Question

open response practice #1
astronaut mark watney is going to mars as part of the ares 3 mission. before his journey, he
undergoes rigorous training and medical evaluations. on earth, nasa measures his mass as 84kg.
note that on earth, ( g_{\text{earth}} = 10m/s^{2} ), while on mars ( g_{\text{mars}} = 3.7m/s^{2} ).
a. what is his weight on earth? show your calculations and include units in your answer.
b. what is his mass on mars? state your answer clearly, with calculations to support it if necessary.
explain why this value either does change or does not change from its value on earth.
c. what is his weight on mars? state your answer clearly, with calculations to support it if necessary.
explain why this value either does change or does not change from its value on earth.

Explanation:

Step1: Calculate weight on Earth

Weight \( W = mg \), where \( m = 84\,\text{kg} \) and \( g_{\text{Earth}}=10\,\text{m/s}^2 \).

$$ W_{\text{Earth}}=84\times10 = 840\,\text{N} $$

Step2: Determine mass on Mars

Mass is an intrinsic property. It does not depend on the gravitational field. So, \( m_{\text{Mars}}=m_{\text{Earth}} = 84\,\text{kg} \)

Step3: Calculate weight on Mars

Using \( W = mg \), with \( m = 84\,\text{kg} \) and \( g_{\text{Mars}}=3.7\,\text{m/s}^2 \)

$$ W_{\text{Mars}}=84\times3.7=310.8\,\text{N} $$

Answer:

a. \( 840\,\text{N} \)
b. \( 84\,\text{kg} \) (mass does not change as it is an intrinsic property)
c. \( 310.8\,\text{N} \) (weight changes because it depends on \( g \), and \( g_{\text{Mars}}
eq g_{\text{Earth}} \))