This animation works through three static equilibrium problems involving hanging masses supported by cables, ropes, and springs at various angles. Each scenario breaks down force components using sine and cosine, applies Newton's first law through horizontal and vertical force balance equations, and solves for unknown tensions step by step. Useful for physics students practicing vector decomposition and equilibrium analysis in real-world support structures like signs, lamps, and suspended blocks.
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Scene 8: Advanced Exercises (Problems 8, 9, & 10)Problem 8 (Exercise A - 8.0 kg Shop Sign with Asymmetric Cables):Visual Prompt: An 8.0 kg shop sign suspended by two cables attached to a horizontal beam: Left cable at 30° to horizontal, Right cable at 55° to horizontal (g = 9.8 m/s²). Voiceover & Step-by-Step Breakdown:Given: m = 8.0 kg, Weight W = 8.0 * 9.8 = 78.4 N, θ1 = 30°, θ2 = 55°. Horizontal Balance (ΣFx = 0): T1 * cos(30°) = T2 * cos(55°) => 0.866 * T1 = 0.574 * T2 => T1 = 0.663 * T2. Vertical Balance (ΣFy = 0): T1 * sin(30°) + T2 * sin(55°) = 78.4 => (0.663 * T2 * 0.5) + (T2 * 0.819) = 78.4 => 0.3315 * T2 + 0.819 * T2 = 78.4 => 1.1505 * T2 = 78.4. Results: T2 = 68.14 N (Right cable at 55°), T1 = 45.18 N (Left cable at 30°). Conclusion: The steeper 55° cable experiences greater tension. Problem 9 (Exercise B - 3.0 kg Lamp with Wall Tie Wire):Visual Prompt: A 3.0 kg lamp suspended by a cable fixed to the ceiling at 25° to the vertical, held horizontally away from a wall by a horizontal rope P. Voiceover & Step-by-Step Breakdown:Given: m = 3.0 kg, Weight W = 3.0 * 9.8 = 29.4 N, Angle with vertical = 25°. (i) Tension T in main ceiling cable:Vertical Balance (ΣFy = 0): T * cos(25°) = W => T * 0.906 = 29.4. Result: T = 32.45 N. (ii) Tension P in horizontal rope:Horizontal Balance (ΣFx = 0): P = T * sin(25°) = 32.45 * 0.423. Result: P = 13.72 N. Problem 10 (Exercise C - 1.5 kg Block Supported by Two Springs):Visual Prompt: A 1.5 kg metal block suspended symmetrically by two identical springs, each making a 40° angle with the vertical, with spring constant k = 60 N/m. Voiceover & Step-by-Step Breakdown:Given: m = 1.5 kg, Weight W = 1.5 * 9.8 = 14.7 N, Angle with vertical θ = 40°, k = 60 N/m. (i) Force F in each spring:Vertical Balance: 2 * F * cos(40°) = 14.7 => 2 * F * 0.766 = 14.7 => 1.532 * F = 14.7. Result: F = 9.60 N in each spring. (ii) Extension x in each spring:Using Hooke's Law (F = k * x): x = F / k = 9.60 / 60. Result: x = 0.16 meters (16 cm). IMPORTANT LANGUAGE RULE: All on-screen text must be in Arabic EXCEPT mathematical equations, formulas, laws, symbols, variables, and numerical expressions. Keep every equation, formula, and law exactly as provided, without translating or changing it. Translate only the explanatory text, headings, labels, and descriptions into Arabic. Arabic text must use proper RTL direction and correct Arabic typography. Do not use English text anywhere else on the screen. Audience: student