The inclined plane

Equipment

• 3D block-on-incline model with force vectors
• Angle θ, friction μₖ, and mass sliders
• Acceleration readout and Pause button

Procedure

1. No friction: a = g sin θ

   Set μₖ = 0 and sweep «Angle θ» through 15°, 30°, 45°. Read the acceleration and compare with $a=g\sin\theta$: ~2.6, 4.9, 6.9 m/s². Note only the downslope component $mg\sin\theta$ drives motion; $mg\cos\theta$ is balanced by the normal force N.

2. Add friction

   Hold θ = 30° and step μₖ up to 0.6. Read a fall according to $a=g(\sin\theta-\mu_k\cos\theta)$; at $\mu_k=\tan\theta\approx0.577$ a → 0 and the block slides uniformly or stays put — check it on the readout.

3. Does mass matter?

   Hold θ = 30°, μₖ = 0.2 and vary «Mass» 1 → 12 kg. The acceleration stays ~3.2 m/s² because m cancels in $a=g(\sin\theta-\mu_k\cos\theta)$ — Galileo's conclusion: sliding/falling acceleration is mass-independent when forces scale with m.

4. Galileo's problem: measure g indirectly

   Set μₖ = 0, small angle θ = 10°, and measure the sliding distance/time on the model to infer $a=g\sin\theta$, hence $g=a/\sin\theta$. This is Galileo's trick to «dilute» gravity: a gentle slope makes the motion slow enough to time with a water clock.

Simulation

Experiment history

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