Introduction to Work

Overview

• Introduction to the concept of "work" in a scientific context.
• Explanation of how work relates to energy.

Scientific Formula for Work

• Formula: ( W = F \cdot \Delta x \cdot \cos(\theta) )
  • ( F ): Force acting on the object.
  • ( \Delta x ): Displacement of the object.
  • ( \cos(\theta) ): Determines if energy is added or removed.
• Work and energy are interchangeable terms in physics.
  • Positive work: Energy added to the object.
  • Negative work or work removed: Energy taken from the object.

Understanding ( \cos(\theta) )

• Helps determine if the work done is positive or negative.
• ( \theta ) is the angle between the force direction and displacement.
  • ( \cos(0^\circ) = 1 ): Force and displacement in the same direction.
  • ( \cos(180^\circ) = -1 ): Force and displacement in opposite directions.

Examples of Work Calculation

Example 1: Force Acting on an Object

• Scenario: Force of 5 newtons moves an object 20 meters.
  • Force ( F = 5 ) newtons.
  • Displacement ( \Delta x = 20 ) meters.
  • ( \theta = 0^\circ ): Force and displacement same direction.
  • ( \cos(0^\circ) = 1 ).
  • Work ( W = 5 \times 20 \times 1 = 100 ) joules.
• Key Point: Energy added to the object results in increased speed.

Example 2: Object Not Moving

• Scenario: Mandy exerts a force of 75 newtons on a fridge, which does not move.
  • Force ( F = 75 ) newtons.
  • Displacement ( \Delta x = 0 ) meters.
  • Work ( W = 75 \times 0 = 0 ) joules.
• Key Point: No energy added to the fridge means no work is done despite personal exertion.

Example 3: Holding an Object While Walking

• Scenario: Felix holds a box with a vertical force of 20 newtons and walks 10 meters horizontally.
  • Force ( F = 20 ) newtons (upward).
  • Displacement ( \Delta x = 10 ) meters (horizontal).
  • ( \theta = 90^\circ ): Force and displacement at right angles.
  • ( \cos(90^\circ) = 0 ).
  • Work ( W = 20 \times 10 \times 0 = 0 ) joules.
• Key Point: No work is done because the force is perpendicular to the displacement.

Conclusion

• Introduction to work and its calculation using force, displacement, and angle.
• Upcoming lessons will delve deeper into different types of work and applications in physics.