Question

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.

Short answer

(a) The mass of the astronaut is 56kg.

(b) The vehicle will not recoil.

Step-by-step solution

Concept of Newton’s second law of motion

The Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. It is mathematically represented as:

${\mathbf{F}}_{\mathbf{net}}\mathbf{=}\mathbf{ma}$ …….…….. (i)

where F_net is the net force, m is the mass, and a is the acceleration.

Given Data

• Acceleration of the astronaut = 0.893 m/s².
• Net external force = 50 N.

(a) Determine the mass of the astronaut

By putting values 50 N for F_net and 0.893 m/s² for a in equation (i) and we get,

$\begin{array}{c}50\text{\hspace{0.33em}N}=m\times 0.893{\text{\hspace{0.33em}m/s}}^{\text{2}}\\ m=\frac{50\text{\hspace{0.33em}kg}\cdot {\text{m/s}}^{\text{2}}}{0.893{\text{\hspace{0.33em}m/s}}^2}\\ m=56\text{kg}\end{array}$

Hence, the mass of the astronaut is 56 kg.

(b) Determine the relationship between the acceleration due to mass experienced by another source

Write the expression for determining the acceleration due to another source.

$a_{meas}=a_{astr.}+a_{vehicle}$

Here, $a_{meas}$is the acceleration due to mass experienced by another source, $a_{astr.}$. Is the acceleration of the astronaut, and $a_{vehicle}$is the acceleration of the vehicle.

$a_{vehicle}=\frac{m_{astr.}\cdot a_{astr.}}{m_{vehicle}}$

When the force is exerted by another source, then the vehicle will not be able to recoil. Hence, the vehicle will not recoil.