Chapter 8.5, Problem 47PPS

a.

To determine

To calculate the gravitational force that Moon and Earth exerts upon each other.

Answer to Problem 47PPS

The gravitational force of attraction between Earth and Moon is approximately $2\times {10}^{20}$ N

Explanation of Solution

Given information:

The given equation is

  $F=\frac{G{m}_1{m}_2}{d^2},G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{/kg}}^2$

  $m_1,m_2$ masses of two bodies, d is the between them and F is the attractive force

Mass of Moon ( $m_1$ ) is $7.36\times {10}^{22}$ kilograms

Mass of Earth ( $m_2$ ) is $5.97\times {10}^{24}$ kilograms

The distance between Earth and Moon is $3.84\times {10}^8$ meters

Calculation:

To calculate the force substitute the value of variables in the equation

  $\begin{array}{l}F=\frac{G{m}_1{m}_2}{d^2}\\ F=\frac{6.67\times {10}^{-11}\times 7.36\times {10}^{22}\times 5.97\times {10}^{24}}{{\left(3.84\times {10}^8\right)}^2}\\ F\approx 2\times {10}^{20}\text{newtons}\end{array}$

Therefore,

The gravitational force of attraction between Earth and Moon is approximately $2\times {10}^{20}$ N

b.

To determine

To calculate the gravitational force that Sun and Earth exerts upon each other.

Answer to Problem 47PPS

The gravitational force of attraction between Earth and Sun is approximately $3.5\times {10}^{22}$ N

Explanation of Solution

Given information:

The given equation is

  $F=\frac{G{m}_1{m}_2}{d^2},G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{/kg}}^2$

  $m_1,m_2$ masses of two bodies, d is the between them and F is the attractive force

Mass of Sun ( $m_1$ ) is $1.98\times {10}^{30}$ kilograms

Mass of Earth ( $m_2$ ) is $5.97\times {10}^{24}$ kilograms

The distance between Earth and Sun is $1.5\times {10}^{11}$ meters

Calculation:

To calculate the force substitute the value of variables in the equation

  $\begin{array}{l}F=\frac{G{m}_1{m}_2}{d^2}\\ F=\frac{6.67\times {10}^{-11}\times 1.98\times {10}^{30}\times 5.97\times {10}^{24}}{{\left(1.5\times {10}^{11}\right)}^2}\\ F\approx 3.5\times {10}^{22}\text{newtons}\end{array}$

Therefore,

The gravitational force of attraction between Earth and Sun is approximately $3.5\times {10}^{22}$ N

c.

To determine

To calculate the gravitational force that two iron balls exerts upon each other.

Answer to Problem 47PPS

The gravitational force of attraction between two iron balls is approximately $6.67\times {10}^{-3}$ N

Explanation of Solution

Given information:

The given equation is

  $F=\frac{G{m}_1{m}_2}{d^2},G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{/kg}}^2$

  $m_1,m_2$ masses of two bodies, d is the between them and F is the attractive force

Mass of iron ball ( $m_1=m_2$ ) is $1000$ kilograms

The distance between two balls is $0.1$ meter

Calculation:

To calculate the force substitute the value of variables in the equation

  $\begin{array}{l}F=\frac{G{m}_1{m}_2}{d^2}\\ F=\frac{6.67\times {10}^{-11}\times 1000\times 1000}{{\left(0.1\right)}^2}\\ F\approx 6.67\times {10}^{-3}\text{newtons}\end{array}$

Therefore,

The gravitational force of attraction between two iron balls is approximately $6.67\times {10}^{-3}$ N