Electron Line: Forces on an Inclined Plane

Introduction

• Examination of forces (friction, normal, reaction) when an object is on an inclined plane.
• Initial scenario: block on a horizontal surface.
  • Weight of block pushes down, normal force pushes back.
  • Normal force = Reaction force = Weight of block.
  • Maximum friction force = Normal force x Coefficient of static friction.
  • No horizontal forces means no friction forces; block is static.

Inclined Plane

• Block on an inclined surface.
  • Forces: weight of block acts downward, can be divided into:
    • Perpendicular component: weight x cos(θ).
    • Parallel component: weight x sin(θ).
• Normal force aligned with mg cos(θ), perpendicular to surface.
• Reaction force is a vector sum of normal force and friction force.

Friction Forces on Incline

• Maximum friction force = Normal force x coefficient of static friction (μs).
• If mg sin(θ) < maximum friction force:
  • Friction force limited to applied force mg sin(θ).
  • Reaction force components: mg sin(θ) for friction, normal force as perpendicular.

Increasing the Incline Angle

• As angle increases:
  • mg sin(θ) increases, mg cos(θ) decreases.
  • Normal force = mg cos(θ).
• When mg sin(θ) = maximum friction force (mg cos(θ) x μs), the block is on the verge of moving.

Block in Motion

• When block moves:
  • mg sin(θ) > maximum friction force.
  • Friction force = Normal force x coefficient of kinetic friction (μk).
  • Reaction force is now at an angle relative to vertical.

Calculating Reaction Force Angle

• Reaction force sum of normal and friction force.
• Angle (φ) between normal and reaction force:
  • tan(φ) = Friction force / Normal force = μk.
  • φ = arctan(μk).
• Important observation:
  • When block is moving, reaction force is at an angle due to smaller friction force.

Conclusion

• When block is static, reaction force is vertical; when moving, it is at an angle.
• Next video: adding additional forces to blocks on inclines to calculate reaction forces.