Work, Energy and Power

Answer

Work is defined as the dot product of force and displacement. Formula: W = F⃗·S⃗ = FS cos θ where θ is the angle between force and displacement. SI Unit: Joule (J) = Newton × metre (N·m) One joule

Answer

Given: - Force F = 8 N - Angle θ = 30° - Displacement s = 3 m Formula: W = FS cos θ Solution: W = 8 × 3 × cos 30° W = 24 × (√3/2) W = 24 × 0.866 W = 20.8 J The work done is 20.8 J.

Answer

(a) Positive Work (θ = 0°): When force and displacement are in the same direction. Example: Engine force while car accelerates (b) Negative Work (θ = 180°): When force and displacement are opposite.

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For variable force, work is calculated by integration: 1. Divide displacement into small intervals Δx 2. For each interval: ΔW = F(x)Δx 3. Total work: W = ΣF(x)Δx 4. As Δx → 0: W = lim[Δx→0] ΣF(x)Δx

Answer

Given: - Spring constant k = 200 N/m - Compression x = 0.1 m For spring force F = -kx: Work done by external force = ∫₀ˣ kx dx = ½kx² Solution: W = ½ × 200 × (0.1)² W = ½ × 200 × 0.01 W = 1 J Elast

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Kinetic Energy: Energy possessed by a body due to its motion. Derivation: For constant force: F = ma, v² = u² + 2as ∴ a = (v² - u²)/(2s) Work done: W = F × s = ma × s = m × (v² - u²)/(2s) × s W = ½m

Answer

Given: m = 2 kg, u = 0, v = 10 m/s, s = 5 m (a) Final KE = ½mv² = ½ × 2 × (10)² = 100 J (b) Work done = ΔKE = 100 - 0 = 100 J (c) Using W = Fs: 100 = F × 5 F = 20 N Verification: a = (v² - u²)/(2s

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Potential Energy: Stored energy possessed by a body by virtue of its position or configuration. Gravitational PE: When mass m is lifted to height h against gravity: Work done = Force × displacement =