1. Problem: A 2 kg object is moving at a velocity of 3 m/s. Calculate its kinetic energy (KE) in SI units and then convert it to English units (foot-pounds).
2. Formula: Kinetic energy is given by $$KE = \frac{1}{2}mv^2$$ where $m$ is mass and $v$ is velocity.
3. Calculation in SI units:
$$KE = \frac{1}{2} \times 2 \times 3^2 = \frac{1}{2} \times 2 \times 9 = 9 \text{ joules}$$
4. Conversion to English units:
1 joule = 0.73756 foot-pounds
$$KE = 9 \times 0.73756 = 6.638 \text{ foot-pounds}$$
5. Problem: A 5 kg object is lifted to a height of 10 meters. Calculate its potential energy (PE) in SI units and convert to English units (foot-pounds).
6. Formula: Potential energy is given by $$PE = mgh$$ where $g = 9.81 \text{ m/s}^2$ is acceleration due to gravity and $h$ is height.
7. Calculation in SI units:
$$PE = 5 \times 9.81 \times 10 = 490.5 \text{ joules}$$
8. Conversion to English units:
$$PE = 490.5 \times 0.73756 = 361.7 \text{ foot-pounds}$$
9. Problem: A 3 lb object is moving at 20 ft/s. Calculate its kinetic energy in English units and convert to SI units (joules).
10. Formula: In English units, kinetic energy is $$KE = \frac{1}{2}mv^2$$ where $m$ is mass in slugs. Convert pounds to slugs by dividing by $32.174$ (acceleration due to gravity in ft/sĀ²).
11. Convert mass:
$$m = \frac{3}{32.174} = 0.0933 \text{ slugs}$$
12. Calculate KE in English units:
$$KE = \frac{1}{2} \times 0.0933 \times 20^2 = 0.04665 \times 400 = 18.66 \text{ ft-lbf}$$
13. Convert KE to joules:
1 foot-pound = 1.35582 joules
$$KE = 18.66 \times 1.35582 = 25.3 \text{ joules}$$
These problems demonstrate how to calculate kinetic and potential energy in both SI and English units and convert between them.
Ke Pe Thermodynamics 5E5Af3
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