Lecture on Free Body Diagrams

Introduction

• Topic: Drawing free body diagrams
• Purpose: To show all forces acting on an object

Key Concepts

• Free Body Diagram (FBD): A visual representation of forces acting on an object
• Weight Force (W):
  • Calculated as mass times gravitational acceleration (9.8 m/s² on Earth)
• Normal Force:
  • Perpendicular to the surface, equal to weight force when at rest
• Tension Force: Force exerted through a rope

Situational FBDs

Part A: Box Resting on a Table

• Forces:
  • Weight force (W)
  • Normal force (N)
• Condition: Resting (no acceleration)
  • Forces are equal (W = N)

Part B: Block Hanging from a Ceiling

• Forces:
  • Weight force (W/F_gravity)
  • Tension force (T)
• Condition: At rest
  • Tension equals weight (T = W)

Part C: Block Pulled Upward at Constant Velocity

• Forces:
  • Weight force (W)
  • Tension force (T)
• Condition: Constant velocity
  • Forces cancel (T = W)

Part D: Block Pulled Upward with Acceleration

• Forces:
  • Weight force (W)
  • Tension force (T)
• Condition: Accelerating
  • Tension greater than weight (T = W + ma)

Part E: Block Descending with Acceleration

• Forces:
  • Weight force (W)
  • Tension force (T)
• Condition: Descending
  • Weight greater than tension (W > T)

Additional Examples

Part A: Block on Frictionless Surface at Constant Speed

• Forces:
  • Normal force equals weight
  • No friction or applied force in x-direction

Part B: Box Pushed Right at Constant Speed

• Forces:
  • Applied force equals kinetic friction
  • Normal force equals weight

Part C: Box Accelerated Across Surface with Friction

• Forces:
  • Applied force greater than kinetic friction

Part D: Block Pulled Right with Rope

• Forces:
  • Tension equals kinetic friction

Part E: Rope at Angle Pulling Block Right with Friction

• Forces:
  • Tension greater than kinetic friction
  • Components: T_x (horizontal), T_y (vertical)

Inclined Planes

Part A: Block Slides Down Frictionless Incline

• Forces:
  • Weight force (W)
  • Normal force (N = mg cos θ)
  • Component of gravity (F_g = mg sin θ)
• Acceleration: g sin θ

Part B: Block at Rest on Incline

• Forces:
  • Static friction equals component of gravity (F_s = F_g)

Part C: Block Sliding Down with Friction

• Forces:
  • F_g greater than kinetic friction
• Acceleration: g sin θ - μ_k g cos θ

Part D: Block Pulled Up Incline at Constant Velocity

• Forces:
  • Tension equals kinetic friction

Conclusion

• Understanding and drawing free body diagrams is essential for analyzing forces and motion in physics.
• Practice with various scenarios helps solidify understanding of how forces interact in different conditions.