Physic Labs

Newtonian mechanics

Friction force

Measure kinetic friction on an incline while varying the angle, friction coefficient, and mass. Verify Ff=μkNF_f=\mu_k N with N=mgcos⁡θN=mg\cos\theta and the slip condition tan⁡θ>μs\tan\theta>\mu_s.

Middle school

Equipment

  • 3D model of a block sliding on an inclined plane
  • Incline-angle θ, friction-coefficient μ, and mass m sliders
  • Acceleration readout, force vectors, and Reset button

Procedure

  1. Find the angle of slip

    Set μ = 0.2, mass 5 kg, then raise «Incline angle θ» until the block just begins to slide. Record the critical angle θ_c and check tan⁡θc=μs\tan\theta_c=\mu_s: for μ = 0.2, θ_c ≈ 11°.

  2. Measure the sliding acceleration

    At a fixed 30° angle, step μ through several values and read the acceleration. Verify a=g(sin⁡θ−μkcos⁡θ)a=g(\sin\theta-\mu_k\cos\theta): at θ = 30°, μ_k = 0.2 gives a ≈ 3.3 m/s²; μ larger than tan θ means no slip.

  3. Check the role of mass

    With θ and μ fixed, change «Mass m» from 1 to 20 kg. The measured acceleration stays constant because a=g(sin⁡θ−μkcos⁡θ)a=g(\sin\theta-\mu_k\cos\theta) contains no m — gravity and friction both scale with m and cancel; press «Reset» and rerun to confirm.

  4. Predict before measuring

    Pick θ = 45°, μ = 0.3 and compute by hand a=g(sin⁡45°−0.3cos⁡45°)≈4.8a=g(\sin45°-0.3\cos45°)\approx 4.8 m/s² before looking at the readout. After checking, tune μ so the block just holds then creeps; record the threshold and relate it to pushing a cabinet: starting is harder than keeping it moving because μs>μk\mu_s>\mu_k.

Simulation

Experiment history

Leonardo da Vinci noted around 1493 that friction scales with load and is independent of contact area, but his notebooks went unpublished. Guillaume Amontons rediscovered the rules in 1699 before the French Academy, and Charles-Augustin de Coulomb in 1781 distinguished static from kinetic friction — the «Coulomb friction» model Ff=μNF_f=\mu N still in use. The microscopic mechanism came much later: Bowden and Tabor (1940s–50s) showed real contact happens only at microscopic asperities, so friction scales with load rather than apparent area. The model is an approximation: lubrication, adhesion, and stick-slip need richer theory.

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