Chapter 7, Problem 40A

a.

To determine

The gravitation attractive force between a person of mass 50.0-kg and the Earth.

Answer to Problem 40A

  $489.1\text{N}$

Explanation of Solution

Given:

The mass of the Earth is $5.97\times {10}^{24}\text{}\text{kg}$ and its radius is $6.38\times {10}^6\text{}\text{m}$ .

Formula used:

Gravitational force:

  $F=\frac{G{m}_1{m}_2}{r^2}$

Where, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between the masses.

Calculation:

The value of gravitational constant is,

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Then using the given values of mass of the balls and the distance between them, the gravitational force between the balls will be,

  $\begin{array}{c}F=\frac{G{m}_1{m}_2}{r^2}\\ =\frac{6.67\times {10}^{-11}\times 5.97\times {10}^{24}\text{}\times 50}{{\left(6.38\times {10}^6\right)}^2}\\ =489.1\text{N}\end{array}$

Conclusion:

Thus, the gravitational attractive force between a person and the Earth is $489.1\text{N}$ .

b.

To determine

The weight of a person of mass 50.0-kg on the Earth.

Answer to Problem 40A

  $490\text{N}$

Explanation of Solution

Given:

The mass of the person is 50.0-kg.

Formula used:

The weight of an object of mass mcan be obtained by:

  $W=mg$

Where, g is the strength of the gravitational field.

Calculation:

The value of “ g ” on Earth is

  $g=9.8\text{}{\text{m/s}}^{\text{2}}$

Then, the weight of the person is,

  $\begin{array}{c}W=mg\\ =50\times 9.8\\ =490\text{N}\end{array}$

Conclusion:

Thus, the weight of the person is $490\text{N}$ .