Chapter 1, Problem 23P

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

To determine

The weight of a $1\text{kg}$ substance in $\text{N}$, $\text{kN}$, $\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}$, $\text{kgf}$, $\text{lbf}\cdot \text{ft}/{\text{s}}^{\text{2}}$ and $\text{lbf}$.

Answer to Problem 23P

The weight of a $1\text{kg}$ substance in $\text{N}$ is $9.81\text{N}$.

The weight of a $1\text{kg}$ substance in $\text{kN}$ is $9.81\times {10}^{-3}\text{kN}$.

The weight of a $1\text{kg}$ substance in $\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}$ is. $9.81\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}$.

The weight of a $1\text{kg}$ substance in $\text{kgf}$ is $\text{1}\text{kgf}$.

The weight of a $1\text{kg}$ substance in $\text{lbf}\cdot \text{ft}/{\text{s}}^{\text{2}}$ is $\text{70}\text{.84}\text{lbf}\cdot \text{ft}/{\text{s}}^{\text{2}}$.

The weight of a $1\text{kg}$ substance in $\text{lbf}$ is $\text{2}\text{.2}\text{lbf}$.

Explanation of Solution

Given information:

The mass of the object is $1kg$.

Write the expression for weight of the object.

  $W=mg$...... (I)

Here, the mass of the object is $m$ and the acceleration due to gravity is $g$.

Calculation:

Substitute $1kg$ for $m$ and $9.81m/s^2$ for $g$ in Equation (I).

  $\begin{array}{c}W=1\text{kg}\times 9.81\text{m}/{\text{s}}^{\text{2}}\\ =9.81\frac{\text{kg}}{\text{m}/{\text{s}}^{\text{2}}}\times \frac{1\text{N}}{1\frac{\text{kg}}{\text{m}/{\text{s}}^{\text{2}}}}\\ =9.81\text{N}\end{array}$

Substitute $1kg$ for $m$ and $9.81m/s^2$ for $g$ in Equation (I).

  $\begin{array}{c}W=1\text{kg}\times 9.81\text{m}/{\text{s}}^{\text{2}}\\ =9.81\frac{\text{kg}}{\text{m}/{\text{s}}^{\text{2}}}\times \frac{1\times {10}^{-3}\text{kN}}{1\frac{\text{kg}}{\text{m}/{\text{s}}^{\text{2}}}}\\ =9.81\times {10}^{-3}\text{kN}\end{array}$

Substitute $1kg$ for $m$ and $9.81m/s^2$ for $g$ in Equation (I).

  $\begin{array}{c}W=1\text{kg}\times 9.81\text{m}/{\text{s}}^{\text{2}}\\ =9.81\frac{\text{kg}}{\text{m}/{\text{s}}^{\text{2}}}\\ =9.81\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}\end{array}$

Substitute $1kg$ for $m$ and $32.2\text{ft}/{\text{s}}^2$ for $g$ in Equation (I).

  $\begin{array}{c}W=1\text{kg}\times 32.2\text{ft}/{\text{s}}^2\\ =1\text{kg}\times \frac{2.2\text{lbm}}{1\text{kg}}\times 32.2\text{ft}/{\text{s}}^2\\ =70.84\text{lbm}\cdot \text{ft}/{\text{s}}^2\end{array}$

Substitute $1kg$ for $m$ and $32.2\text{ft}/{\text{s}}^2$ for $g$ in Equation (I).

  $\begin{array}{c}W=1\text{kg}\times 32.2\text{ft}/{\text{s}}^2\\ =1\text{kg}\times \frac{2.2\text{lbm}}{1\text{kg}}\times 32.2\text{ft}/{\text{s}}^2\\ =70.84\text{lbm}\cdot \text{ft}/{\text{s}}^2\times \frac{1\text{lbf}}{32.2\text{lbm}\cdot \text{ft}/{\text{s}}^2}\\ =2.2\text{lbf}\end{array}$

Since $9.81m/s^2$ is $1\text{kgf}$ the value of the value of $1\text{kg}$ in $\text{kgf}$ will be $1\text{kgf}$.

Conclusion:

The weight of a $1\text{kg}$ substance in $\text{N}$ is $9.81\text{N}$.

The weight of a $1\text{kg}$ substance in $\text{kN}$ is $9.81\times {10}^{-3}\text{kN}$.

The weight of a $1\text{kg}$ substance in $\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}$ is. $9.81\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}$.

The weight of a $1\text{kg}$ substance in $\text{kgf}$ is $\text{1}\text{kgf}$.

The weight of a $1\text{kg}$ substance in $\text{lbf}\cdot \text{ft}/{\text{s}}^{\text{2}}$ is $\text{70}\text{.84}\text{lbf}\cdot \text{ft}/{\text{s}}^{\text{2}}$.

The weight of a $1\text{kg}$ substance in $\text{lbf}$ is $\text{2}\text{.2}\text{lbf}$.