Work and Energy

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Work is done when: 1. A force acts on an object 2. The object moves/displaces in the direction of force Work = Force × Displacement (W = F × s) Both conditions must be satisfied. If either force is z

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Given: m = 20 kg, h = 2 m, g = 10 m/s² Force needed = Weight = mg = 20 × 10 = 200 N Displacement = 2 m (upward) Work done = F × s = 200 N × 2 m = 400 J The porter does 400 J of work against gravity

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Scientifically, no work is done because displacement = 0. However, the person gets tired because: 1. Muscles continuously contract to balance the weight 2. Energy is spent in maintaining muscle tensio

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Energy is the capacity to do work. Key points: • Energy enables objects to do work • Same unit as work (Joule) • When work is done ON an object, it gains energy • When work is done BY an object, it l

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Given: m = 5 kg, v = 6 m/s Formula: KE = ½mv² KE = ½ × 5 × (6)² KE = ½ × 5 × 36 KE = ½ × 180 KE = 90 J The kinetic energy of the ball is 90 J.

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When velocity is doubled: Original KE = ½mv² New KE = ½m(2v)² = ½m(4v²) = 4(½mv²) Result: KE becomes 4 times the original Example: If initial KE = 50 J and velocity doubles, New KE = 4 × 50 = 200 J

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Potential Energy: Energy possessed by an object due to its position or configuration. Gravitational Potential Energy: PE = mgh Where: • m = mass (kg) • g = acceleration due to gravity (9.8 m/s²) • h

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Given: m = 2 kg, h = 3 m, g = 10 m/s² Formula: PE = mgh PE = 2 × 10 × 3 PE = 60 J The potential energy of the book is 60 J. This energy can be converted to kinetic energy if the book falls.