Transcripción 11/12/2025, 2:58:35 p. m.

Apuntes

• Work and Energy Principles Work (W) relates to energy changes and is expressed as: \[ W = \Delta KE = KE_{f} - KE_{i} \] where kinetic energy (KE) is: \[ KE = \frac{1}{2} mv^2 \] The work done by a force \( F \) over a displacement \( \Delta x \) is: \[ W = F \cdot \Delta x \] which equals the change in kinetic energy: \[ F \cdot \Delta x = \frac{1}{2} mv_{f}^2 - \frac{1}{2} mv_{i}^2 \] The SI unit for energy and work is the Joule (J). Potential energy (PE) can be calculated as: \[ PE = mgh \quad \text{or} \quad PE = \frac{1}{2} k x^2 \] • Quiz #1 Calculations **A)** The kinetic energy of a 3900 kg mass moving at 6 m/s: \[ KE = \frac{1}{2} \times 3900 \times 6^2 = 70200\, \text{J} \] **B)** To find the kinetic energy at 12 m/s: \[ KE = 3900 \times 12^2 = 561600\, \text{J} \] (Note: The original calculation was incomplete, but the process involves squaring velocity and multiplying by mass.) • Conversion of grams to kilograms \[ 13\, \text{g} = 0.013\, \text{kg} \] **Kinetic energy of a small object:** \[ KE = \frac{1}{2} \times 0.013 \times 8.5^2 = 0.4692\, \text{J} \] • Physics Problem: Mass of a boat Given KE = 15,000 J and \( v = ...