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Inclined Plane Force Decomposition

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About This MicroSim

This simulation demonstrates the key technique for solving inclined plane problems: decomposing the weight vector into components parallel and perpendicular to the surface. This choice of coordinate system simplifies the analysis dramatically.

Key Equations

  • Weight component parallel to incline: \(mg \sin\theta\) (causes sliding)
  • Weight component perpendicular to incline: \(mg \cos\theta\) (balanced by N)
  • Normal force: \(N = mg \cos\theta\)
  • Maximum static friction: \(f_s^{max} = \mu_s N\)
  • Critical angle: \(\theta_c = \arctan(\mu_s)\)

Key Insights

  • Choose axes parallel and perpendicular to the incline surface
  • Normal force exactly balances the perpendicular weight component
  • The parallel component drives the block down the slope
  • At the critical angle, friction can no longer prevent sliding

Controls

  • Angle θ: Inclination angle of the plane
  • Mass: Mass of the block
  • μs: Coefficient of static friction
  • Show decomposition: Toggle the weight component vectors
  • Show tilted axes: Display the rotated coordinate system