Chapter 4, Problem 68A

To determine

The meaning of the statement that $1\text{kg}$ is equivalent to $2.21\text{lb}$ .

Explanation of Solution

Introduction:

The mass of an object in Earth is the measurement of the quantity of matter present in a substance whereas the weight of the same substance is the measurement of the gravitational pull of Earth on that substance.

The mass of the substance is independent of place, whereas the weight of the substance varies with the place of measurement.

A substance weighing $1\text{kg}$ means that the mass of the substance is $1\text{kg}$ .

A substanceweighing $2.21\text{lb}$ means that the weight of the substance is $2.21\text{lb}$ .

Hence, the meaning of the statement “ $1\text{kg}$ is equivalent to $2.21\text{lb}$ ” means that the mass of $1\text{kg}$ of a substance in Earth is equivalent to the weight of $2.21\text{lb}$ of the substance.

In general, the comparison of measurement can only be done between two similar quantities. That is, the mass of a substance can be compared with the mass of another substance. Similarly, the weight of the substance can be compared with the weight of another substance.

Consider the acceleration due to the gravity of the Earth is $g=9.81\text{kg}\cdot {\text{m/s}}^2$ .

Find the weight $\left(F_{\text{g}}\right)$ of a substance of mass $1\text{kg}$ as follows:

  $\begin{array}{c}{F}_{\text{g}}=mg\\ =1\text{kg}\times 9.80{\text{m/s}}^2\\ =9.80\text{kg}\cdot {\text{m/s}}^2\times \left(\frac{1\text{N}}{1\text{kg}\cdot {\text{m/s}}^2}\right)\\ =9.80\text{N}\end{array}$

Hence, the proper way of comparison is that the weight of $9.80\text{N}$ is equivalent to $2.21\text{lb}\text{.}$

Conclusion:

The meaning of the statement “ $1\text{kg}$ is equivalent to $2.21\text{lb}$ ” means that the mass of $1\text{kg}$ of a substance in Earth is equivalent to the weight of $2.21\text{lb}$ of the substance.

The proper way of comparison is that the weight of $9.80\text{N}$ is equivalent to $2.21\text{lb}$ .