1. Work
- Definition: Work is said to be done when a force (push or pull) applied to an object causes a displacement of the object.
- Conditions for work:
- There must be a force acting on the object.
- The object must undergo a displacement.
- The force must have a component in the direction of the displacement.
- Equation: W = F ⋅ d cosθ (where W is work, F is force, d is displacement, and θ is the angle between the force and displacement vectors)
- Work is a scalar quantity.
- Positive work: When the force and displacement are in the same direction (θ < 90°).
- Negative work: When the force and displacement are in opposite directions (90° < θ < 180°).
- Zero work: When the force and displacement are perpendicular (θ = 90°) or when either force or displacement is zero.
- Units: The SI unit of work is the joule (J), which is equal to newton-meter (N⋅m).
2. Energy
- Definition: Energy is the capacity to do work. It exists in various forms, including:
- Kinetic Energy (KE): Energy possessed by an object due to its motion. KE = (1/2)mv² (where m is mass and v is velocity)
- Potential Energy (PE): Energy possessed by an object due to its position or configuration.
- Gravitational Potential Energy: PE = mgh (where m is mass, g is acceleration due to gravity, and h is height)
- Elastic Potential Energy: Energy stored in a stretched or compressed spring. PE = (1/2)kx² (where k is the spring constant and x is the displacement from equilibrium)
- Other forms: Thermal energy, chemical energy, nuclear energy, etc.
- Work-Energy Theorem: The work done on an object is equal to the change in its kinetic energy: W = ΔKE
- Conservation of Mechanical Energy: In a closed system with no non-conservative forces (like friction), the total mechanical energy (KE + PE) remains constant.
3. Power
- Definition: Power is the rate at which work is done or energy is transferred.
- Equation: P = W/t (where P is power, W is work, and t is time) or P = F ⋅ v (where F is force and v is velocity)
- Units: The SI unit of power is the watt (W), which is equal to joule per second (J/s).
Key Concepts for JEE
- Conservative and Non-conservative Forces:
- Conservative forces: Forces for which the work done is independent of the path taken (e.g., gravity, spring force).
- Non-conservative forces: Forces for which the work done depends on the path taken (e.g., friction).
- Work Done by a Variable Force: Calculating work done when the force is not constant, using integration.
- Collision Problems: Applying the concepts of work, energy, and power to analyze collisions (elastic and inelastic).
- Power and Efficiency: Understanding the relationship between power output, power input, and efficiency in machines.
Tips for JEE Preparation
- Master the fundamentals: Build a strong foundation by understanding the definitions, equations, and units related to work, energy, and power.
- Practice problem-solving: Solve a variety of problems involving different forms of energy, work-energy theorem, and power calculations.
- Focus on applications: Learn how these concepts apply to real-world situations, such as roller coasters, projectiles, and collisions.
- Develop analytical skills: Be able to analyze systems and identify the different forms of energy involved and how they are transformed.