WORK ENERGY AND POWER ONE SHOT CLASS 11 PHYSICS FOR 2024-2025 || CLASS 11 PHYSICS || MUNIL SIR

Key Concepts

• Work: Force applied over a distance, resulting in displacement.
• Energy: The ability to do work.
• Power: The rate at which work is done.
• Work Done by a Constant Force: Work = Force × Displacement × cos(θ), where θ is the angle between force and displacement.
• Work Done by a Variable Force: Requires integration: ∫ F(x) dx, where F(x) is the force as a function of displacement.
• Nature of Work Done: Work can be positive (force aids displacement), negative (force opposes displacement), or zero (force and displacement are perpendicular).
• Kinetic Energy: Energy due to motion (1/2 * mv^2).
• Potential Energy: Energy due to position or configuration (e.g., gravitational potential energy: mgh).
• Work-Energy Theorem: The net work done on an object equals the change in its kinetic energy.
• Conservative Force: A force where the work done is path-independent (e.g., gravity).
• Non-Conservative Force: A force where the work done depends on the path taken (e.g., friction).
• Mechanical Energy: The sum of kinetic and potential energy.
• Conservation of Mechanical Energy: In the absence of non-conservative forces, the total mechanical energy of a system remains constant.
• Spring Force: The force exerted by a spring, proportional to its displacement from equilibrium (F = -kx).
• Potential Energy of a Spring: Energy stored in a spring due to its compression or extension (1/2 * kx^2).
• Momentum: Mass in motion (p = mv).
• Relation Between Kinetic Energy and Momentum: K = p^2 / 2m.
• Coefficient of Restitution (e): A measure of the "bounciness" of a collision, defined as the ratio of the relative velocity of separation to the relative velocity of approach.
• Elastic Collision: A collision where kinetic energy is conserved.
• Inelastic Collision: A collision where kinetic energy is not conserved (some energy is lost to heat, sound, etc.).
• Vertical Circular Motion: Motion in a vertical circle, where speed and tension vary due to gravity.

Work Done

• Definition: Work is done when a force causes displacement. If there is no displacement, there is no work done, regardless of the force applied.
• Formula for Constant Force: W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between them.
• Example: Pushing a heavy almirah without moving it results in zero work done, even if significant force is applied.
• Angle Consideration: Only the component of force in the direction of displacement contributes to work. If the force is perpendicular to the displacement (θ = 90°), the work done is zero.
• Formula for Variable Force: W = ∫ F(x) dx, where F(x) is the force as a function of displacement.
• Example: If F = 3x^2, the work done from x = 2 to x = 10 is calculated by integrating 3x^2 from 2 to 10, resulting in 992 Joules.
• Graphical Interpretation: The area under the force-displacement graph represents the work done.

Nature of Work Done

• Positive Work: Occurs when the angle between force and displacement is less than 90 degrees. The force aids the displacement.
• Negative Work: Occurs when the angle between force and displacement is greater than 90 degrees. The force opposes the displacement.
• Zero Work: Occurs when the angle between force and displacement is 90 degrees, or when either force or displacement is zero.
• Examples:
  • Friction: Always does negative work as it opposes motion.
  • Coolie Carrying Load: The work done by the force of gravity on the load is zero because the force is vertical and the displacement is horizontal (90 degrees).
  • Centripetal Force in Circular Motion: Does zero work because it's always perpendicular to the displacement.
  • Tension in a Simple Pendulum: Does zero work because it's always perpendicular to the displacement.

Work Done by Variable Force

• Concept: When the force applied is not constant but changes with displacement, the work done is calculated using integration.
• Formula: W = ∫ F(x) dx, where F(x) is the force as a function of displacement.
• Example: If F = 2y + 3y^2, the work done from y = 0 to y = 1 is calculated by integrating 2y + 3y^2 from 0 to 1.

Energy

• Definition: The ability to do work.
• Kinetic Energy: Energy possessed by an object due to its motion.
  • Formula: KE = 1/2 * mv^2, where m is mass and v is velocity.
  • Derivation: Starting from v^2 - u^2 = 2as, multiplying both sides by 1/2 * m leads to KE = F * s.
• Potential Energy: 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.
  • Concept: Lifting an object against gravity stores potential energy, which can be converted back to kinetic energy when the object is released.

Work-Energy Theorem

• Statement: The net work done on an object is equal to the change in its kinetic energy.
• Formula: W = ΔKE = KE_final - KE_initial = 1/2 * mv_final^2 - 1/2 * mv_initial^2.
• Proof for Constant Force: Starting from v^2 - u^2 = 2as, multiplying both sides by 1/2 * m leads to W = ΔKE.
• Proof for Variable Force: Using W = ∫ F(x) dx and F = ma = m(dv/dt), substituting and integrating leads to W = ΔKE.

Relation Between Kinetic Energy and Momentum

• Formulas:
  • Kinetic Energy (K) = p^2 / 2m, where p is momentum and m is mass.
  • Momentum (p) = √(2mK).
• Application: If kinetic energy is increased by a factor of 4, the momentum increases by a factor of 2 (square root of 4).
• Percentage Change: Percentage increase in momentum can be calculated using the formula: ((Final Value - Initial Value) / Initial Value) * 100.

Example Problems

• Cyclist Stopping:
  • The work done by the road on the cycle is negative (due to friction) and calculated as -2000 J.
  • The work done by the cycle on the road is zero because the road does not move.
• Kinetic Energy Increase:
  • If the kinetic energy of an object increases by 300%, the momentum increases by 100%.
• Bullet Through Plywood:
  • A bullet loses 90% of its kinetic energy passing through plywood. The emergent speed is calculated using the remaining 10% of the initial kinetic energy.
• Raindrop Falling:
  • The work done by gravity on a raindrop falling from 1 km is 10 J.
  • The work done by air resistance is calculated using the work-energy theorem, considering the change in kinetic energy and the work done by gravity.

Potential Energy of a Spring

• Spring Force: F = -kx, where k is the spring constant and x is the displacement from equilibrium.
• Potential Energy: PE = 1/2 * kx^2.
• Proof of Spring Force Being Conservative: If the initial and final positions are the same (cyclic process), the net work done is zero, indicating a conservative force.
• Graphical Representation: The potential energy of a spring increases parabolically with displacement (both positive and negative), while the kinetic energy decreases.

Collisions

• Elastic Collision: A collision where kinetic energy is conserved.
• Inelastic Collision: A collision where kinetic energy is not conserved (some energy is lost).
• Momentum Conservation: Momentum is conserved in both elastic and inelastic collisions.
• Coefficient of Restitution (e):
  • e = 1 for elastic collisions.
  • e = 0 for perfectly inelastic collisions.
  • 0 < e < 1 for inelastic collisions.
• Elastic Collision in One Dimension:
  • Formulas for final velocities (v1 and v2) are derived using conservation of momentum and kinetic energy.
  • Velocity of approach equals velocity of separation.
• Special Cases:
  • Equal Masses, One at Rest: The moving object stops, and the stationary object starts moving with the initial velocity of the first object.
  • Equal Masses, Both Moving: The objects exchange velocities.
  • Light Body Strikes Heavy Stationary Body: The light body rebounds with the same speed in the opposite direction, and the heavy body remains at rest.
• Elastic Collision in Two Dimensions:
  • Involves component breaking of velocities and applying conservation of momentum in both x and y directions.
  • Also involves conservation of kinetic energy.

Loss in Kinetic Energy in Inelastic Collision

• Scenario: Two bodies collide and stick together.
• Formula: The loss in kinetic energy is derived using conservation of momentum to find the final velocity and then calculating the difference between initial and final kinetic energies.
• Final Formula: ΔKE = (1/2) * (m1 * m2 / (m1 + m2)) * u1^2, where u1 is the initial velocity of the moving body.

Vertical Circular Motion

• Concept: Analyzing the motion of an object moving in a vertical circle, considering gravity and tension.
• Key Points:
  • The speed and tension vary at different points in the circle.
  • At the top of the circle (point C), the weight balances the centripetal force (mg = mv^2/r).
• Formulas:
  • Speed at the top (vc) = √(gr).
  • Speed at the horizontal position (vb) = √(3gr).
  • Speed at the bottom (va) = √(5gr).
• Energy Conservation: The total mechanical energy (kinetic + potential) remains constant throughout the motion.
• Procedure:
  1. Calculate the total mechanical energy at different points (A, B, C).
  2. Use energy conservation to relate the speeds at different points.
  3. Use the condition at the top (mg = mv^2/r) to find the speed at the top.

Conclusion

The video provides a comprehensive overview of work, energy, and power, covering various concepts, formulas, and problem-solving techniques. It emphasizes the importance of understanding the underlying principles and applying them to solve numerical problems. The video also highlights the significance of energy conservation and its applications in different scenarios.