NOTES Chapter 11: "Work and Energy" from Class 9 Science CBSE NCERT:

 summary of Chapter 11: "Work and Energy" from Class 9 Science CBSE NCERT:

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1. What is Work?

• Work is said to be done when a force acts on an object, and the object moves in the direction of the force.

• Formula:

  $$W = F \times d \times \cos(\theta)$$
  

  Where:

  • $W$ = Work done
  • $F$ = Force applied
  • $d$ = Displacement of the object
  • $\theta$ = Angle between the direction of force and the displacement

• SI Unit of Work: Joule (J), where 1 Joule = 1 Newton meter (1 J = 1 N·m)

• Condition for work to be done:

  • A force must be applied.
  • There must be displacement in the direction of the applied force.

Example: If you push a box, and it moves, work is done. If you push a box but it doesn’t move, no work is done.

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2. Work Done by a Constant Force

• When force is applied in the direction of displacement: Work done = $F \times d$
  
• When force is applied at an angle: $$W = F \times d \times \cos(\theta)$$
  
• Work is positive when the force and displacement are in the same direction.
• Work is negative when the force and displacement are in opposite directions (e.g., friction).

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3. Energy

• Energy is the capacity to do work. An object possesses energy if it has the ability to perform work.
• SI Unit of Energy: Joule (J), the same as work.

There are various forms of energy:

• Kinetic Energy: The energy possessed by an object due to its motion.
• Potential Energy: The energy possessed by an object due to its position or state.

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4. Kinetic Energy (KE)

• Kinetic Energy is the energy of an object due to its motion.

• Formula:

  $$KE = \frac{1}{2} m v^2$$
  

  Where:

  • $KE$ = Kinetic Energy
  • $m$ = Mass of the object
  • $v$ = Velocity of the object

• Example: A moving car, a flying bird, or a rolling ball all possess kinetic energy.

• Key Point: Kinetic energy increases with the increase in speed (velocity) and mass of an object. For example, a fast-moving car has more kinetic energy than a slow-moving car of the same mass.

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5. Potential Energy (PE)

• Potential Energy is the energy possessed by an object due to its position or state.

• Formula:

  $$PE = mgh$$
  

  Where:

  • $PE$ = Potential Energy
  • $m$ = Mass of the object
  • $g$ = Acceleration due to gravity
  • $h$ = Height above the ground

• Example: A book placed on a shelf has potential energy due to its height. The higher the object, the more potential energy it has.

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6. Law of Conservation of Energy

• State: Energy can neither be created nor destroyed, but it can change from one form to another.

• Example: In a pendulum, at the highest point, the pendulum has maximum potential energy and minimum kinetic energy. As it swings down, potential energy is converted to kinetic energy. At the lowest point, it has maximum kinetic energy and minimum potential energy.

• In real life, energy is often lost as heat (e.g., friction converts mechanical energy to heat energy).

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7. Work-Energy Theorem

• State: The work done on an object is equal to the change in its kinetic energy.

  $$W = \Delta KE$$
  

  Where $\Delta KE$ is the change in kinetic energy.

• Example: When you push a car and it starts moving, the work you do is converted into kinetic energy.

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8. Power

• Power is the rate at which work is done or energy is transferred.

• Formula:

  $$P = \frac{W}{t}$$

  Where:

  • $P$ = Power
  • $W$ = Work done
  • $t$ = Time taken

• SI Unit of Power: Watt (W), where 1 Watt = 1 Joule per second (1 W = 1 J/s)

• Example: If a person lifts a heavy box quickly, more power is used than when the same box is lifted slowly.

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9. Energy and Power in Daily Life

• Electricity: Energy is consumed in homes through electrical appliances like fans, lights, and air conditioners. The amount of electrical energy used depends on the power rating of the appliance and the time for which it is used.
• Engines and Motors: Engines use energy from fuel to perform work. The efficiency of engines depends on how well they convert energy.

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10. Efficiency

• Efficiency is the ratio of useful energy output to the total energy input, usually expressed as a percentage.

  $$\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100$$
  

• Example: A car engine might convert only 30% of the fuel’s energy into useful work, and the rest is lost as heat.

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Key Takeaways

1. Work is done when a force causes an object to move.
2. Energy is the capacity to do work, and it exists in various forms, including kinetic energy (motion) and potential energy (position).
3. Kinetic Energy: $KE = \frac{1}{2} m v^2$
4. Potential Energy: $PE = mgh$
5. Law of Conservation of Energy: Energy cannot be created or destroyed, only converted from one form to another.
6. Work-Energy Theorem: Work done is equal to the change in kinetic energy.
7. Power is the rate of doing work or transferring energy: $P = \frac{W}{t}$
8. Efficiency measures how effectively energy is converted into useful work.

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Important Formulas

1. Work Done: $$W = F \times d \times \cos(\theta)$$
   
2. Kinetic Energy: $$KE = \frac{1}{2} m v^2$$
   
3. Potential Energy: $$PE = mgh$$
   
4. Power: $$P = \frac{W}{t}$$
5. Efficiency: $$\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100$$