Lecture Notes: Work and Energy

Introduction

• Focus on understanding work and energy, which will be the basis of Homework Packet 4.
• Key Concepts:
  • Definition and measurement of work.
  • Definition and measurement of energy.
  • Both work and energy are measured in Joules.

What is Work?

• Definition: The amount of energy transferred by a force when it moves an object through a displacement.
• Context: Not about daily tasks but energy transfer in physics.
• Work involves:
  • Adding energy to a system.
  • Removing energy from a system.
  • Transferring energy between systems.

What is Energy?

• Definition: The ability of an object to produce change in itself or its environment.
• Types of Energy:
  • Potential Energy: Energy stored due to position, like a stretched rubber band.
  • Mechanical Energy: Energy due to an object's position or motion.
  • Does not include electrical, light, thermal, or nuclear energy.

Measurement and Units

• Units: Both work and energy are measured in Joules.
• Joules are based on Newtons and meters, common units in physics.

Characteristics of Work

• Scalar quantity: No direction, but has a sign (positive or negative).
  • Positive Work: Energy added to a system (e.g., pitcher throwing a baseball).
  • Negative Work: Energy removed from a system (e.g., catcher catching a baseball).

Determining Work

• Positive Work: Force and displacement are in the same direction.
• Negative Work: Force and displacement are in opposite directions.
• Zero Work:
  • Force does not act in the direction of displacement.
  • Either force or displacement is zero.

Examples

• Basketball Player: Positive work (force and displacement in the same direction).
• Goalie Saving a Ball: Negative work (force opposes displacement).
• Skater: Zero work (force does not affect displacement).
• Pushing a Door: Zero work (no displacement).

Work Equation

• Equation includes force, displacement, and angle (theta).
• Dot Product: Component of force parallel to the displacement.
• Work = Force x Displacement x cos(theta).

Types of Mechanical Energy

• Kinetic Energy: Energy due to motion.
  • Depends on mass and speed.
  • Equation: ( \frac{1}{2}mv^2 )
• Gravitational Potential Energy: Energy due to position in a gravitational field.
  • Involves force against gravity over displacement.
  • Equation: ( mgh )
• Elastic Potential Energy: Energy stored by stretching or compressing elastic materials.

Work-Energy Theorem

• Net Work: Equals change in kinetic energy.
  • Positive net work: increase in kinetic energy.
  • Negative net work: decrease in kinetic energy.

Gravitational Potential Energy

• Variable: ( U )
• Different notations: GPE, PE_sub_g, U_sub_g.
• Equation: ( mgh )
• Units Check: Consistent with Joules.

Important Concepts

• Zero Height Reference: Potential energy based on an arbitrary reference point.
• Path Independence: Only final position matters for gravitational potential energy.

Conclusion

• Defined work and energy.
• Related different kinds of energy to work.
• Upcoming: Detailed problem-solving examples.