A set of worked practice problems extends the two-cable hanging-mass model: symmetric lamps at 50° and 40° angles, plus an asymmetric case with cables at 30° and 60°. Each scenario applies horizontal and vertical equilibrium equations to solve for cable tension, showing how steeper angles reduce tension and how unequal angles produce unequal tensions. Useful for students practicing force resolution and equilibrium problem-solving in introductory physics or statics courses.
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Scene 6: Practice Problems (Problems 3, 4, & 5)Problem 3 (Try Yourself - Lamp at 50° Angle):Visual Prompt: Same 6.0 kg lamp suspended by two cables, but now at a steeper 50° angle with the horizontal. Voiceover & Step-by-Step Breakdown:Given: m = 6.0 kg, W = 58.8 N, θ = 50°. Equation: 2 * T * sin(50°) = 58.8. Calculation: T = 58.8 / (2 * 0.766) = 58.8 / 1.532 = 38.38 N.Comparison: Increasing the angle from 30° to 50° reduces tension from 58.8 N to 38.38 N. Problem 4 (Try - Part A: Asymmetric Lamp Angles 30° and 60°):Visual Prompt: A 20 kg street lamp supported by two cables at different angles: Left cable at 30° and Right cable at 60° to the horizontal. Voiceover & Step-by-Step Breakdown:Given: m = 20 kg, W = 20 * 9.8 = 196 N, θ1 = 30°, θ2 = 60°. Horizontal Equilibrium (ΣFx = 0): T1 * cos(30°) = T2 * cos(60°) => 0.866 * T1 = 0.5 * T2 => T2 = 1.732 * T1. Vertical Equilibrium (ΣFy = 0): T1 * sin(30°) + T2 * sin(60°) = 196 => 0.5 * T1 + (1.732 * T1) * 0.866 = 196 => 0.5 * T1 + 1.5 * T1 = 196 => 2 * T1 = 196. Results: T1 = 98 N (Left cable), T2 = 169.7 N (Right cable). Conclusion: The steeper 60° cable carries the larger tension. Problem 5 (Try - Part B: 5.0 kg Sign at 40° Angle):Visual Prompt: A 5.0 kg street sign suspended symmetrically by two cables making 40° angles with the horizontal. Voiceover & Step-by-Step Breakdown:Given: m = 5.0 kg, W = 5.0 * 9.8 = 49 N, θ = 40°. Calculation: 2 * T * sin(40°) = 49 => T = 49 / (2 * 0.643) = 49 / 1.286. Result: T = 38.1 N in each cable. 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