Lecture Notes: Work and Energy

Key Concepts

• Work Done (W):

  • Formula: ( W = F \times d \times \cos(\theta) )
  • Represents the amount of energy transferred to or from an object.

• Positive Work:

  • Occurs when a force gives energy to an object.
  • Example: A force that results in a positive 200 joules of energy transfer means the object gains 200 joules of energy.

• Negative Work:

  • Occurs when a force takes away energy from an object.
  • Example: If an object loses energy due to an opposing force, the work done is negative.

Example Scenarios

• Skateboarder Example:

  • Initial Conditions:
    • Mass = 50 kg
    • Starts at rest
    • Achieves velocity = 10 m/s
  • Work Done by Force:
    • Kinetic energy gained = 2,500 joules
    • Work done = +2,500 joules (positive because energy is gained)
  • Collision with Bricks:
    • Skateboarder stops (velocity = 0)
    • Work done by bricks = -2,500 joules (negative because energy is lost)

• Lifting Bricks Example:

  • Brick Details:
    • Mass = 500 kg
    • Distance lifted = 4 meters
  • Work Done Calculation:
    • Gravitational potential energy gained = 19,600 joules
    • Work done = +19,600 joules (positive because energy is gained)

General Principle

• Energy Transfer and Work:
  • Work can be determined through energy changes: kinetic, potential, or other forms.
  • The principle applies universally across different types of energy.