Convert these units.
a) From 1 kg-m/s2 to 1bm-ft2/s2.
b) From 1 ft-lbę to dyne-cm.
c) From 1 lb/ft2-h to kg/m2-s.
The correct answer and explanation is :
Let’s solve each conversion step by step.
(a) Convert 1 kg·m/s² to lbm·ft/s²
1 kg·m/s² is equivalent to 1 Newton (N). We convert it to pound-mass (lbm) and feet:
- ( 1 ) kg = ( 2.20462 ) lbm
- ( 1 ) m = ( 3.28084 ) ft
Thus,
[
1 \text{ kg·m/s²} = (1 \times 2.20462) \text{ lbm} \times (1 \times 3.28084) \text{ ft/s²}
]
[
= 2.20462 \times 3.28084 \text{ lbm·ft/s²}
]
[
= 7.233 lbm·ft/s²
]
(b) Convert 1 ft·lbf to dyne·cm
1 foot-pound force (ft·lbf) is defined as:
[
1 \text{ ft·lbf} = 1.35582 \text{ J}
]
Since 1 Joule = ( 10^7 ) dyne·cm,
[
1.35582 \times 10^7 = 1.35582 \times 10^7 \text{ dyne·cm}
]
(c) Convert 1 lb/ft²·h to kg/m²·s
1 lb/ft²·h means pounds per square foot per hour. Convert step by step:
- ( 1 ) lb = ( 0.453592 ) kg
- ( 1 ) ft² = ( 0.092903 ) m²
- ( 1 ) hour = ( 3600 ) s
[
1 \frac{\text{lb}}{\text{ft}^2\cdot \text{h}} = \frac{0.453592}{0.092903 \times 3600} \text{ kg/m}^2\text{·s}
]
[
= \frac{0.453592}{334.45}
]
[
= 0.001356 \text{ kg/m}^2\text{·s}
]
Explanation (300 words)
Unit conversion is an essential concept in physics and engineering. It allows quantities to be expressed in different measurement systems. Here, we converted three different units using fundamental conversion factors.
In part (a), we converted Newton (kg·m/s²) to lbm·ft/s² using the conversion factors for mass (1 kg = 2.20462 lbm) and length (1 m = 3.28084 ft). By multiplying these values, we obtained 7.233 lbm·ft/s².
For part (b), we converted foot-pound force (ft·lbf) to dyne-centimeters (dyne·cm). Since 1 ft·lbf equals 1.35582 Joules, and 1 Joule equals ( 10^7 ) dyne·cm, simple multiplication gave 1.35582 × ( 10^7 ) dyne·cm.
In part (c), we converted pound per square foot per hour (lb/ft²·h) to kilogram per square meter per second (kg/m²·s). The conversion used fundamental relationships: 1 lb = 0.453592 kg, 1 ft² = 0.092903 m², and 1 hour = 3600 seconds. After dividing, we obtained 0.001356 kg/m²·s.
Understanding these conversions is crucial in real-world applications such as engineering, physics, and material science. It ensures consistency in calculations, compatibility between different unit systems, and proper analysis of physical phenomena across international standards.