Convert each of the following and express the answer using an appropriate prefix: (a) 175 lb/ft3 to kN/m3, (b) 6 ft/h to mm/s, (c) 835 lb * ft to kN * m
The Correct Answer and Explanation is:
Let’s convert the following step by step and express answers with appropriate SI prefixes.
(a) Convert 175 lb/ft³ to kN/m³
Step 1: Convert pounds to newtons
1 pound-force = 4.44822 newtons
So,
175 lb = 175 × 4.44822 = 778.4385 N
Step 2: Convert ft³ to m³
1 ft = 0.3048 m, so
1 ft³ = (0.3048)³ = 0.0283168 m³
Now,
175 lb/ft³ = 778.4385 N / 0.0283168 m³ ≈ 27496.55 N/m³
Step 3: Convert N/m³ to kN/m³
1 kN = 1000 N
27496.55 N/m³ = 27.49655 kN/m³
Final Answer: (a) ≈ 27.5 kN/m³
(b) Convert 6 ft/h to mm/s
Step 1: Convert feet to millimeters
1 ft = 0.3048 m = 304.8 mm
6 ft = 6 × 304.8 = 1828.8 mm
Step 2: Convert hours to seconds
1 hour = 3600 seconds
Now,
6 ft/h = 1828.8 mm / 3600 s ≈ 0.508 mm/s
Final Answer: (b) ≈ 0.508 mm/s
(c) Convert 835 lb·ft to kN·m
Step 1: Convert pounds to newtons
1 lb = 4.44822 N
Step 2: Convert feet to meters
1 ft = 0.3048 m
Now,
835 lb·ft = 835 × 4.44822 × 0.3048
= 835 × 1.35582 ≈ 1131.1077 N·m
Step 3: Convert N·m to kN·m
= 1131.1077 / 1000 = 1.131 kN·m
Final Answer: (c) ≈ 1.13 kN·m
Explanation
Unit conversion is a fundamental process in engineering and science for maintaining consistency across measurement systems. Each part of this problem involves converting from imperial units to metric SI units, which are preferred in scientific contexts due to their standardization.
In part (a), the density unit lb/ft³ was converted to kN/m³. This required converting pounds to newtons (a measure of force) and cubic feet to cubic meters. Since density includes volume, and volume conversions involve cubing the length unit, ft³ to m³ becomes (0.3048)³. After calculating the density in newtons per cubic meter, the value was scaled to kilonewtons for a more readable format.
In part (b), we converted a velocity from feet per hour to millimeters per second. This required converting both distance (feet to millimeters) and time (hours to seconds). Since the final result was a small number, using millimeters per second (rather than meters per second) kept the value meaningful without needing scientific notation.
In part (c), torque or work in lb·ft was converted to kN·m. Each component of the unit (pounds and feet) was individually converted to its SI counterpart, and then combined. The final unit, kilonewton-meter, expresses the same physical quantity but in a format aligned with international standards.
Using appropriate SI prefixes like kilo (k) and milli (m) makes results clearer and avoids cumbersome decimal places. This process ensures measurements are accurate, consistent, and easily understood in technical fields.
