Work and Energy

Class 9 Science: Quick Revision Notes

Chapter: Work and Energy (कार्य और ऊर्जा)

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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).

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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).

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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).

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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

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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 ($E = K.E. + P.E. = \text{Constant}$)

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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) = $746\text{ W}$

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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).