Work and Energy Summary

Overview of Work and Energy

• Work is the energy transferred between objects due to a force acting over a distance.

• The unit of work is the joule, equivalent to energy.

Definition of Work

• Work (W) = Force (F) × Displacement (d) × cos(θ)

  • F and d must be multiplied as positive magnitudes.

  • θ is the angle between the force and displacement vectors.

Calculating Work

• Example 1: Pulling a box

  • Force = 3 N, Displacement = 5 m, θ = 0° (parallel) => W = 3 × 5 × cos(0) = 15 J (positive work)

• Example 2: Stopping force on a cart

  • Force = 100 N, Displacement = 2.5 m, θ = 180° (antiparallel) => W = 100 × 2.5 × cos(180) = -250 J (negative work)

Interpretation of Work

• Positive work: force aids motion.

• Negative work: force opposes motion.

Work by Gravity

• Gravity performs work depending on the direction of motion:

  • Downward motion: positive work (W = mg × h)

  • Upward motion: negative work (W = -mg × h)

• Example: Falling book

  • Mass = 5.1 kg, Distance = 2 m => Work by gravity = W = mg × d = 5.1 × 9.8 × 2 = 100 J

• Conservation of energy: Work done by gravity equals the gain/loss of kinetic energy.