Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

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.

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

(b) The vehicle will not recoil.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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:

$F_{net} = ma$ …….…….. (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,

$\begin{matrix} 50 N = m \times 0.893 {m/s}^{2} \\ m = \frac{50 kg \cdot {m/s}^{2}}{0.893 {m/s}^{2}} \\ m = 56 kg \end{matrix}$

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.

$a_{m e a s} = a_{a s t r .} + a_{v e h i c l e}$

Here, $a_{m e a s}$ is the acceleration due to mass experienced by another source, $a_{a s t r .}$ . Is the acceleration of the astronaut, and $a_{v e h i c l e}$ is the acceleration of the vehicle.

$a_{v e h i c l e} = \frac{m_{a s t r .} \cdot a_{a s t r .}}{m_{v e h i c l e}}$

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

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College Physics (Urone)

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Short Answer

Step by Step Solution

Step 1: Concept of Newton’s second law of motion

Step 2: Given Data

Step 3: (a) Determine the mass of the astronaut

Step 4: (b) Determine the relationship between the acceleration due to mass experienced by another source

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College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Concept of Newton’s second law of motion

Step 2: Given Data

Step 3: (a) Determine the mass of the astronaut

Step 4: (b) Determine the relationship between the acceleration due to mass experienced by another source

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