Chapter 4, Problem 2P

To determine

The weight of an astronaut on −

1. Earth
2. Moon
3. On Mars
4. In outer space traveling with constant velocity

Answer to Problem 2P

Solution:

1. The weight of an astronaut on Earth is $\text{666}\text{.4 N}$
2. The weight of an astronaut on Moon is $115.6\text{ N}$
3. The weight of an astronaut on Mars is $251.6\text{ N}$
4. The weight of an astronaut in an outer space is $\text{0 N}$

Explanation of Solution

The weight of an object is the product of the mass of an object to the acceleration due to the gravity. The expression of weight is given as follows:

  $W=mg$

Here, $m$ is the mass of an astronaut and $g$ is the acceleration due to gravity.

Given:

Mass of an astronaut $m=68\text{ kg}$

Gravity of Moon $g=1.7{\text{ m/s}}^2$

Gravity of Mars $g=3.7{\text{ m/s}}^2$

Formula used:

  $W=mg$

Calculation:

Part (a):

Substitute, $m=68\text{ kg}$ and $g=\text{9}{\text{.8 m/s}}^2$ in equation (1) so the weight of an astronaut on Earth is given as follows:

  $\begin{array}{c}W=mg\\ \text{=9}{\text{.8 m/s}}^2\left(68\text{ kg}\right)\\ =666.4\text{ N}\end{array}$

Part (b):

Substitute, $m=68\text{ kg}$ and $g=1.7{\text{ m/s}}^2$ in equation (1) so the weight of an astronaut on the moon is given as follows:

  $\begin{array}{c}W=mg\\ \text{=1}{\text{.7 m/s}}^2\left(68\text{ kg}\right)\\ =115.6\text{ N}\end{array}$

Part (c):

Substitute, $m=68\text{ kg}$ and $g=3.7{\text{ m/s}}^2$ in equation (1) so the weight of an astronaut on Mars is given as follows:

  $\begin{array}{c}W=mg\\ \text{=3}{\text{.7 m/s}}^2\left(68\text{ kg}\right)\\ =251.6\text{ N}\end{array}$

Part (d):

The effect of gravity on in outer space is zero so the weight of an astronaut in an outer space is given as follows:

  $\begin{array}{c}W=mg\\ {\text{=0 m/s}}^2\left(68\text{ kg}\right)\\ =0\text{ N}\end{array}$

Conclusion:

1. Hence, the weight of an astronaut on Earth is $\text{666}\text{.4 N}$ .
2. Hence, the weight of an astronaut on Moon is $115.6\text{ N}$ .
3. Hence, the weight of an astronaut on Mars is $251.6\text{ N}$ .
4. Hence, the weight of an astronaut in an outer space is $\text{0 N}$ .