Coefficient of Static Friction (Critical Angle)

Tilt a model ramp until the block slips; record the critical angle θ and estimate μ_s ≈ tan θ from several trials, then compare to the reference value.

School· 30 min·Related simulator: Classical MechanicsInclined Plane

Goal

Estimate the coefficient of static friction μ_s between the block and the ramp by finding the critical tilt angle where sliding begins and using μ_s ≈ tan θ.

Equipment

  • Wooden block on a rough ramp
  • Angle scale (slider)
  • Simulated protractor reading noise

Theory

On a rough incline at limiting equilibrium, the component of gravity along the plane equals the maximum static friction: mg sin θ = μ_s mg cos θ, hence μ_s = tan θ. Repeating the angle measurement reduces random error in reading θ.

Procedure

  1. Read the theory: the ramp hides a fixed static friction coefficient; you only see geometry and motion.
  2. Increase the angle θ with the slider and press “Release block” to test. If tan θ > μ_s the block slides a short distance; otherwise it stays put.
  3. Bracket the smallest angle where you observe sliding, then press “Record measurement” at your best estimate of the critical angle (small protractor noise is simulated).
  4. Repeat for at least 5 independent trials (re‑aim each time).
  5. The table lists θ and μ = tan θ for each trial. Take the sample mean of μ as your result.
  6. Compare the mean μ_s with the expected value and write the conclusion.

Experiment

Conclusion

The mean value of μ_s from tan θ agrees with the reference coefficient within tolerance. Main uncertainties: judging the exact onset of slip, reading θ, and the idealisation μ_s = tan θ at threshold.