Quick Revision Notes: Work, Energy and Power

Class: 11 Physics (MP Board)

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### 1. Work (कार्य)

• Definition: Work is done when a force acting on a body produces a displacement in the body. It is a scalar quantity.

• Formula: W = F * s * cos(θ) Where:

  • F = Force (बल)
  • s = Displacement (विस्थापन)
  • θ = Angle between Force and Displacement vectors.

• Special Cases:

  1. If θ = 0° (Force and displacement in the same direction): W = F * s (Maximum Work)
  2. If θ = 90° (Force perpendicular to displacement): W = 0 (Zero Work, e.g., carrying a load horizontally).
  3. If θ = 180° (Force opposite to displacement): W = -F * s (Minimum/Negative Work, e.g., frictional force).

• Units & Dimensions:

  • SI Unit: Joule (J) or Newton-metre (N·m)
  • CGS Unit: erg
  • Relation: 1 Joule = 10^7 erg
  • Dimensional Formula: [M^1 L^2 T^-2]

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### 2. Energy (ऊर्जा)

• Definition: The capacity of a body to do work is called energy. It is a scalar quantity.
• SI Unit: Joule (J)
• Dimensional Formula: [M^1 L^2 T^-2]

A. Kinetic Energy (गतिज ऊर्जा)

• Definition: Energy possessed by a body by virtue of its motion.
• Formula: K = (1/2) * m * v^2 Where m = mass, v = velocity.
• Relation between Momentum (p) and Kinetic Energy (K): p = sqrt(2 * m * K) or K = p^2 / (2 * m)

B. Potential Energy (स्थिति ऊर्जा)

• Definition: Energy possessed by a body by virtue of its position or configuration.
• Gravitational Potential Energy: U = m * g * h Where m = mass, g = acceleration due to gravity, h = height.
• Spring Potential Energy: U = (1/2) * k * x^2 Where k = spring constant (बल नियतांक), x = extension/compression.

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### 3. Work-Energy Theorem (कार्य-ऊर्जा प्रमेय)

• Statement: The work done by a net force on a object equals the change in its kinetic energy.
• Formula: W = ΔK = K_f - K_i W = (1/2) * m * v^2 - (1/2) * m * u^2 (Where v is final velocity and u is initial velocity)

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### 4. Conservation of Mechanical Energy (यांत्रिक ऊर्जा संरक्षण का नियम)

• Statement: The total mechanical energy (Kinetic Energy + Potential Energy) of a system remains constant if the internal forces are conservative.
• Formula: E = K + U = constant K_i + U_i = K_f + U_f

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### 5. Power (शक्ति)

• Definition: The rate of doing work or the rate of transfer of energy is called power. It is a scalar quantity.
• Formulas:
  • Average Power: P_avg = W / t
  • Instantaneous Power: P = F * v (where v is velocity)
• Units & Dimensions:
  • SI Unit: Watt (W) or Joule/second (J/s)
  • Practical Unit: Horsepower (hp) -> 1 hp = 746 Watts
  • Commercial Unit of Energy: Kilowatt-hour (kWh) -> 1 kWh = 3.6 * 10^6 Joules
  • Dimensional Formula: [M^1 L^2 T^-3]

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### 6. Collisions (संघर्ष / टक्कर)

Collisions are generally of two types in one dimension:

1. Elastic Collision (प्रत्यास्थ टक्कर):

   • Both Momentum and Kinetic Energy are conserved.
   • p_initial = p_final and K_initial = K_final
   • Coefficient of restitution, e = 1.

2. Inelastic Collision (अप्रत्यास्थ टक्कर):

   • Only Momentum is conserved. Kinetic energy is not conserved (lost as heat, sound, etc.).
   • p_initial = p_final and K_initial ≠ K_final
   • Coefficient of restitution, e = 0 (for perfectly inelastic collision where bodies stick together).