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.
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
- Read the theory: the ramp hides a fixed static friction coefficient; you only see geometry and motion.
- 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.
- 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).
- Repeat for at least 5 independent trials (re‑aim each time).
- The table lists θ and μ = tan θ for each trial. Take the sample mean of μ as your result.
- 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.