📝 Chapter Notes & Revision

Work and Energy

🏫 MP BoardClass 9Science

📐 Formula & Cheat Sheet (English)

Class 9 Science: Quick Revision Notes

Chapter: Work and Energy (कार्य और ऊर्जा)

1. Introduction to Work (कार्य)

In physics, "work" has a specific scientific meaning. Work is said to be done only when a force acts on an object and the object gets displaced in the direction of the force.

  • Conditions for Work to be Done:
    1. A force must act on the object.
    2. The object must be displaced (moved).

2. Work Done by a Constant Force (स्थिर बल द्वारा किया गया कार्य)

When a force $F$ moves an object through a distance $s$ in the direction of the force, the work done ($W$) is given by the product of force and displacement.

  • Formula: W = F × s

  • Where:

    • $W$ = Work done
    • $F$ = Force applied
    • $s$ = Displacement

  • SI Unit of Work: Joule (J) or Newton-metre (N·m)

  • Scalar or Vector? Work is a scalar quantity (it has magnitude only, no direction).

Special Cases of Work Done (Angle dependent):

  1. When force and displacement are in the same direction ($\theta = 0^\circ$): W = F × s (Maximum positive work)
  2. When force and displacement are perpendicular to each other ($\theta = 90^\circ$): W = 0 (Zero work, e.g., a coolie carrying a load on his head walks horizontally).
  3. When force and displacement are in opposite directions ($\theta = 180^\circ$): W = -F × s (Negative work, e.g., work done by friction).

3. Energy (ऊर्जा)

Energy is the capacity of an object to do work.

  • SI Unit of Energy: Joule (J) (Same as work)
  • Unit of Energy (Commercial/Electrical): Kilowatt-hour (kWh) or Board of Trade (BOT) unit.
    • 1 kWh = 3.6 × 10^6 Joules (also known as 1 "unit" of electricity).

4. Forms of Energy (ऊर्जा के रूप)

A. Kinetic Energy (गतिज ऊर्जा - K.E.)

The energy possessed by an object due to its motion.

  • Formula: K.E. = (1/2) × m × v^2
  • Where:
    • $m$ = Mass of the object
    • $v$ = Velocity of the object

B. Potential Energy (स्थितिज़ ऊर्जा - P.E.)

The energy possessed by an object due to its position, shape, or configuration.

  • Gravitational Potential Energy Formula: P.E. = m × g × h
  • Where:
    • $m$ = Mass of the object
    • $g$ = Acceleration due to gravity
    • $h$ = Height above the ground

5. Law of Conservation of Energy (ऊर्जा संरक्षण का नियम)

  • Statement: Energy can only be converted from one form to another; it can neither be created nor destroyed. The total energy of an isolated system remains constant.
  • Total Mechanical Energy = Kinetic Energy + Potential Energy ($E = K.E. + P.E. = \text{Constant}$)

6. Power (शक्ति)

Power is defined as the rate of doing work or the rate of transfer of energy.

  • Formula: P = W / t

  • Where:

    • $P$ = Power
    • $W$ = Work done (or Energy consumed)
    • $t$ = Time taken

  • SI Unit of Power: Watt (W) or Joule per second (J/s)

  • Larger Units:

    • 1 Kilowatt (kW) = $1000\text{ W}$
    • 1 Horsepower (hp) = $746\text{ W}$

Quick Important Conversions for Numerical Problems:

  1. Mass ($m$) must be in kilograms (kg).
  2. Distance/Displacement ($s$ or $h$) must be in meters (m).
  3. Time ($t$) must be in seconds (s).
  4. Velocity ($v$) must be in meters per second (m/s).
  5. Force ($F$) must be in Newtons (N).