Chapter 13, Problem 22A

Calculate the force of gravity on a 1-kg mass at Earth’s surface. The mass of Earth is $6\times {10}^{24}kg$, and its radius is $6.4\times {10}^{6}m$.

To determine

The force of gravity.

Answer to Problem 22A

The force of gravity acting on a $1\text{kg}$ mass on the Earth is $9.8\text{N}$ .

Explanation of Solution

Given:

The mass of the Earth is $M=6\times {10}^{24}\text{kg}$ .

The mass of the object is $m=1\text{kg}$ .

The radius of the Earth is $r=6.4\times {10}^6\text{m}$ .

Formula used:

Consider an object of mass $m$ on the surface of the Earth.

The expression for the force of gravity $\left(F\right)$ acting on the object is,

  $F=G\frac{Mm}{r^2}$

Here, $M$ is the mass of the Earth and $G$ is the gravitational constant.

Calculation:

Consider the value of the gravitational constant is $G=6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2$ .

The force of gravity $\left(F\right)$ acting on the object is,

  $\begin{array}{l}F=G\frac{Mm}{r^2}\\ F=\left(6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2\right)\times \frac{\left(6\times {10}^{24}\text{kg}\right)\times \left(1\text{kg}\right)}{{\left(6.4\times {10}^6\text{m}\right)}^2}\\ F\approx 9.8\text{N}\end{array}$

Conclusion:

Thus, the force of gravity acting on a $1\text{kg}$ mass on the Earth is $9.8\text{N}$ .