Problem 17 IYPT 2027: 17. Falling book cover

Problem Description & Analysis

A book is placed horizontally, and the partially open cover is allowed to fall. Investigate the motion of the falling book cover.

Interactive Simulation (Python)

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طول ورق L (mm) 150 mm

جرم m (g) 10 g

عرض ورق (mm) 100 mm

چگالی هوا ρ (kg/m³) 1.2 kg/m³

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Python Code Lab

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Python — Editable

# آزمایش سقوط جلد کتاب — طبقه‌بندی رژیم برحسب I*
import numpy as np
import matplotlib.pyplot as plt

rho_a = 1.2

# --- بخش ۱: داده‌های شما ---
# چند ورق با ابعاد و جرم متفاوت
sample = np.array([
    # L(cm),  W(cm), m(g), رژیم مشاهده‌شده (0=flutter,1=tumble,2=chaos)
    [15,  10,  2,   0],
    [15,  10,  8,   1],
    [20,  10,  4,   0],
    [20,  10, 15,   1],
    [25,   8, 25,   2],
    [10,  10,  1,   0],
    [30,  20, 30,   2],
    [12,   8,  3,   0],
])

# --- بخش ۲: محاسبهٔ I* ---
L = sample[:,0]/100; W = sample[:,1]/100; m = sample[:,2]/1000
I = m*(L**2 + W**2)/12
I_star = I/(rho_a * L**4 * W)
regime = sample[:,3].astype(int)

def predict_regime(Istar):
    if Istar < 0.05: return 0
    if Istar < 0.5:  return 1
    return 2

pred = np.array([predict_regime(x) for x in I_star])
correct = np.sum(pred == regime)

# --- بخش ۳: نمودار ---
fig, ax = plt.subplots(figsize=(9, 4.6))
colors = ['green','orange','red']
names  = ['flutter','tumble','chaotic']
for r in range(3):
    mask = regime == r
    ax.scatter(np.arange(len(I_star))[mask], I_star[mask], s=120,
               c=colors[r], edgecolor='k', label=f'obs: {names[r]}')
ax.axhspan(0, 0.05, alpha=0.15, color='green')
ax.axhspan(0.05, 0.5, alpha=0.15, color='orange')
ax.axhspan(0.5, 1e3, alpha=0.15, color='red')
ax.set_yscale('log')
ax.set_xlabel('sample index'); ax.set_ylabel('I* = I/(ρ L⁴ W)')
ax.set_title(f'Regime classification — {correct}/{len(regime)} correct')
ax.legend(); ax.grid(True, which='both', alpha=0.3)
plt.tight_layout()

# --- بخش ۴: نتایج ---
print(" sample  L(cm) W(cm) m(g)   I*      predicted   observed")
for i, (L_i,W_i,m_i,r_i) in enumerate(sample):
    p_i = predict_regime(I_star[i])
    mark = "✓" if p_i == r_i else "✗"
    print(f"   {i+1}     {L_i:4.0f}  {W_i:4.0f}  {m_i:4.0f}  {I_star[i]:6.3f}   {names[p_i]:8}   {names[r_i]:8} {mark}")
print(f"nAccuracy = {correct}/{len(regime)} = {100*correct/len(regime):.0f}%")

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Problem Description & Analysis

Interactive Simulation (Python)

Python Code Lab

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