1. **Problem Statement:** Calculate the kinetic energy (KE) and potential energy (PE) of an object in thermodynamics context, given mass, velocity, and height. Use both SI and English units. 2. **Formulas:** - Kinetic Energy: $$KE = \frac{1}{2} m v^2$$ where $m$ is mass and $v$ is velocity. - Potential Energy: $$PE = m g h$$ where $g$ is acceleration due to gravity and $h$ is height. 3. **Important Notes:** - In SI units, mass $m$ is in kilograms (kg), velocity $v$ in meters per second (m/s), height $h$ in meters (m), and $g = 9.81$ m/s$^2$. - In English units, mass $m$ is in slugs, velocity $v$ in feet per second (ft/s), height $h$ in feet (ft), and $g = 32.2$ ft/s$^2$. 4. **Example Calculation (SI units):** - Given: $m = 2$ kg, $v = 3$ m/s, $h = 5$ m. - Calculate KE: $$KE = \frac{1}{2} \times 2 \times 3^2 = \frac{1}{2} \times 2 \times 9 = 9 \text{ J}$$ - Calculate PE: $$PE = 2 \times 9.81 \times 5 = 98.1 \text{ J}$$ 5. **Example Calculation (English units):** - Given: $m = 2$ slugs, $v = 10$ ft/s, $h = 15$ ft. - Calculate KE: $$KE = \frac{1}{2} \times 2 \times 10^2 = \frac{1}{2} \times 2 \times 100 = 100 \text{ ft}\cdot\text{lb}_f$$ - Calculate PE: $$PE = 2 \times 32.2 \times 15 = 966 \text{ ft}\cdot\text{lb}_f$$ 6. **Summary:** - Kinetic energy depends on mass and square of velocity. - Potential energy depends on mass, gravity, and height. - Units must be consistent for correct results.