Understanding Friction on an Incline Plane

Key Concepts

• Incline Plane Dynamics: Non-static scenario where net forces are not zero, leading to acceleration.
• Objective: Identify forces such as normal force, friction force, resultant force, and angles.
• Net Force Calculation: Focused on forces along the incline plane.

Forces Involved

• Weight of the Object (mg): 100 Newtons acting vertically downward.
• Applied Force: 20 Newtons, horizontal and not parallel to the incline.
• Normal Force (N): Perpendicular to the incline surface.
• Friction Force (Ff): Opposes motion along the incline, calculated with the normal force and the friction coefficient.

Calculating Forces

Normal Force

• Components:
  • Perpendicular to the weight: (W \times \cos(\theta))
  • Perpendicular component of applied force: (F \times \sin(\theta))
• Calculation:
  • (N = 100 \times \sin(30^\circ) + 20 \times \sin(30^\circ) = 86.6 + 10 = 96.6) Newtons

Friction Force

• Formula: (F_f = N \times \text{coefficient of friction})
• Calculation:
  • (F_f = 96.6 \times 0.2 = 19.32) Newtons

Force Down the Incline

• Weight Component: (W \times \sin(\theta) = 100 \times 0.5 = 50) Newtons
• Applied Force Component: (F \times \cos(\theta) = 20 \times 0.866 = 17.32) Newtons

Net Force Calculation

• Components:
  • Downward weight component: 50 N
  • Friction force: 19.3 N
  • Applied force component: 17.3 N
• Net Force: (50 - 19.3 - 17.3 = 13.4) Newtons (down the incline)

Angles Involved

• Reactionary/Resultant Force Triangle:
  • Normal force: 96.6 N
  • Friction force: 19.32 N
• Angle (\Phi) using tangent:
  • (\tan(\Phi) = \frac{19.32}{96.6})
  • (\Phi = \arctan(\frac{19.32}{96.6}) = 11.31^\circ)

Angle with Vertical ((\alpha))

• Formula: (\alpha = \theta - \Phi)
• Calculation: (30^\circ - 11.3^\circ = 18.7^\circ)

Summary

• Calculating net forces on an incline involves understanding weight components, applied forces, and friction.
• The net force results in acceleration down the incline.
• The angles involved help in understanding the orientation and resultant forces acting on the object.

This lecture provides a detailed exploration of forces acting on an incline plane and how they contribute to motion, focusing on practical applications in physics.