Two worked examples show a lamp suspended by two symmetric cables in static equilibrium. The animation breaks down how total weight splits into vertical tension components, first for a 5.0 kg lamp at 40° and then a 6.0 kg lamp at 30°, solving step by step with ΣFy = 0. It highlights why smaller angles require larger cable tension, making it useful for students learning force resolution and equilibrium in introductory physics.
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Scene 5: Quick Application & Solved Example (Problems 1 & 2)Problem 1 (Quick Application - Hanging Lamp Vertical Component):Visual Prompt: Graphic illustration of a 5.0 kg lamp suspended by two cables, each making a 40° angle with the horizontal (g = 9.8 m/s²). Voiceover & Step-by-Step Breakdown:Given: Mass m = 5.0 kg, Cable angle with horizontal = 40°, g = 9.8 m/s². Goal: Calculate the vertical component of tension required from each cable. Step 1: Calculate total weight: W = m * g = 5.0 * 9.8 = 49 N. Step 2: Because two cables share the weight equally in equilibrium (ΣFy = 0): 2 * Ty = W. Step 3: Vertical component per cable: Ty = 49 / 2 = 24.5 N. Problem 2 (Solved Example - 6.0 kg Lamp at 30°):Visual Prompt: Diagram showing a 6.0 kg lamp supported symmetrically by two cables making a 30° angle with the horizontal. Voiceover & Step-by-Step Breakdown:Given: m = 6.0 kg, θ = 30°, g = 9.8 m/s². Step 1: Total Weight W = 6.0 * 9.8 = 58.8 N. Step 2: Equilibrium along Y-axis: 2 * T * sin(30°) = W. Step 3: Solve for Tension T: T = 58.8 / (2 * sin 30°) = 58.8 / (2 * 0.5) = 58.8 N (~59 N). Insight: At a 30° angle, cable tension equals the full weight of the lamp because each cable only provides half its tension vertically. 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