# College Physics 4.4 – Measuring the mass of astronauts in orbit

## Solution:

### Part A

From Newton’s second law of motion, we know that

$\text{net Force}=\text{mass}\times \text{acceleration}$

For this particular problem, we are solving for the mass. Hence, the formula for mass is

$\displaystyle \text{mass}=\frac{\text{net force}}{\text{acceleration}}$

In symbols, that is

$\displaystyle \text{m}=\frac{\sum \text{F}}{\text{a}}$

Substituting the given values and solving for the unknown, we have

$\displaystyle \text{m}=\frac{50.0\:\text{N}}{0.893\:\text{m/s}^2}$

$\text{m}=55.9910\:\text{kg}$

The mass of the austronaut is about 55.9910 kilograms.

## Part B

If the force could be exerted on the astronaut by another source other than the spaceship, then the spaceship would not experience a recoil.