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1. Work:

In physics, work is done when a force acts on an object and causes it to move in the direction of that force.

Key Points:

• Work (W) is a measure of the energy transferred when a force acts on an object over a distance.
• The formula for work is:
  $$W = F times d times cos(theta)$$ 

  Where:

  • 
    $W$ 

    = Work

  • 
    $F$ 

    = Force applied

  • 
    $d$ 

    = Distance moved by the object

  • 
    $theta$ 

    = The angle between the direction of the force and the direction of motion.

What Does This Mean?

• If you push a box across the floor, you’re doing work on the box because you’re applying a force that makes the box move.
• If the force is in the same direction as the motion, the work is positive. If the force is in the opposite direction (like friction), the work is negative.
• No work is done if there is no movement or if the force is applied in a direction perpendicular to the motion (like pushing a wall).

Everyday Example:

• Lifting a book: If you lift a book off the ground, you’re doing work because you apply an upward force to the book, and it moves upward.

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2. Energy:

Energy is the ability to do work. There are many types of energy, but the most common ones are kinetic energy and potential energy.

Key Points:

• Kinetic Energy (KE): The energy an object has due to its motion. The faster an object moves, the more kinetic energy it has.
  • Formula:
    $$KE = frac{1}{2} m v^2$$ 

    Where:

    • 
      $m$ 

      = Mass of the object

    • 
      $v$ 

      = Speed of the object

• Potential Energy (PE): The energy an object has due to its position or condition. The higher an object is above the ground, the more gravitational potential energy it has.
  • Formula:
    $$PE = m g h$$ 

    Where:

    • 
      $m$ 

      = Mass of the object

    • 
      $g$ 

      = Acceleration due to gravity (9.8 m/s² on Earth)

    • 
      $h$ 

      = Height of the object above the ground

What Does This Mean?

• Kinetic Energy: If a car is moving, it has kinetic energy. The faster it goes, the more kinetic energy it has.
• Potential Energy: If you hold a ball above the ground, it has potential energy. The higher you hold it, the more potential energy it has.

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3. Work-Energy Theorem:

The Work-Energy Theorem states that the work done on an object is equal to the change in its kinetic energy.

Key Points:

• When you apply a force to an object and make it move, you’re doing work on the object.
• The work done is related to the change in the object’s kinetic energy.
• The formula is:
  $$W = Delta KE = KE_{text{final}} – KE_{text{initial}}$$ 

  This means if you push a car and it speeds up, the work done by your push causes an increase in the car’s kinetic energy.

What Does This Mean?

• If you push an object and it speeds up, the work you do increases its kinetic energy.
• If you slow something down, the work done on it reduces its kinetic energy.

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4. Conservation of Energy:

The Conservation of Energy principle states that energy cannot be created or destroyed, only transformed from one form to another.

Key Points:

• Energy can change from one form to another. For example, potential energy can change into kinetic energy, and kinetic energy can change into thermal energy (heat).
• In a closed system, the total amount of energy remains constant.
• For example, if you lift a book and hold it in the air, the work you do increases its potential energy. If you drop the book, the potential energy turns into kinetic energy as it falls.

What Does This Mean?

• Energy is always conserved. It might change forms (like from kinetic to potential or into heat), but it doesn’t disappear.
• For example, when a roller coaster goes up a hill, it has potential energy. As it goes down, that potential energy turns into kinetic energy, making it go faster.

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5. Power:

Power is the rate at which work is done or energy is transferred. It measures how quickly energy is used or transferred.

Key Points:

• Power is measured in Watts (W). 1 watt is equal to 1 joule of energy used per second.
• The formula for power is:
  $$P = frac{W}{t}$$ 

  Where:

  • 
    $P$ 

    = Power (in watts)

  • 
    $W$ 

    = Work done (in joules)

  • 
    $t$ 

    = Time taken (in seconds)

What Does This Mean?

• Power tells you how fast energy is being used.
• If you do the same amount of work (like lifting a box), but it takes you less time, you are using more power.

Everyday Example:

• Running vs Walking: If you lift the same box, but you do it quickly, you’re using more power because you’re doing the work faster.
• Light Bulb: A 100-watt light bulb uses more power than a 60-watt bulb because it uses more energy per second.

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Summary of Key Concepts:

• Work: Work is done when a force moves an object a certain distance. Formula:
  $W = F times d$ 

  .

• Energy: Energy is the ability to do work. It can be kinetic (motion) or potential (position). Formula for kinetic energy:
  $KE = frac{1}{2} m v^2$ 

  , and for potential energy: $PE = mgh$ 

  .

• Work-Energy Theorem: The work done on an object is equal to the change in its kinetic energy:
  $W = Delta KE$ 

  .

• Conservation of Energy: Energy cannot be created or destroyed; it only changes form.
• Power: Power is the rate at which work is done or energy is transferred. Formula:
  $P = frac{W}{t}$ 

  .

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Everyday Examples:

1. Work: Lifting a box.
2. Energy: A moving car has kinetic energy; a book held above your head has potential energy.
3. Work-Energy Theorem: Pushing a car makes it speed up, increasing its kinetic energy.
4. Conservation of Energy: A roller coaster’s potential energy at the top turns into kinetic energy as it goes down.
5. Power: A race car uses more power than a regular car because it does more work in less time.

 

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