Q4.3-4PE - College Physics (Urone)

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.

Step-by-Step Solution

Answer

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

(b) The vehicle will not recoil.

Step 1: 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.

Step 2: Given Data

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

Step 3: (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.

Step 4: (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.