Lecture on Work and Energy Examples

Example 1: Box Being Pushed

Problem: Box pushed to the right with a force of 10 N, frictional force of 4 N, over a distance of 10 meters.
Question A: Determine the work due to the person pushing.
- Work (W) = Force (F) × Displacement (d) × cos(θ)
- Force of person, F = 10 N
- Displacement, d = 10 m
- Angle, θ = 0° (because both force and displacement are in the same direction)
- cos(0°) = 1
- Calculation: W = 10 N × 10 m × 1 = 100 Joules (J) added to the box
Question B: Determine the work due to friction.
- Frictional Force, F = 4 N
- Displacement, d = 10 m
- Angle, θ = 180° (force opposes the direction of motion)
- cos(180°) = -1
- Calculation: W = 4 N × 10 m × -1 = -40 J (40 J removed from the box)
Question C: Net work added to the box?
- Calculation: 100 J (added) - 40 J (removed) = 60 J (net work)
- Box will speed up due to positive net work.
- Formula Review: W_net = F_net × d × cos(θ)
  - F_net = 10 N - 4 N = 6 N
  - Calculation: F_net = 6 N (same direction as displacement)
  - W_net = 6 N × 10 m × 1 (cos(0°)) = 60 J net work

Problem: Box initially moving on a frictionless floor, encountering a section with 4 N friction over 10 m.
Determine Work due to Friction:
- Force of Friction, F_friction = 4 N
- Displacement, d = 10 m
- Angle, θ = 180° (friction opposes motion)
- cos(180°) = -1
- Calculation: W_friction = 4 N × 10 m × -1 = -40 J
  - 40 J of energy is removed from the box, causing it to slow down.
- Future topics: Calculating new velocity after energy removal.

Understand work calculations using the formula: W = F × d × cos(θ)
Recognize how the angle between force and displacement affects the work (positive or negative).
Apply the net work formula to find the overall effect on an object’s energy.