Work, Power, and Energy Revision - JEE Advanced Level
Work, Power, and Energy are fundamental concepts in mechanics. Understanding these concepts is crucial for solving problems related to energy conservation, work done by forces, and power output. In this post, we will cover the key formulas, interactive examples, and simulations to help you master these concepts.
1. Key Formulas
Below is a table summarizing the important formulas related to work, power, and energy:
| Concept | Formula | Description |
|---|---|---|
| Work Done | \[ W = F \cdot d \cdot \cos(\theta) \] | Work done is the product of force, displacement, and the cosine of the angle between them. |
| Kinetic Energy | \[ KE = \frac{1}{2} mv^2 \] | Kinetic energy is the energy of motion, dependent on mass and velocity. |
| Potential Energy | \[ PE = mgh \] | Potential energy is the energy stored due to an object's position in a gravitational field. |
| Power | \[ P = \frac{W}{t} \] | Power is the rate of doing work or the rate of energy transfer. |
| Work-Energy Theorem | \[ W = \Delta KE \] | The net work done on an object is equal to the change in its kinetic energy. |
2. Interactive Example: Calculating Work Done
Calculate the work done when a force of 10 N is applied to move an object 5 meters in the direction of the force:
Work Done (W) = Force (F) × Displacement (d) × cos(θ)
Given:
- Force, F = 10 N
- Displacement, d = 5 m
- Angle, θ = 0° (since force is in the direction of displacement)
Work Done (W) = 50 J
Example 1: A 2 kg object is moving with a velocity of 3 m/s. Calculate its kinetic energy.
Example 2: A force of 50 N is applied at an angle of 60° to the direction of motion of an object that moves 10 meters. Calculate the work done.
4. Interactive Simulation: Work-Energy Theorem
Change the mass and velocity of an object to see how its kinetic energy changes:
5 kgKinetic Energy (KE): 250 J
5. Conclusion
Understanding work, power, and energy is crucial for solving a variety of physics problems. By mastering these concepts, you'll be able to tackle complex problems with confidence. Make sure to practice using the formulas and interactive examples provided in this post to reinforce your knowledge.
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