College Physics 4.4 – Measuring the mass of astronauts in orbit


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

\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.