Question

What is the weight of a 1 -kg substance in \(\mathrm{N}, \mathrm{kN}\) \(\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}, \mathrm{kgf}, \mathrm{lbm} \cdot \mathrm{ft} / \mathrm{s}^{2},\) and lbf?

Short answer

The weight of a 1-kg substance is approximately: - 9.81 Newtons (N) - 0.00981 kiloNewtons (kN) - 9.81 kg⋅m/s² - 1 kilogram-force (kgf) - 70.91 pound-mass⋅feet/s² (lbm⋅ft/s²) - 2.20462 pound-force (lbf)

Step-by-step solution

Calculate the weight in Newtons (N)

First, we need to calculate the weight of the 1-kg substance in Newtons using the formula W = m*g, where m = 1 kg and g = 9.81 m/s² (approximate value of Earth's gravitational acceleration). Thus, W = 1 kg * 9.81 m/s² = 9.81 N.

Convert the weight to kiloNewtons (kN)

Since there are 1000 Newtons (N) in a kiloNewton (kN), we can convert 9.81 N to kN by dividing it by 1000: 9.81 N ÷ 1000 = 0.00981 kN.

Weight in kg⋅m/s²

The units of kg⋅m/s² are equivalent to Newtons (N). Thus, the weight of the 1-kg substance in kg⋅m/s² is equal to its weight in Newtons: 9.81 kg⋅m/s².

Convert the weight to kilogram-force (kgf)

One kilogram-force (kgf) is approximately equal to 9.80665 N (this value is the conventional gravitational acceleration). To convert 9.81 N to kgf, we can divide it by this value: 9.81 N ÷ 9.80665 N/kgf ≈ 1 kgf.

Convert the weight to lbm⋅ft/s²

First, we have to convert the mass from kg to lbm (pound-mass). Using the conversion factor, 1 kg ≈ 2.20462 lbm, 1 kg = 2.20462 lbm. Now, we need to convert the gravitational acceleration from m/s² to ft/s². Using the conversion factor, 1 m/s² ≈ 3.28084 ft/s², 9.81 m/s² ≈ 32.174 ft/s² (approximate value). Finally, we can calculate the weight in lbm⋅ft/s²: W = 2.20462 lbm * 32.174 ft/s² ≈ 70.91 lbm⋅ft/s².

Convert the weight to pound-force (lbf)

We can convert the weight from lbm⋅ft/s² to lbf using the equivalence, 1 lbf ≈ 32.174 lbm⋅ft/s². Thus, 70.91 lbm⋅ft/s² ÷ 32.174 ≈ 2.20462 lbf. In summary, the weight of a 1-kg substance is approximately: - 9.81 N - 0.00981 kN - 9.81 kg⋅m/s² - 1 kgf - 70.91 lbm⋅ft/s² - 2.20462 lbf