Work, Energy, and Energy Conservation (Real-life Photos) Replace the gray photo placeholders with real photos (instructions in placeholders)
Dot (Scalar) Product Definition (words): The dot product multiplies vectors and gives a scalar; used in work calculation. Example: F = 10.0 N, d = 5.0 m, θ = 60° → W = 25.000 J. Photo idea: person pulling a sled at angle. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Work Done by a Force Definition: Energy transfer by force over a displacement: W = F d cosθ. Example: F = 20.0 N, d = 3.0 m → W = 60.0 J. Photo idea: person pushing a box. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Work–Energy Relation Definition: Net work = change in kinetic energy. Example: Car m = 1000 kg, ΔK = 150000.0 J. Photo idea: accelerating car. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Kinetic Energy Definition: K = ½ m v² (energy of motion). Example: m = 2.0 kg, v = 5.0 m/s → K = 25.0 J. Photo idea: rolling ball. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Power Definition: Power = rate of doing work, P = W/t. Example: lift 50.0 N by 2.0 m in 5.0 s → P = 20.0 W. Photo idea: weightlifter or worker. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Conservative vs Non-Conservative Conservative forces (gravity, springs): path-independent work; non-conservative (friction) dissipate energy. Photo idea: block sliding with friction. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Gravitational Potential Energy Definition: U = m g h. Example: m = 2.0 kg, h = 5.0 m → U = 98.0 J. Photo idea: lifting an object. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Elastic Potential Energy Definition: U = ½ k x² for springs. Example: k = 200.0 N/m, x = 0.1 m → U = 1.000 J. Photo idea: compressed spring/trampoline. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Equilibria & Potential Energy Stable: local minimum; Unstable: local maximum; Neutral: flat. Photo idea: pendulum. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Energy Conservation Total mechanical energy conserved if no dissipative forces act. Example: drop from 10.0 m → v ≈ 14.0 m/s. Photo idea: falling ball. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File
Worked Problems Problem 1: Ball dropped from 10 m → v = sqrt(2 g h) = 14.0 m/s. Problem 2: Worker: W = 2000 J, P = 250 W. Photos: ball free-fall; worker pulling crate. Photo placeholder (Insert real photo) Right-click → Change Picture → From a File