# Measuring the mass of an Austronaut| Newton’s Second Law of Motion: Concept of a System| Dynamics| College Physics| Problem 4.4

### Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s² (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which the recoil of the vehicle is avoided.

SOLUTION:

PART A

From Newton’s second law of motion, we know that $net\:Force=mass\times acceleration$. For this particular problem, we are solving for the mass. Hence, the formula for mass is

$mass=\frac{net\:force}{acceleration}$

In symbols, that is

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

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

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

$m=55.9910\:kg$

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.