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Measure friction by tilting

Script by Ordinate 2D ✓ · Dynamics

Tilt a platform slowly: the block slips when tan θ = μ.

"""Measuring friction by tilting: a block starts to slide when tan θ = μ.

The platform is tilted slowly (2° per second). The script notes the angle at which the block first moves
(a speed above 2 cm/s) and compares tan θ with the block's coefficient of static friction, 0.45.

Runs in the studio (Script tab → Run) and locally:  python3 friction_critical_angle.py
"""
import math
import studio as s

MU, RATE = 0.45, 2.0                    # static friction; degrees per second
THICK = 0.2

s.clear()
s.gravity = (0, -9.81)
platform = s.box(0, 0, 5, THICK, static=True, name="Platform", friction=MU, color="#8b939b")
block = s.box(0, THICK / 2 + 0.15, 0.5, 0.3, mass=2, name="Block", friction=MU, restitution=0, color="#e5484d")
slipped = False


@s.on_start
def begin():
    global slipped
    slipped = False
    platform.angle = 0


@s.on_step
def tilt(t, dt):
    global slipped
    if slipped:
        return
    angle = math.radians(RATE * t)
    platform.angle = -angle                       # the platform's right end goes down: the block slides to the right
    if round(t / dt) % 24 == 0:
        s.record(t=t, angle_deg=RATE * t, tan_angle=math.tan(angle), block_speed=block.speed)
    if t > 1 and block.speed > 0.02:
        slipped = True
        print(f"it slipped at {math.degrees(angle):.1f}°: tan θ = {math.tan(angle):.3f}, μ = {MU}")
        s.stop()


s.run(30)