Mechanical Energy
Mechanical energy is the sum of kinetic and potential energies.
E = K + U
Mechanical energy plays a key role in analyzing motion under conservative forces.
8. Law of Conservation of Mechanical Energy
If only conservative forces act on a system, the total mechanical energy remains constant.
This means energy is neither created nor destroyed but transformed from one form to another.
Example: A freely falling body converts potential energy into kinetic energy.
9. Power
Power is the rate at which work is done or energy is transferred.
9.1 Average Power
Average Power = Work done / Time taken
9.2 Instantaneous Power
Instantaneous power is given by:
P = F · v
9.3 SI Unit of Power
The SI unit of power is watt (W).
1 watt is the power when 1 joule of work is done in 1 second.
10. Efficiency
Efficiency of a machine is defined as:
Efficiency = (Useful output energy / Input energy)
Efficiency is always less than 1 due to energy losses.
11. Important Applications
- Design of machines and engines
- Understanding motion of vehicles
- Power rating of electrical appliances
- Analysis of mechanical systems
12. Conceptual & Practice Questions
- Define work in physics. When is work said to be zero?
- Derive the expression for kinetic energy.
- State and explain the work–energy theorem.
- What is potential energy? Explain gravitational potential energy.
- Distinguish between conservative and non-conservative forces.
- State the law of conservation of mechanical energy.
- Define power and write its SI unit.
- Why is efficiency of a machine always less than 100%?
End of Work, Energy and Power Notes
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