Bihar Board - Class 11 physics - Chapter 6: Work, Energy, and Power Handwritten Notes

The chapter "Work, Energy, and Power" deals with the concepts of work done by a force, different forms of energy, and the rate at which work is performed (power). These concepts are foundational in understanding the conservation of energy and solving mechanical problems in physics.

Key Points

1. Work

   • Definition: Work is done when a force is applied to an object, and it causes displacement in the direction of the force.
   • Formula:
     $W = F \cdot d \cdot \cos \theta$, where:
     $F$ = Force, $d$ = Displacement, $\theta$ = Angle between force and displacement.
   • Positive Work: When force and displacement are in the same direction.
   • Negative Work: When force and displacement are in opposite directions.

2. Energy

   • Definition: The capacity to do work.
   • Kinetic Energy (KE): Energy of an object in motion:
     $KE = \frac{1}{2}mv^2$, where $m$ = mass, $v$ = velocity.
   • Potential Energy (PE): Energy of an object due to its position:
     $PE = mgh$, where $h$ = height, $g$ = acceleration due to gravity.
   • Mechanical Energy: Sum of kinetic and potential energy in a system.

3. Work-Energy Theorem

   • States that the work done on an object is equal to the change in its kinetic energy:
     $W = \Delta KE$.

4. Power

   • Definition: The rate at which work is done.
   • Formula:
     $P = \frac{W}{t}$, where $W$ = Work, $t$ = Time.
   • Measured in watts ($W$).

5. Conservation of Energy

   • Energy cannot be created or destroyed; it can only be transformed from one form to another.
   • Example: Conversion between potential and kinetic energy in a pendulum.

6. Collisions

   • Elastic Collisions: Both momentum and kinetic energy are conserved.
   • Inelastic Collisions: Momentum is conserved, but kinetic energy is not.

7. Power and Efficiency

   • Efficiency is the ratio of useful work output to the total work input, expressed as a percentage.
   • Formula:
     $\text{Efficiency} = \frac{\text{Useful Work Output}}{\text{Work Input}} \times 100\%$.

Conclusion

"Work, Energy, and Power" is a critical chapter that provides insights into how forces interact with objects, leading to motion, energy transformations, and the concept of efficiency. These principles are essential in solving problems across various domains of physics and engineering.

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