Chapter 7, Problem 9TS

A $\text{3-kg}$ newborn baby at the Earth’s surface is gravitationally attracted to Earth with a force of about $30\text{N}$ . (a) Calculate the force of gravity with which the baby on Earth is attracted to the planet Mars when Mars is closest to Earth. (The mass of Mars is $6.4\times {10}^{23}\text{kg}$ and its closest distance is $5.6\times {10}^{10}\text{m}$ .) (b) Calculate the force of gravity between the baby and the physician who delivers it. Assume the physician has a mass of $100\text{kg}$ and is $0.5\text{m}$ from the baby. (c) How do the forces compare?

To determine

The force of gravity with which a new born baby on Earth is attracted to the planet Mars when Mars is closest to Earth.

Answer to Problem 9TS

The force of gravity with which a new born baby on Earth is attracted to the planet when Mars is closest to Earth is $4.1\times {10}^{-8}\text{N}$ .

Explanation of Solution

Given info: The mass of new born baby is $3\text{kg}$ , the mass of Mars is $6.4\times {10}^{23}\text{kg}$ , the force on the baby by the Earth is $30\text{N}$ and the closest distance of Mars is $5.6\times {10}^{10}\text{m}$ .

Write the expression for the force of gravity.

$F=G\frac{m_b{m}_m}{d^2}$

Here,

$F$ is the force of gravity

$G$ is the universal gravitational constant

$m_b$ is the mass of the baby

$m_m$ is the mass of Mars

$d$ is the distance of separation

Substitute $6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}/{\text{kg}}^{\text{2}}$ for G , $3\text{kg}$ for $m_b$ ,$6.4\times {10}^{23}\text{kg}$ for $m_m$ and $5.6\times {10}^{10}\text{m}$ for $d$ in the above expression to get $F$ .

$\begin{array}{c}F=6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}/{\text{kg}}^{\text{2}}\times \frac{3\text{kg}\times 6.4\times {10}^{23}\text{kg}}{{\left(5.6\times {10}^{10}\text{m}\right)}^2}\\ =4.1\times {10}^{-8}N\end{array}$

Conclusion:

Therefore, the force of gravity with which a new born baby on Earth is attracted to the planet Mars when Mars is closest to Earth is $4.1\times {10}^{-8}\text{N}$ .

To determine

The force of gravity between the baby and the physician.

Answer to Problem 9TS

The force of gravity between the baby and the physician is $8\times {10}^{-8}\text{N}$ .

Explanation of Solution

Given info: The mass of new born baby is $3\text{kg}$ , the mass of physician is $100\text{kg}$ and the distance between baby and physician is $0.5\text{m}$ .

Write the expression for the force of gravity.

$F=G\frac{m_b{m}_p}{d^2}$

Here,

$F$ is the force of gravity

$G$ is the universal gravitational constant

$m_b$ is the mass of the baby

$m_p$ is the mass of the physician

$d$ is the distance of separation

Substitute $6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}/{\text{kg}}^{\text{2}}$ for G ,$3\text{kg}$ for $m_b$ ,$100\text{kg}$ for $m_p$ and $0.5\text{m}$ for $d$ in the above equation to get $F$ .

$\begin{array}{c}F=6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^{\text{2}}/{\text{kg}}^{\text{2}}\times \frac{3\text{kg}\times 100\text{kg}}{{\left(\text{0}\text{.5}\text{m}\right)}^2}\\ =8\times {10}^{-8}N\end{array}$

Conclusion:

Therefore, the force of gravity between the baby and the physician is $8\times {10}^{-8}N$ .

To determine

The comparison between the forces.

Answer to Problem 9TS

The force of gravity between the baby and the physician is about two times greater than the force of gravity between the baby and the Mars.

Explanation of Solution

The force of gravity between the baby and the Mars is $4.1\times {10}^{-8}\text{N}$. The force of gravity between the baby and the physician is $8\times {10}^{-8}N$. Hence it is clear that the force of gravity between the baby and the physician is about two times greater than the force of gravity between the baby and the physician.

Conclusion:

Therefore, the force of gravity between the baby and the physician is about two times of the force of gravity between the baby and the Mars.