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 recoil of the vehicle is avoided.

Solution:

We are given the following: \sum F = 50.0 \ \text{N}, and a=0.893 \ \text{m/s}^{2}.

Part A. We can solve for the mass, m by using Newton’s second law of motion.

\begin{align*}
\sum F & = ma \\
50.0 \ \text{N} & = m \left( 0.893 \ \text{m/s}^{2} \right) \\
m & = \frac{50.0 \ \text{N}}{0.893 \ \text{m/s}^{2}} \\
m & = 56.0 \ \text{kg}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

Part B. The measured acceleration is equal to the sum of the accelerations of the astronauts and the ship. That is

a_{measured}=a_{astronaut}+a_{ship}

If a force acting on the astronaut came from something other than the spaceship, the spaceship would not undergo a recoil. \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)